4 3 ⁢ § ⁢ 4 ⠼⠒⠈⠠⠎⠼⠲ three section four 3 4 3 ⁢ # ⁢ 4 ⠼⠒⠨⠼⠼⠲ three hash four 3 4 3 ∗ 4 ⠼⠒⠈⠼⠼⠲ three asterisk four 3 † ⁢ 3 ⠸⠻⠼⠒ dagger three 3 3 ⠼⠒ three 0 0 ⠼⠴ zero .3 .3 ⠼⠨⠒ point three 2 2 ⠼⠆ two 4356 4356 ⠼⠲⠒⠢⠖ four three five six 1 i 1 i 1 , i , − 1 , − i ⠼⠂⠠⠀⠊⠠⠀⠤⠼⠂⠠⠀⠤⠊ one comma i comma minus one comma minus i 1 1 i 1 , i , − 1 , − i ⠷⠂⠠⠀⠊⠠⠀⠤⠂⠠⠀⠤⠊⠾ open parenthesis one comma i comma minus one comma minus i close parenthesis a b ( a , b ] ⠷⠁⠠⠀⠃⠈⠾ open parenthesis a comma b close bracket 1 4 1 2 x 3 4 x 2 1 4 , 1 2 + x , 3 4 + x 2 ⠷⠹⠂⠌⠲⠼⠠⠀⠹⠂⠌⠆⠼⠬⠭⠠⠀⠹⠒⠌⠲⠼⠬⠭⠘⠆⠐⠾ open parenthesis begin fraction one over four end fraction comma begin fraction one over two end fraction plus x comma begin fraction three over four plus x squared close parenthesis 1 2 3 1 , 2 , 3 ⠼⠂⠠⠀⠼⠆⠠⠀⠼⠒ one comma two comma three 1 2 3 1 , 2 , 3 ⠷⠂⠠⠀⠆⠠⠀⠒⠾ open parenthesis one comma two comma three close parenthesis h ft k in h ⁢ ⁢ ft , k ⁢ ⁢ in ⠷⠓⠀⠋⠞⠠⠀⠅⠀⠊⠝⠾ open parenthesis h feet comma k inches close parenthesis 1 st 2 nd 3 rd 1 ⁢ st , 2 ⁢ nd , 3 ⁢ rd ⠼⠂⠎⠞⠠⠀⠼⠆⠝⠙⠠⠀⠼⠒⠗⠙ one s t comma two n d comma three r d 1 st 2 nd 3 rd 1 ⁢ st , 2 ⁢ nd , 3 ⁢ rd ⠷⠂⠎⠞⠠⠀⠆⠝⠙⠠⠀⠒⠗⠙⠾ open parenthesis one s t comma two n d comma three r d close parenthesis x s y s z s x ⁢ ' ⁢ s , y ⁢ ' ⁢ s , z ⁢ ' ⁢ s ⠷⠭⠄⠎⠠⠀⠽⠄⠎⠠⠀⠵⠄⠎⠾ open parenthesis x apostrophe s comma y apostrophe s comma z apostrophe s close parenthesis 1 1 ∠ ⁡ ⁣ 1 ⁢ ° , sin ⁡ 1 ⁢ ° ⠈⠷⠫⠪⠀⠼⠂⠘⠨⠡⠠⠀⠎⠊⠝⠀⠼⠂⠘⠨⠡⠐⠈⠾ open bracket angle one degrees comma sine one degrees close bracket a b a , b , … ⠷⠁⠠⠀⠃⠠⠀⠄⠄⠄⠾ open parenthesis a comma b comma ellipsis close parenthesis x 1 x 2 x 5 x + 1 , x + 2 , ? , ? , x + 5 ⠷⠭⠬⠂⠠⠀⠭⠬⠆⠠⠀⠿⠠⠀⠿⠠⠀⠭⠬⠢⠾ open parenthesis x plus one comma x plus two comma question mark comma question mark comma x plus five close parenthesis x 1 2 10 x = 1 , 2 , … , 10 ⠭⠀⠨⠅⠀⠼⠂⠠⠀⠼⠆⠠⠀⠄⠄⠄⠠⠀⠼⠂⠴ x equals one comma two comma ellipsis comma ten x 1 2 10 x = 1 , 2 , … , 10 ⠷⠭⠀⠨⠅⠀⠼⠂⠠⠀⠼⠆⠠⠀⠄⠄⠄⠠⠀⠼⠂⠴⠾ open parenthesis x equals one comma two comma ellipsis comma ten close parenthesis a 1 b 2 c 4 a = 1 , b = 2 , c = − 4 ⠁⠀⠨⠅⠀⠼⠂⠠⠀⠃⠀⠨⠅⠀⠼⠆⠠⠀⠉⠀⠨⠅⠀⠤⠼⠲ a equals one comma b equals two comma c equals minus four a 1 b 2 c 4 a = 1 , b = 2 , c = − 4 ⠷⠁⠀⠨⠅⠀⠼⠂⠠⠀⠃⠀⠨⠅⠀⠼⠆⠠⠀⠉⠀⠨⠅⠀⠤⠼⠲⠾ open parenthesis a equals one comma b equals two comma c equals minus four close parenthesis u v x y u , v , x , y ⠷⠥⠠⠀⠧⠠⠀⠭⠠⠀⠽⠾ open parenthesis u comma v comma x comma y close parenthesis 1 2 3 1 , 2 , 3 ⠼⠂⠠⠀⠼⠆⠠⠀⠼⠒ one comma two comma three 1 2 3 1 , 2 , 3 ⠷⠂⠠⠀⠆⠠⠀⠒⠾ open parenthesis one comma two comma three close parenthesis 0 1 [ 0 , 1 ] ⠈⠷⠴⠠⠀⠂⠈⠾ open bracket zero comma one close bracket 1 2 3 − 1 , − 2 , − 3 ⠷⠤⠂⠠⠀⠤⠆⠠⠀⠤⠒⠾ open parenthesis minus one comma minus two comma minus three close parenthesis 1 h 2 k 0 1 + h , 2 + k , 0 ⠷⠂⠬⠓⠠⠀⠆⠬⠅⠠⠀⠴⠾ open parenthesis one plus h comma two plus k comma zero close parenthesis 0 1 2 0 , − 1 , ± 2 ⠷⠴⠠⠀⠤⠂⠠⠀⠬⠤⠆⠾ open parenthesis zero comma minus one comma plus or minus two close parenthesis 2 30 3 60 2 ⁢ sin ⁡ 30 ⁢ ° , 3 ⁢ cos ⁡ 60 ⁢ ° ⠷⠆⠎⠊⠝⠀⠼⠒⠴⠘⠨⠡⠠⠀⠒⠉⠕⠎⠀⠼⠖⠴⠘⠨⠡⠐⠾ open parenthesis two sine thirty degrees comma 3 cosine sixty degrees close parenthesis 1 2 3 4 5 6 7 8 9 10 11 12 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 ⠷⠂⠠⠀⠆⠠⠀⠒⠠⠀⠲⠠⠀⠢⠠⠀⠖⠠⠀⠶⠠⠀⠦⠠⠀⠔⠠⠀⠂⠴⠠⠀⠂⠂⠠⠀⠂⠆⠾ open parenthesis one comma two comma three comma four comma five comma six comma seven comma eight comma nine comma ten comma eleven comma twelve close parenthesis x 7 8 y x , 7 , 8 , y ⠷⠭⠠⠀⠶⠠⠀⠦⠠⠀⠽⠾ open parenthesis x comma seven comma eight comma y close parenthesis 3.14159 26535 π = 3.14159 26535 ⠨⠏⠀⠨⠅⠀⠼⠒⠨⠂⠲⠂⠢⠔⠀⠆⠖⠢⠒⠢ pi equals three point one four one five nine space two six five three five 947, 147, 592 947, 147, 592 ⠼⠔⠲⠶⠠⠀⠂⠲⠶⠠⠀⠢⠔⠆ nine four seven comma space one four seven comma space five nine two x 2 x 2 ⠭⠘⠆ x squared 3 x 3 x ⠹⠒⠌⠭⠼ begin fraction three over x end fraction r 5 r ⋅ 5 ⠗⠐⠢ r five a x 3 b x 2 y c x y 2 d y 3 e x 2 y 2 7 a ⁢ x 3 + b ⁢ x 2 ⁢ y + c ⁢ x ⁢ y 2 + d ⁢ y 3 + e ⁢ x 2 + y 2 − 7 ⠁⠭⠘⠒⠐⠬⠃⠭⠘⠆⠐⠽⠬⠉⠭⠽⠘⠆⠐⠬⠙⠽⠘⠒⠐⠬⠑⠭⠘⠆⠐⠬⠽⠘⠆⠐⠤⠶ a x cubed plus b x squared y plus c x y squared plus d y cubed plus e x squared plus y squared minus seven x 5 x − 5 ⠭⠤⠢ x minus five 2 4 2 × 4 ⠼⠆⠈⠡⠲ two times sign four 10,000 10,000 ⠼⠂⠴⠠⠴⠴⠴ ten comma thousand 3 | − 3 | ⠳⠤⠒⠳ absolute value of minus three 100,000,000,000,000 100,000,000,000,000 ⠼⠂⠴⠴⠠⠴⠴⠴⠠⠴⠴⠴⠠⠴⠴⠴⠠⠴⠴⠴ one hundred comma trillion 100000000000000 100000000000000 ⠼⠂⠴⠴⠴⠴⠴⠴⠴⠴⠴⠴⠴⠴⠴⠴ one hundred trillion 13TE7 13TE7 ⠼⠂⠒⠞⠑⠶ one three ten eleven seven 3FFE2 3FFE2 ⠼⠒⠋⠋⠑⠆ three fifteen fifteen fourteen two t2e4 t2e4 ⠼⠞⠆⠑⠲ ten two eleven four 3t.t8 3t.t8 ⠼⠒⠞⠨⠞⠦ three ten point ten eight FA9,B7C.0A FA9,B7C.0A ⠼⠋⠁⠔⠠⠃⠶⠉⠨⠴⠁ fifteen ten nine comma eleven seven twelve point zero ten Q Q ⠠⠟ latin upper case q Γ ⠨⠠⠛ greek upper case gamma Ψ ⠨⠠⠽ greek upper case psi A B C △ ⁡ A ⁣ B ⁣ C ⠫⠞⠀⠠⠁⠠⠃⠠⠉ triangle A B C α ⠨⠁ greek lower case alpha β ⠨⠃ greek lower case beta γ ⠨⠛ greek lower case gamma δ ⠨⠙ greek lower case delta ε ⠨⠑ greek lower case epsilon ζ ⠨⠵ greek lower case zeta η ⠨⠱ greek lower case eta θ ⠨⠹ greek lower case theta ι ⠨⠊ greek lower case iota κ ⠨⠅ greek lower case kappa λ ⠨⠇ greek lower case lambda μ ⠨⠍ greek lower case mu ν ⠨⠝ greek lower case nu ξ ⠨⠭ greek lower case xi ο ⠨⠕ greek lower case omicron π ⠨⠏ greek lower case pi ρ ⠨⠗ greek lower case rho σ ⠨⠎ greek lower case sigma τ ⠨⠞ greek lower case tau υ ⠨⠥ greek lower case upsilon φ ⠨⠋ greek lower case phi χ ⠨⠯ greek lower case chi ψ ⠨⠽ greek lower case psi ω ⠨⠺ greek lower case omega ϐ ⠨⠈⠃ greek lower case beta symbol ϵ ⠨⠈⠑ greek lower case epsilon symbol ϑ ⠨⠈⠹ greek lower case theta symbol ϰ ⠨⠈⠅ greek lower case kappa symbol ϖ ⠨⠈⠏ greek lower case pi symbol ϱ ⠨⠈⠗ greek lower case rho symbol ϕ ⠨⠈⠋ greek lower case phi symbol Α ⠨⠠⠁ greek upper case alpha Β ⠨⠠⠃ greek upper case beta Γ ⠨⠠⠛ greek upper case gamma Δ ⠨⠠⠙ greek upper case delta Ε ⠨⠠⠑ greek upper case epsilon Ζ ⠨⠠⠵ greek upper case zeta Η ⠨⠠⠱ greek upper case eta Θ ⠨⠠⠹ greek upper case theta Ι ⠨⠠⠊ greek upper case iota Κ ⠨⠠⠅ greek upper case kappa Λ ⠨⠠⠇ greek upper case lambda Μ ⠨⠠⠍ greek upper case mu Ν ⠨⠠⠝ greek upper case nu Ξ ⠨⠠⠭ greek upper case xi Ο ⠨⠠⠕ greek upper case omicron Π ⠨⠠⠏ greek upper case pi Ρ ⠨⠠⠗ greek upper case rho Σ ⠨⠠⠎ greek upper case sigma Τ ⠨⠠⠞ greek upper case tau Υ ⠨⠠⠥ greek upper case upsilon Φ ⠨⠠⠋ greek upper case phi Χ ⠨⠠⠯ greek upper case chi Ψ ⠨⠠⠽ greek upper case psi Ω ⠨⠠⠺ greek upper case omega α ⠨⠁ greek lower case alpha Σ ⠨⠠⠎ greek upper case sigma π ⠨⠏ greek lower case pi ϕ ⠨⠈⠋ greek phi symbol α ⁢ β ⠨⠁⠨⠃ alpha times beta Α ⁢ α + Β ⁢ β ⠨⠠⠁⠨⠁⠬⠨⠠⠃⠨⠃ upper case alpha times alpha plus upper case beta times beta 3 30 3 ∶ 30 ⠼⠒⠀⠐⠂⠀⠼⠒⠴ three ratio thirty f x y f ∶ ( x , y ) ⠋⠀⠐⠂⠀⠷⠭⠠⠀⠽⠾ f ratio open parenthesis x comma y close parenthesis 1 3 5 7 1 , 3 , 5 , … , 7 ⠼⠂⠠⠀⠼⠒⠠⠀⠼⠢⠠⠀⠄⠄⠄⠠⠀⠼⠶ one comma three comma five comma ellipsis comma seven x y “ ⁢ x , y ⁢ ” ⠦⠭⠠⠀⠽⠴ left double quote x comma y close double quote 3 4 “ ⁢ 3 ⁢ ” , “ ⁢ 4 ⁢ ” ⠦⠼⠒⠴⠠⠀⠦⠼⠲⠴ left double quote three right double quote comma left double quote four right double quote x y x , y ⠷⠭⠠⠀⠽⠾ open parenthesis x comma y close parenthesis 3 2 ( − 3 , 2 ) ⠷⠤⠒⠠⠀⠆⠾ open parenthesis minus three comma two close parenthesis 1,000,000 1,000,000 ⠼⠂⠠⠴⠴⠴⠠⠴⠴⠴ one comma million 947, 147, 592 947, 147, 592 ⠼⠔⠲⠶⠠⠀⠂⠲⠶⠠⠀⠢⠔⠆ nine four seven comma space one four seven comma space five nine two 5 3 5 − — = 3 ⠼⠢⠤⠀⠤⠤⠤⠤⠀⠨⠅⠀⠼⠒ five minus long dash equals three 15 2 3 — 15 = 2 3 ⠹⠤⠤⠤⠤⠌⠂⠢⠼⠀⠨⠅⠀⠹⠆⠌⠒⠼ begin fraction long dash over fifteen end fraction equals begin fraction two over three end fraction 4 6 8 — , 4 , 6 , 8 , — ⠷⠤⠤⠤⠤⠠⠀⠲⠠⠀⠖⠠⠀⠦⠠⠀⠤⠤⠤⠤⠾ open parenthesis long dash comma four comma six comma eight comma long dash close parenthesis 2 3 $ ⁢ 2 + $ ⁢ 3 = $ ⁢ — ⠈⠎⠆⠬⠈⠎⠒⠀⠨⠅⠀⠈⠎⠤⠤⠤⠤ two dollars plus three dollars equals long dash dollars 2 3 2 ⁢ ¢ + 3 ⁢ ¢ = — ⁢ ¢ ⠼⠆⠈⠉⠬⠒⠈⠉⠀⠨⠅⠀⠤⠤⠤⠤⠈⠉ two cents plus three cents equals long dash cents 2 3 2 ⁢ % + 3 ⁢ % = — ⁢ % ⠼⠆⠈⠴⠬⠒⠈⠴⠀⠨⠅⠀⠤⠤⠤⠤⠈⠴ two percent plus three percent equals long dash percent 2 3 £ ⁢ 2 + £ ⁢ 3 = £ ⁢ — ⠈⠇⠆⠬⠈⠇⠒⠀⠨⠅⠀⠈⠇⠤⠤⠤⠤ two pound plus three pound equals long dash pound 4 . 4 ⁢ % = . ⁢ — ⠼⠲⠈⠴⠀⠨⠅⠀⠨⠐⠤⠤⠤⠤ four percent equals dot long dash 12 12 ′ = — ″ ⠼⠂⠆⠄⠀⠨⠅⠀⠤⠤⠤⠤⠄⠄ twelve prime equals long dash double prime 1 3 5 15 1 , 3 , 5 , … , 15 ⠼⠂⠠⠀⠼⠒⠠⠀⠼⠢⠠⠀⠄⠄⠄⠠⠀⠼⠂⠢ one comma three comma five comma ellipsis comma fifteen a a r a r 2 a , a ⁢ r , a ⁢ r 2 , … ⠁⠠⠀⠁⠗⠠⠀⠁⠗⠘⠆⠠⠀⠄⠄⠄ a comma a r comma a r squared comma ellipsis x y x + y + … ⠭⠬⠽⠬⠀⠄⠄⠄ x plus y plus ellipsis 1 3 5 15 1 , 3 , 5 , … , 15 ⠼⠂⠠⠀⠼⠒⠠⠀⠼⠢⠠⠀⠄⠄⠄⠠⠀⠼⠂⠢ one comma three comma five comma ellipsis comma one five p 1 1 p r r p 1 α 1 ⁢ … ⁢ p r α r ⠏⠂⠘⠨⠁⠘⠰⠂⠐⠄⠄⠄⠀⠏⠰⠗⠘⠨⠁⠘⠰⠗ p sub one super alpha sub one ellipsis p sub r super alpha sub r 1 0 1 … , − 1 , 0 , 1 , … ⠷⠄⠄⠄⠠⠀⠤⠂⠠⠀⠴⠠⠀⠂⠠⠀⠄⠄⠄⠾ open parenthesis ellipsis comma minus one comma zero comma one comma ellipsis close parenthesis 12 14 12 ⁢ ¢ + 14 ⁢ ¢ = … ⁢ ¢ ⠼⠂⠆⠈⠉⠬⠂⠲⠈⠉⠀⠨⠅⠀⠄⠄⠄⠀⠈⠉ twelve cent plus fourteen cent equals ellipsis cent 3 27 ( ? ) 3 = 27 ⠷⠿⠾⠘⠒⠀⠨⠅⠀⠼⠆⠶ open parenthesis omission close parenthesis cubed equals twenty seven 92 in ft in 92 ⁢ ⁢ in = ? ⁢ ⁢ ft ⁢ ? ⁢ ⁢ in ⠼⠔⠆⠀⠊⠝⠀⠨⠅⠀⠿⠀⠋⠞⠿⠀⠊⠝ ninety two inches equals omission feet omission inches 7 2 14 7 × 2 ? 14 ⠼⠶⠈⠡⠆⠀⠿⠀⠼⠂⠲ seven times sign two omission fourteen 10 ? + ? = 10 ⠿⠬⠿⠀⠨⠅⠀⠼⠂⠴ omission plus omission equals ten 7 5 7 − ? = 5 ⠼⠶⠤⠿⠀⠨⠅⠀⠼⠢ seven minus omission equals five 9 5 9 − 5 = ? ⠼⠔⠤⠢⠀⠨⠅⠀⠿ nine minus five equals omission 5 15 7 13 ( 5 , ) + ( , 15 ) = ( 7 , 13 ) ⠷⠢⠠⠀⠿⠾⠬⠷⠿⠠⠀⠂⠢⠾⠀⠨⠅⠀⠷⠶⠠⠀⠂⠒⠾ open parenthesis five comma omission close parenthesis plus open parenthesis omission comma fifteen close parenthesis equals open parenthesis seven comma thirteen close parenthesis 5 25 5 × 25 = ⠼⠢⠈⠡⠆⠢⠀⠨⠅⠀⠿ five times sign twenty five equals omission five fifteen ⁢ five × ⁢ — = ⁢ fifteen ⠋⠊⠧⠑⠈⠡⠀⠤⠤⠤⠤⠀⠨⠅⠀⠋⠊⠋⠞⠑⠑⠝ five times sign long dash equals fifteen 2 4 6 10 2 , 4 , 6 , … , 10 ⠼⠆⠠⠀⠼⠲⠠⠀⠼⠖⠠⠀⠄⠄⠄⠠⠀⠼⠂⠴ two comma four comma six comma ellipsis comma ten 5 □ + ○ = 5 ⠫⠲⠬⠫⠉⠀⠨⠅⠀⠼⠢ square plus circle equals five 5 7 35 5 × 7 ? 35 ⠼⠢⠈⠡⠶⠀⠿⠀⠼⠒⠢ five times sign seven omission thirty five x x y 1 y ⁣ x ⁣ x ⁢ y = 1 y ⠹⠪⠭⠻⠌⠪⠭⠻⠽⠼⠀⠨⠅⠀⠹⠂⠌⠽⠼ begin fraction cancel x end cancel over cancel x end cancel y end fraction equals begin fraction one over y end fraction 5 25 1 5 ⁣ 5 ⁣ 25 = 1 5 ⠹⠪⠢⠻⠌⠪⠆⠢⠻⠼⠀⠨⠅⠀⠹⠂⠌⠢⠼ begin fraction cancel five end cancel over cancel twenty five end cancel end fraction equals begin fraction one over five end fraction x y x y y z 1 y z ⁣ ( x + y ) ⁣ ( x + y ) ⁢ ( y + z ) = 1 y + z ⠹⠪⠷⠭⠬⠽⠾⠻⠌⠪⠷⠭⠬⠽⠾⠻⠷⠽⠬⠵⠾⠼⠀⠨⠅⠀⠹⠂⠌⠽⠬⠵⠼ begin fraction cancel open parenthesis x plus y close parenthesis end cancel over cancel open parenthesis x plus y close parenthesis end cancel open parenthesis y plus z close parenthesis end fraction equals begin fraction one over y plus z end fraction x y x y z 1 z ⁣ x ⁢ ⁣ y ⁣ x ⁢ ⁣ y ⁢ z = 1 z ⠹⠪⠭⠻⠪⠽⠻⠌⠪⠭⠻⠪⠽⠻⠵⠼⠀⠨⠅⠀⠹⠂⠌⠵⠼ begin fraction cancel x end cancel cancel y end cancel over cancel x end cancel cancel y end cancel z end fraction equals begin fraction one over z end fraction 1 3 1 3 ⠹⠂⠌⠒⠼ begin fraction one over three end fraction x 1 2 x 1 2 ⠭⠘⠹⠂⠌⠆⠼ x power begin fraction one over two end fraction a b c a + b c ⠹⠁⠬⠃⠌⠉⠼ begin fraction a plus b over c end fraction x 1 2 2 x 1 2 2 ⠹⠭⠘⠹⠂⠌⠆⠼⠐⠌⠆⠼ begin fraction x power begin fraction one over two end fraction over two end fraction rate distance time ⁢ rate = ⁢ distance ⁢ time ⠗⠁⠞⠑⠀⠨⠅⠀⠹⠙⠊⠎⠞⠁⠝⠉⠑⠌⠞⠊⠍⠑⠼ rate equals begin fraction distance over time end fraction a b c d a + b ⁄ c + d ⠹⠁⠬⠃⠸⠌⠉⠬⠙⠼ begin fraction a plus b slash c plus d end fraction 3 x y 3 ⁢ x ⁄ y ⠼⠒⠹⠭⠸⠌⠽⠼ three begin fraction x slash y end fraction 4 3 8 4 ⁤ 3 8 ⠼⠲⠸⠹⠒⠌⠦⠸⠼ four and three over eight 2 3 4 x 2 ⁤ 3 ⁄ 4 ⁢ x ⠼⠆⠸⠹⠒⠸⠌⠲⠸⠼⠭ two and three over four x 1 3 1 ⁢ ⁄ ⁢ 3 ⠼⠂⠸⠌⠒ one slash three 1 3 1 ⁄ 3 ⠹⠂⠸⠌⠒⠼ begin fraction one slash three end fraction x 1 2 x 1 ⁢ ⁄ ⁢ 2 ⠭⠘⠂⠸⠌⠆ x power one slash two x 1 2 x 1 ⁄ 2 ⠭⠘⠹⠂⠸⠌⠆⠼ x power begin fraction one slash two end fraction x 1 2 2 x 1 2 ⁢ ⁄ ⁢ 2 ⠭⠘⠹⠂⠌⠆⠼⠐⠸⠌⠆ x power begin fraction one over two end fraction slash two x 1 2 2 x 1 2 ⁄ 2 ⠹⠭⠘⠹⠂⠌⠆⠼⠐⠸⠌⠆⠼ begin fraction x power begin fraction one overtwo end fraction slash two end fraction x 1 2 7 x 1 ⁢ ⁄ ⁢ 2 ⁢ ⁄ ⁢ 7 ⠭⠘⠂⠸⠌⠆⠐⠸⠌⠶ x power one slash two baseline slash seven x 1 2 7 x 1 ⁄ 2 ⁄ 7 ⠹⠭⠘⠹⠂⠸⠌⠆⠼⠐⠸⠌⠶⠼ begin fraction x power begin fraction one slash two end fraction baseline slash seven end fraction a b c d a + b ⁢ ⁄ ⁢ c + d ⠁⠬⠃⠸⠌⠉⠬⠙ a plus b slash c plus d a b c d a + b ⁄ c + d ⠁⠬⠹⠃⠸⠌⠉⠼⠬⠙ a plus begin fraction b slash c end fraction plus d a b c d ( a + b ) ⁢ ⁄ ⁢ ( c + d ) ⠷⠁⠬⠃⠾⠸⠌⠷⠉⠬⠙⠾ open parenthesis a plus b close parenthesis slash open parenthesis c plus d close parenthesis a b c d ( a + b ) ⁄ ( c + d ) ⠹⠷⠁⠬⠃⠾⠸⠌⠷⠉⠬⠙⠾⠼ begin fraction open parenthesis a plus b close parenthesis slash open parenthesis c plus d close parenthesis end fraction I n I ⁢ ⁄ ⁢ ( n ) ⠠⠊⠸⠌⠷⠝⠾ capital I slash open parenthesis n close parenthesis I n I ⁄ ( n ) ⠹⠠⠊⠸⠌⠷⠝⠾⠼ begin fraction capital I slash open parenthesis n close parenthesis end fraction 1 31 70 1 ⁢ ⁄ ⁢ 31 ⁢ ⁄ ⁢ 70 ⠼⠂⠸⠌⠒⠂⠸⠌⠶⠴ one slash thirty one slash seventy 1 31 70 1 ⁄ 31 ⁄ 70 ⠠⠹⠹⠂⠸⠌⠒⠂⠼⠠⠸⠌⠶⠴⠠⠼ begin fraction begin fraction one slash thirty one end fraction slash seventy end fraction 4 3 8 4 ⁤ 3 8 ⠼⠲⠸⠹⠒⠌⠦⠸⠼ four and three over eight 4 3 8 4 ⁤ 3 ⁄ 8 ⠼⠲⠸⠹⠒⠸⠌⠦⠸⠼ four and three slash eight x 3 8 x ⁢ 3 8 ⠭⠹⠒⠌⠦⠼ x begin fraction three over eight end fraction x 3 8 x ⁢ 3 ⁄ 8 ⠭⠹⠒⠸⠌⠦⠼ x begin fraction three slash eight end fraction 3 1 y 3 ⁢ 1 ⁄ y ⠼⠒⠹⠂⠸⠌⠽⠼ three begin fraction one slash y end fraction 3 8 5 3 8 5 ⠠⠹⠹⠒⠌⠦⠼⠠⠌⠢⠠⠼ begin fraction begin fraction three over eight end fraction over five 1 2 2 2 3 1 ⁢ ⁄ ⁢ 2 2 ⁤ 2 3 ⠠⠹⠂⠸⠌⠆⠠⠌⠆⠸⠹⠆⠌⠒⠸⠼⠠⠼ begin fraction one slash two over two and begin fraction two over three end fraction end fraction 1 2 2 2 3 1 ⁄ 2 2 ⁤ 2 3 ⠠⠹⠹⠂⠸⠌⠆⠼⠠⠌⠆⠸⠹⠆⠌⠒⠸⠼⠠⠼ begin fraction begin fraction one slash two end fraction over two and begin fraction two over three end fraction end fraction 2 3 3 2 2 ⁢ ⁄ ⁢ 3 3 ⁢ ⁄ ⁢ 2 ⠹⠆⠸⠌⠒⠌⠒⠸⠌⠆⠼ begin fraction two slash three over three slash two end fraction 2 3 3 2 2 ⁄ 3 3 ⁄ 2 ⠠⠹⠹⠆⠸⠌⠒⠼⠠⠌⠹⠒⠸⠌⠆⠼⠠⠼ begin fraction begin fraction two slash three end fraction over begin fraction two slash three end fraction end fraction 5 4 3 8 5 4 ⁤ 3 8 ⠠⠹⠢⠠⠌⠲⠸⠹⠒⠌⠦⠸⠼⠠⠼ begin fraction five over four and three over eight end fraction 3 4 5 3 ⁢ ⁄ ⁢ 4 5 ⠹⠒⠸⠌⠲⠌⠢⠼ begin fraction three slash four over five end fraction 3 4 5 3 ⁄ 4 5 ⠠⠹⠹⠒⠸⠌⠲⠼⠠⠌⠢⠠⠼ begin fraction begin fraction three slash four end fraction over five end fraction 1 2 3 4 1 2 ⁄ 3 4 ⠠⠹⠹⠂⠌⠆⠼⠠⠸⠌⠹⠒⠌⠲⠼⠠⠼ begin fraction begin fraction one over two end fraction slash begin fraction three over four end fraction a b 3 4 5 6 a b 3 4 5 6 ⠹⠁⠌⠃⠘⠠⠹⠹⠒⠌⠲⠼⠠⠌⠹⠢⠌⠖⠼⠠⠼⠐⠼ begin fraction a over b power begin fraction begin fraction three over four end fraction over begin fraction five over six end fraction end fraction baseline end fraction 1 1 4 1 3 5 5 1 ⁤ 1 4 1 ⁤ 3 5 5 ⠠⠠⠹⠠⠹⠂⠸⠹⠂⠌⠲⠸⠼⠠⠌⠂⠸⠹⠒⠌⠢⠸⠼⠠⠼⠠⠠⠌⠢⠠⠠⠼ begin fraction begin fraction one and begin fraction one over four end fraction end fraction over one and begin fraction three over five end fraction end fraction over five end fraction 1 x d d x 2 x 2 x d d x 1 x 1 x 2 1 2 x 1 x 2 ( 1 − x ) ⁢ d d ⁢ x ⁢ ( 2 ⁢ x ) − 2 ⁢ x ⁢ d d ⁢ x ⁢ ( 1 − x ) ( 1 − x ) 2 1 + ( 2 ⁢ x 1 − x ) 2 ⠠⠠⠹⠠⠹⠷⠂⠤⠭⠾⠹⠙⠌⠙⠭⠼⠷⠆⠭⠾⠤⠆⠭⠹⠙⠌⠙⠭⠼⠷⠂⠤⠭⠾⠠⠌⠷⠂⠤⠭⠾⠘⠆⠐⠠⠼⠠⠠⠌⠂⠬⠷⠹⠆⠭⠌⠂⠤⠭⠼⠾⠘⠆⠐⠠⠠⠼ fraction fraction parenthesis one minus x close parenthesis times fraction d over d times x end fraction times parenthesis two times x close parenthesis minus two times x times fraction d over d times x end fraction times parenthesis one minus x close parenthesis over parenthesis one minus x close parenthesis squared end fraction over one plus parenthesis fraction two times x over one minus x end fraction close parenthesis squared end fraction 2 1 1 2 1 2 1 2 1 2 2 = 1 + 1 2 + 1 2 + 1 2 + 1 2 + … ⠜⠆⠻⠀⠨⠅⠀⠼⠂⠬⠠⠠⠠⠹⠂⠠⠠⠠⠌⠆⠬⠠⠠⠹⠂⠠⠠⠌⠆⠬⠠⠹⠂⠠⠌⠆⠬⠹⠂⠌⠆⠬⠀⠄⠄⠄⠼⠠⠼⠠⠠⠼⠠⠠⠠⠼ root two end root equals one plus begin fraction one over two plus begin fraction one over two plus begin fraction one over two plus begin fraction one over two plus ellipsis end fraction end fraction end fraction end fraction 1 2 2 4 1 + 2 2 + 4 ⠹⠂⠬⠆⠌⠆⠬⠲⠼ begin fraction one plus two over two plus four end fraction x y x y ⠹⠭⠌⠽⠼ begin fraction x over y end fraction rate distance time ⁢ rate = ⁢ distance ⁢ time ⠗⠁⠞⠑⠀⠨⠅⠀⠹⠙⠊⠎⠞⠁⠝⠉⠑⠌⠞⠊⠍⠑⠼ rate equals begin fraction distance over time end fraction 5280 ft 1 mi 60 mi 1 hr 1 hr 60 min 1 min 60 sec 88 ft 1 sec 88 ft sec 5280 ⁢ ⁢ ft 1 ⁢ ⁢ mi ⋅ 60 ⁢ ⁢ mi 1 ⁢ ⁢ hr ⋅ 1 ⁢ ⁢ hr 60 ⁢ ⁢ min ⋅ 1 ⁢ ⁢ min 60 ⁢ ⁢ sec = 88 ⁢ ⁢ ft 1 ⁢ ⁢ sec = 88 ⁢ ⁢ ft ⁢ ⁄ ⁢ sec ⠹⠢⠆⠦⠴⠀⠋⠞⠌⠂⠀⠍⠊⠼⠹⠖⠴⠀⠍⠊⠌⠂⠀⠓⠗⠼⠹⠂⠀⠓⠗⠌⠖⠴⠀⠍⠊⠝⠼⠹⠂⠀⠍⠊⠝⠌⠖⠴⠀⠎⠑⠉⠼⠀⠨⠅⠀⠹⠦⠦⠀⠋⠞⠌⠂⠀⠎⠑⠉⠼⠀⠨⠅⠀⠼⠦⠦⠀⠋⠞⠸⠌⠎⠑⠉ begin fraction five two eight zero feet over one mile end fraction begin fraction sixty miles over one hour end fraction begin fraction one hour over sixty minutes end fraction begin fraction one minute over sixty seconds end fraction equals begin fraction eighty eight feet over one second end fraction equals eight eight feet slash second x y a x y + a ⠭⠘⠽⠐⠬⠁ x super y baseline plus a x y a x y + a ⠭⠘⠽⠬⠁ x super y plus a x y z a x y z + a ⠭⠘⠽⠘⠘⠵⠐⠬⠁ x super y super super z baseline plus a x y z a x y z + a ⠭⠘⠽⠘⠘⠵⠘⠬⠁ x super y super super z super plus a x y z a x y z + a ⠭⠘⠽⠘⠘⠵⠬⠁ x super y super super z plus a x y z w a x y z w + a ⠭⠘⠽⠘⠘⠵⠘⠘⠘⠺⠐⠬⠁ x super y super super z super super super w baseline plus a x y z w a x y z w + a ⠭⠘⠽⠘⠘⠵⠘⠘⠘⠺⠘⠬⠁ x super y super super z super super super w super plus a x y z w a x y z w + a ⠭⠘⠽⠘⠘⠵⠘⠘⠘⠺⠘⠘⠬⠁ x super y super super z super super super w super super plus a x y z w a x y z w + a ⠭⠘⠽⠘⠘⠵⠘⠘⠘⠺⠬⠁ x super y super super z super super super w plus a x y z w v a x y z w v + a ⠭⠘⠽⠘⠘⠵⠘⠘⠘⠺⠘⠘⠘⠘⠧⠐⠬⠁ x super y super super z super super super w super super super super v baseline plus a x y z w v a x y z w v + a ⠭⠘⠽⠘⠘⠵⠘⠘⠘⠺⠘⠘⠘⠘⠧⠘⠬⠁ x super y super super z super super super w super super super super v super plus a x y z w v a x y z w v + a ⠭⠘⠽⠘⠘⠵⠘⠘⠘⠺⠘⠘⠘⠘⠧⠘⠘⠬⠁ x super y super super z super super super w super super super super v super super plus a x y z w v a x y z w v + a ⠭⠘⠽⠘⠘⠵⠘⠘⠘⠺⠘⠘⠘⠘⠧⠘⠘⠘⠬⠁ x super y super super z super super super w super super super super v super super super plus a x y z w v a x y z w v + a ⠭⠘⠽⠘⠘⠵⠘⠘⠘⠺⠘⠘⠘⠘⠧⠬⠁ x super y super super z super super super w super super super super v plus a x 2 x 2 ⠭⠘⠆ x squared x n x n ⠭⠰⠝ x sub n x 2 x 2 ⠭⠘⠆ x squared y 3 y 3 ⠽⠘⠒ y cubed x x ∗ ⠭⠘⠈⠼ x super asterisk x 2 x − 2 ⠭⠘⠤⠆ x super minus two x a x a ⠭⠰⠁ x sub a x 2 x − 2 ⠭⠰⠤⠆ x sub minus two n x y n x y ⠝⠘⠭⠘⠘⠽ n super x super super y x n a x n a ⠭⠘⠝⠘⠰⠁ x super n super sub a x n a x n a ⠭⠰⠝⠰⠘⠁ x sub n sub super a n x y n x y ⠝⠰⠭⠰⠰⠽ n sub x sub sub y n x y z n x y z ⠝⠘⠭⠘⠘⠽⠘⠘⠘⠵ n super x super super y super super super z n x y z n x y z … ⠝⠘⠭⠘⠘⠽⠘⠘⠘⠵⠘⠘⠘⠘⠄⠄⠄ n super x super super y super super super z super super super super ellipsis x y z a x y z a ⠭⠘⠽⠘⠘⠵⠘⠘⠰⠁ x super y super super z super super sub a x y a n x y a n ⠭⠘⠽⠘⠰⠁⠘⠰⠘⠝ x super y super sub a super sub super n n x a j n x a j ⠝⠘⠭⠘⠰⠁⠘⠰⠰⠚ n super x super sub a super sub sub j x a r n x a r n ⠭⠰⠁⠰⠘⠗⠰⠘⠘⠝ x sub a sub super r sub super super n x a n b x a n b ⠭⠰⠁⠰⠘⠝⠰⠘⠰⠃ x sub a sub super n sub super sub b x p a m x p a m ⠭⠰⠏⠰⠰⠁⠰⠰⠘⠍ x sub p sub sub a sub sub super m n x y z n x y z ⠝⠰⠭⠰⠰⠽⠰⠰⠰⠵ n sub x sub sub y sub sub sub z n x y z n x y z … ⠝⠰⠭⠰⠰⠽⠰⠰⠰⠵⠰⠰⠰⠰⠄⠄⠄ n sub x sub sub y sub sub sub z sub sub sub sub dots n x n x ⠘⠭⠐⠝ n pre super x x x − ⠘⠤⠐⠭ x pre super minus n x n x ⠰⠭⠐⠝ n pre sub x n x y n x y ⠰⠭⠐⠝⠰⠽ (n pre sub x) sub y n y x n y x ⠰⠭⠐⠝⠰⠽ (n sub y) pre sub x 10 4 10 4 − ⠼⠂⠴⠘⠘⠤⠘⠲ ten super 4 pre super super minus x n a x n a ⠘⠝⠘⠰⠁⠐⠭ x pre super n super sub a x n a x n a ⠘⠰⠁⠘⠝⠐⠭ x pre super n pre super sub a x n a x n a ⠰⠝⠰⠘⠁⠐⠭ x pre sub n sub super a x n a x n a ⠰⠘⠁⠰⠝⠐⠭ x pre sub n pre sub super a n x y n x y ⠰⠭⠰⠰⠽⠐⠝ n pre sub x sub sub y n x y n x y ⠰⠰⠽⠰⠭⠐⠝ n pre sub x pre sub sub y p b x c p b ⁢ x c ⠏⠘⠃⠘⠉⠐⠭ p super b times x pre super c x 1 x 1 ⠭⠂ x sub one x 11 x 11 ⠭⠂⠂ x sub eleven A 1 A 1 ⠠⠁⠂ capital a sub one x 1 x ′ 1 ⠭⠄⠂ x prime sub one x 2 x ″ 2 ⠭⠄⠄⠆ x prime prime sub two x 3 x 3 ⠰⠒⠐⠭ x pre sub three x i 1 x i 1 ⠭⠰⠊⠰⠰⠂ x sub i sub sub one 2 x log 2 ⁡ x ⠇⠕⠛⠆⠀⠭ log base two of x 12 7 12 7 ⠼⠂⠆⠰⠶ twelve sub seven C O 3 2 ( C ⁢ O 3 ) 2 ⠷⠠⠉⠠⠕⠒⠾⠰⠆ open parenthesis C O sub three close parenthesis sub two N a 2 C O 3 N ⁢ a 2 ⁢ C ⁢ O 3 ⠠⠝⠁⠆⠠⠉⠠⠕⠒ N a sub two C O sub three seven 3 seven 3 ⠎⠑⠧⠑⠝⠰⠒ seven sub three x 1 j x 1 j ⠭⠰⠂⠰⠰⠚ x sub one sub sub j x 2 n x 2 n ⠭⠰⠆⠰⠘⠝ x sub two sub super n x 2 x 2 ′ ⠭⠰⠆⠄ x sub (two prime) x 2 k x 2 + k ⠭⠰⠆⠬⠅ x sub two plus k x 1 2 x 1 ⁢ ⁄ ⁢ 2 ⠭⠰⠂⠸⠌⠆ x sub one slash two x 1 3 x 1 3 ⠰⠒⠐⠭⠂ (x sub one) pre sub three x 3 1 x 3 1 ⠰⠒⠐⠭⠂ (x pre sub 3) sub one A x 1 A x ⋅ 1 ⠠⠁⠰⠭⠂ A sub x one x 10,000 x 10,000 ⠭⠂⠴⠠⠴⠴⠴ x sub ten comma thousand x 1.2 x 1.2 ⠭⠂⠨⠆ x sub one point two x .6 x .6 ⠭⠨⠖ x sub point six 3AF 16 3AF 16 ⠼⠒⠁⠋⠰⠂⠖ three ten fifteen base sixteen x i j k x i , j , k ⠭⠰⠊⠪⠚⠪⠅ x sub i comma j comma k x a b x ( a , b ) ⠭⠰⠷⠁⠠⠀⠃⠾ x sub open parenthesis a comma b close parenthesis x 1 2 x 1 , 2 ⠭⠰⠂⠪⠆ x sub one comma two P n x y P n x , y ⠠⠏⠰⠝⠰⠰⠭⠪⠽ P sub n sub sub x comma y x n 1 n 1 x n 1 n x n n 1 x n − 1 , n − 1 , x n − 1 , n , x n , n − 1 ⠨⠷⠭⠰⠝⠤⠂⠪⠝⠤⠂⠠⠀⠭⠰⠝⠤⠂⠪⠝⠠⠀⠭⠰⠝⠪⠝⠤⠂⠐⠨⠾ open brace x sub n minus one sub comma n minus one baseline comma x sub n minus one sub comma n baseline comma x sub n sub comma n minus one baseline close brace x y ( x , y ) ⠷⠭⠠⠀⠽⠾ open parenthesis x comma y close parenthesis x 2 1 x 2 + 1 ⠭⠘⠆⠐⠬⠂ x squared baseline plus one x a y 2 x a + y 2 ⠭⠰⠁⠐⠬⠽⠘⠆ x sub a baseline plus y squared e x 2 2 e x 2 2 ⠹⠑⠘⠭⠘⠘⠆⠐⠌⠆⠼ fraction e super x super super 2 baseline over two end fraction A n n n n a m n A n + n + n + … + n = a m ⁢ n ⠠⠁⠘⠝⠬⠝⠬⠝⠬⠀⠄⠄⠄⠀⠬⠝⠀⠨⠅⠀⠁⠘⠍⠝ A super n plus n plus n plus dots plus n baseline equals a super m n x 2 x 2 ⠭⠘⠆ x squared x 2 x 3 x 2 , x 3 ⠨⠷⠭⠘⠆⠠⠀⠭⠘⠒⠐⠨⠾ open brace x squared comma x cubed close brace x 10,000 x 10,000 ⠭⠘⠂⠴⠠⠴⠴⠴ x super ten comma thousand x i j x i , j ⠭⠰⠊⠪⠚ x sub i comma j P n 1 n 2 P n 1 , n 2 , … ⠠⠏⠰⠝⠰⠰⠂⠰⠪⠝⠰⠰⠆⠰⠪⠀⠄⠄⠄ P sub n sub sub one sub comma sub n sub sub two sub comma dots 2 p 2 2 ⁢ p 2 ⠼⠆⠏⠘⠆ two p squared 3 10 4 ergs 3 × 10 4 ⁢ ergs ⠼⠒⠈⠡⠂⠴⠘⠲⠐⠑⠗⠛⠎ three times ten super four ergs 6.696 10 8 mph 6.696 × 10 8 ⁢ ⁢ mph ⠼⠖⠨⠖⠔⠖⠈⠡⠂⠴⠘⠦⠀⠍⠏⠓ six point six nine six times sign ten super eight mph b A B C b △ ⁡ A ⁣ B ⁣ C ⠃⠰⠫⠞⠀⠠⠁⠠⠃⠠⠉ b sub triangle A B C x sin ⁡ x ⠎⠊⠝⠀⠭ sine x x 2 cos 2 ⁡ x ⠉⠕⠎⠘⠆⠀⠭ cosine squared x e x e sin ⁡ x ⠑⠘⠎⠊⠝⠀⠭ e super sine x e x i x e sin ⁡ x + i ⁢ cos ⁡ x ⠑⠘⠎⠊⠝⠀⠭⠬⠊⠉⠕⠎⠀⠭ e super sine x plus i cosine x e x x e x + ln ⁡ x ⠑⠘⠭⠬⠇⠝⠀⠭ e super x plus natural logarithm x e x 2 e cos 2 ⁡ x ⠑⠘⠉⠕⠎⠘⠘⠆⠀⠭ e super cosine super super two super x e x 2 y 2 e sin 2 ⁡ x + sin 2 ⁡ y ⠑⠘⠎⠊⠝⠘⠘⠆⠀⠭⠬⠎⠊⠝⠘⠘⠆⠀⠽ e super sine super super two super x plus cosine super super two super y q q a q log q ⁡ a ⠟⠘⠇⠕⠛⠘⠰⠟⠀⠁ q super logarithm base q of a V m n V max ⁡ ( m , n ) ⠠⠧⠰⠍⠁⠭⠀⠷⠍⠠⠀⠝⠾ V sub max open parenthesis m comma n close parenthesis e 3.1415926535 e 3.1415926535 ⠑⠘⠒⠨⠂⠲⠂⠢⠔⠆⠖⠢⠒⠢ e super three point one four one five nine two six five three five x 1 1 2 1 3 1 n x 1 + 1 ⁢ ⁄ ⁢ 2 + 1 ⁢ ⁄ ⁢ 3 + … + 1 ⁢ ⁄ ⁢ n ⠭⠘⠂⠬⠂⠸⠌⠆⠬⠂⠸⠌⠒⠬⠀⠄⠄⠄⠀⠬⠂⠸⠌⠝ x super one plus one over two plus one over three plus dots plus one over n s 1 s n s 1 ⁢ … ⁢ s n ⠎⠂⠀⠄⠄⠄⠀⠎⠰⠝ s sub one ellipsis s sub n 10 3 10 5 10 3 + ⁢ — = 10 5 ⠼⠂⠴⠘⠒⠬⠀⠤⠤⠤⠤⠀⠨⠅⠀⠼⠂⠴⠘⠢ ten super three plus long dash baseline equals ten super five x 2 y 2 z 2 r 2 x 2 + y 2 + z 2 = r 2 ⠭⠘⠆⠐⠬⠽⠘⠆⠐⠬⠵⠘⠆⠀⠨⠅⠀⠗⠘⠆ x squared plus y squared plus z squared equal r squared 2 x 3 x 2 x < 3 x ⠼⠆⠘⠭⠀⠐⠅⠀⠼⠒⠘⠭ two super x less than three super x q q a a q log q ⁡ a = a ⠟⠘⠇⠕⠛⠘⠰⠟⠀⠁⠀⠨⠅⠀⠁ q super logarithm base q of a equals a 1 x 2 2 x 4 ( 1 − sin 2 ⁡ x ) 2 = cos 4 ⁡ x ⠷⠂⠤⠎⠊⠝⠘⠆⠀⠭⠾⠘⠆⠀⠨⠅⠀⠉⠕⠎⠘⠲⠀⠭ open parenthesis one minus sine squared of x close parenthesis squared equals cosine super 4 of x x 2 y 2 x 2 + y 2 ⠜⠭⠘⠆⠐⠬⠽⠘⠆⠐⠻ square root x squared plus y squared end square root e x 2 y 2 e x 2 + y 2 ⠑⠘⠜⠭⠘⠘⠆⠘⠬⠽⠘⠘⠆⠘⠻ e power square root x squared plus y squared end square root 1 x 2 1 x 2 ⠹⠂⠌⠭⠘⠆⠐⠼ fraction one over x squared end fraction d x y 1 x y 2 d ⁢ ( x y ) 1 + ( x y ) 2 ⠠⠹⠙⠷⠹⠭⠌⠽⠼⠾⠠⠌⠂⠬⠷⠹⠭⠌⠽⠼⠾⠘⠆⠐⠠⠼ fraction d open parenthesis fraction x over y end fraction close parenthesis over one plus open parenthesis fraction x over y end fraction close parenthesis squared end fraction x 2 y 2 x 2 ⁢ ⁣ y 2 ⠭⠘⠆⠐⠪⠽⠘⠆⠐⠻ x squared cancel open parenthesis y squared close parenthesis end cancel x 2 y 2 ( x 2 + y 2 ) ⠷⠭⠘⠆⠐⠬⠽⠘⠆⠐⠾ open parenthesis x squared plus y squared close parenthesis x m n x ( m n ) ⠭⠘⠷⠍⠘⠘⠝⠘⠾ x super open parenthesis m super super n close parenthesis p b q c p b ⁢ q c ⠏⠘⠃⠘⠉⠐⠟ p super b times q pre super c P b Q c P b ⁢ Q c ⠠⠏⠰⠃⠰⠉⠐⠠⠟ P sub b times Q pre sub c P 1 Q 2 P 1 ⁢ Q 2 ⠠⠏⠂⠰⠆⠐⠠⠟ P sub one Q pre sub two x 1 1 ( x 1 + 1 ) ⠷⠭⠂⠬⠂⠾ open parenthesis x sub one plus one close parenthesis x 1 y 1 x 2 y 2 ( x 1 ⁢ y 1 + x 2 ⁢ y 2 ) ⠷⠭⠂⠽⠂⠬⠭⠆⠽⠆⠾ open parenthesis x sub one y sub one plus x sub two y sub two close parenthesis x a n x a n ⠭⠰⠁⠘⠝ x sub a super n x a n x a n ⠰⠁⠘⠝⠐⠭ x presub a presuper n x 1 2 x 1 2 ⠭⠂⠘⠆ x sub one super two a n m a n m ⠁⠘⠝⠐⠰⠍ a super n sub m a m n a m n ⠁⠰⠍⠐⠘⠝ a sub m super n x b a x b a ⠘⠁⠐⠰⠃⠐⠭ x pre sub b pre super a x a b x a b ⠰⠃⠐⠘⠁⠐⠭ x pre super a pre sub b x 1 2 x 1 2 ⠭⠂⠐⠘⠆ x sub one super two x a b x ′ a b ⠭⠄⠰⠁⠐⠘⠃ x prime sub a super b x x ′ ⠭⠄ x prime x a x ′ a ⠭⠄⠰⠁ x prime sub a x 2 x ′ 2 ⠭⠄⠘⠆ x prime super 2 x a b x ′ a b ⠭⠄⠰⠁⠘⠃ x prime sub a super b x 1 3 x ″ 1 3 ⠭⠄⠄⠂⠘⠒ x prime prime sub one super three x x ′ ∗ ⠭⠄⠘⠈⠼ x prime super asterisk x x ∗ ′ ⠭⠘⠈⠼⠄ x super asterisk prime A u e A u ⁢ e ∗ ′ ⠠⠁⠰⠥⠑⠘⠈⠼⠄ A sub u e super asterisk prime x x ‾ ⠭⠩⠱ x under bar x y x + y ‾ ⠐⠭⠬⠽⠣⠱⠻ x plus y over bar x 2 x 2 ‾ ⠐⠭⠘⠆⠐⠣⠱⠻ x squared over bar x x ′ ‾ ⠐⠭⠄⠣⠱⠻ x prime over bar x 1 x 1 ‾ ⠐⠭⠂⠣⠱⠻ x sub one over bar x n x n ‾ ⠐⠭⠰⠝⠐⠣⠱⠻ x sub n over bar x x ‾ ⠭⠱ x over bar x y x ‾ + y ‾ ⠭⠱⠬⠽⠱ x over bar plus y over bar x y x ‾ ⁢ y ⠭⠱⠽ x over bar times y x y z x ⁢ y ‾ ⁢ z ⠭⠽⠱⠵ x times y over bar times z x 2 x ‾ 2 ⠭⠱⠘⠆ x over bar squared x x ‾ ′ ⠭⠱⠄ x over bar prime x 1 x ‾ 1 ⠭⠱⠰⠂ x over bar sub one x n x ‾ n ⠭⠱⠰⠝ x over bar sub n Z Z ‾ ⠠⠵⠱ Z over bar 3.5 4 3.5 ⁢ 4 ‾ ⠼⠒⠨⠢⠲⠱ three point five four over bar a A b B ( a ‾ ⁢ A + b ‾ ⁢ B ) ‾ ⠐⠷⠁⠱⠠⠁⠬⠃⠱⠠⠃⠾⠣⠱⠻ open parenthesis a over bar A + b over bar B close parenthesis over bar A x A x ‾ ⠠⠁⠰⠭⠱ A sub x over bar A x y A x ‾ + y ‾ ⠠⠁⠰⠭⠱⠬⠽⠱ A sub x over bar plus y over bar e a x e a ⁢ x ‾ ⠑⠘⠁⠭⠱ e super a x over bar x y a 3 x + y ‾ a = 3 ⠐⠭⠬⠽⠣⠱⠣⠣⠁⠀⠨⠅⠀⠼⠒⠻ x plus y over bar over over a equals three x y a 3 b 2 x + y ‾ a = 3 b = 2 ⠐⠭⠬⠽⠩⠱⠩⠩⠁⠀⠨⠅⠀⠼⠒⠩⠩⠩⠃⠀⠨⠅⠀⠼⠆⠻ x plus y under bar under under a equals three under under under b equals two x y x + y ‾ ‾ ⠐⠭⠬⠽⠩⠱⠣⠱⠻ x plus y under bar over bar x y x + y ‾ ‾ ⠐⠭⠬⠽⠣⠱⠩⠱⠻ x plus y over bar under bar x y a 3 b 2 x + y ‾ a = 3 ‾ b = 2 ⠐⠭⠬⠽⠩⠱⠩⠩⠁⠀⠨⠅⠀⠼⠒⠣⠱⠣⠣⠃⠀⠨⠅⠀⠼⠆⠻ x plus y under bar under under a equals three over bar over over b equals two x x ‾ ‾ ⠐⠭⠣⠱⠱⠻ x over bar over over bar x x ‾ ‾ ‾ ‾ ⠐⠭⠩⠱⠱⠣⠱⠱⠻ x under bar under under bar over bar over over bar x x ‾ ‾ ‾ ⠐⠭⠩⠱⠱⠣⠱⠻ x under bar under under bar over bar x x ‾ ‾ ‾ ⠐⠭⠩⠱⠱⠱⠻ x under bar under under bar under under under bar n k n k ⠷⠝⠩⠅⠾ open parenthesis n over k close parenthesis g j a j g j a j ⠷⠛⠰⠚⠐⠩⠁⠰⠚⠐⠾ open parenthesis g sub j over a sub j close parenthesis A x A x ̃ ⠠⠁⠰⠐⠭⠣⠈⠱⠻ A sub x over tilde A x y A x ̃ + y ̃ ⠠⠁⠰⠐⠭⠣⠈⠱⠻⠬⠰⠐⠽⠣⠈⠱⠻ A sub x over tilde plus y over tilde A x y A x ‾ + y ‾ ⠠⠁⠰⠭⠱⠬⠽⠱ A sub x over bar plus y over bar A ⁣ A ⏜ ⠐⠠⠁⠣⠫⠁⠻ A over arc A B A ⁣ B ⏜ ⠐⠠⠁⠠⠃⠣⠫⠁⠻ A B over arc A ⁣ A ⏝ ⠐⠠⠁⠩⠫⠄⠻ A under arc down A B A ⁣ B ⏝ ⠐⠠⠁⠠⠃⠩⠫⠄⠻ A B under arc down . 3 . ⁢ 3 ‾ ⠼⠨⠒⠱ decimal point three over bar . 7128 . ⁢ 7128 ‾ ⠼⠨⠐⠶⠂⠆⠦⠣⠱⠻ decimal point (seven one two eight) over bar 3.57 29 3.57 ⁢ 29 ‾ ⠼⠒⠨⠢⠶⠐⠆⠔⠣⠱⠻ three decimal point five seven (two nine) over bar . 3 . ⁢ 3 ̇ ⠼⠨⠐⠒⠣⠡⠻ decimal point three over dot .13 5 .13 ⁢ 5 ̇ ⠼⠨⠂⠒⠐⠢⠣⠡⠻ decimal point one three five over dot x x ̈ ⠐⠭⠣⠡⠡⠻ x over dot dot x x ⃛ ⠐⠭⠣⠡⠡⠡⠻ x over dot dot dot root ⠜ root √ ⠜ root x x ⠜⠭⠻ root x end root 3 x x 3 ⠣⠒⠜⠭⠻ cube root x end root x x ⠜⠨⠜⠭⠨⠻⠻ root root x end root end root x x ⠜⠨⠜⠨⠨⠜⠭⠨⠨⠻⠨⠻⠻ root root root x end root end root end root x x ⠜⠨⠜⠨⠨⠜⠨⠨⠨⠜⠭⠨⠨⠨⠻⠨⠨⠻⠨⠻⠻ root root root root x end root end root end root end root 2 2 ⠜⠆⠻ root 2 end root x y x + y ⠜⠭⠬⠽⠻ root x plus y end root x 2 1 x 2 + 1 ⠜⠭⠘⠆⠐⠬⠂⠻ root x squared plus one end root x 2 y 2 x 2 + y 2 ⠜⠭⠘⠆⠐⠬⠽⠘⠆⠐⠻ root x squared plus y squared end root x y x y ⠜⠹⠭⠌⠽⠼⠻ root fraction x over y end fraction end root 3 a 3 ⁢ a ⠼⠒⠜⠁⠻ three root a end root x 3 x 3 ⠜⠭⠻⠘⠒ root x end root super three √ ⠜ root x y √ ⁢ ( x + y ) ⠜⠷⠭⠬⠽⠾ root open parenthesis x plus y close parenthesis 3 2 2 3 ⠣⠒⠜⠆⠻ cube root two end root 3 3 x y 3 ⁢ x + y 3 ⠼⠒⠣⠒⠜⠭⠬⠽⠻ three cube root x plus y end root n a a n ⠣⠝⠜⠁⠻ nth root a end root m n p q p + q m + n ⠣⠍⠬⠝⠜⠏⠬⠟⠻ m plus n root p plus q end root x x y z x + x + y + z ⠜⠭⠬⠨⠜⠭⠬⠽⠨⠻⠬⠵⠻ root x plus root x plus y end root plus z end root 3 x 2 3 x 2 y 2 y 2 x 2 + x 2 + y 2 3 + y 2 3 ⠣⠒⠜⠭⠘⠆⠐⠬⠨⠣⠒⠜⠭⠘⠆⠐⠬⠽⠘⠆⠐⠨⠻⠬⠽⠘⠆⠐⠻ cube root x squared plus cube root x squared plus y squared end root plus y squared end root 3 x 3 x x 3 = x 3 ⠜⠨⠣⠒⠜⠭⠨⠻⠻⠀⠨⠅⠀⠣⠒⠜⠨⠜⠭⠨⠻⠻ root cube root x end root end root equals cube root root x end root end root x y z x + y + z ⠜⠭⠬⠨⠜⠽⠬⠨⠨⠜⠵⠨⠨⠻⠨⠻⠻ root x plus root y plus root z end root end root end root ⊙ ⠫⠉ circle A ⊙ ⁡ ⁣ A ⠫⠉⠀⠠⠁ circle A A B C ⊙ ⁡ A ⁣ B ⁣ C ⠫⠉⠀⠠⠁⠠⠃⠠⠉ circle A B C ⬭ ⠫⠑ ellipse A ⬭ ⁡ ⁣ A ⠫⠑⠀⠠⠁ ellipse A A B C ⬭ ⁡ A ⁣ B ⁣ C ⠫⠑⠀⠠⠁⠠⠃⠠⠉ ellipse A B C △ ⠫⠞ triangle A △ ⁡ ⁣ A ⠫⠞⠀⠠⠁ triangle A A B C △ ⁡ A ⁣ B ⁣ C ⠫⠞⠀⠠⠁⠠⠃⠠⠉ triangle A B C ▽ ⠨⠫ triangle down A ▽ ⁡ ⁣ A ⠨⠫⠀⠠⠁ triangle down A A B C ▽ ⁡ A ⁣ B ⁣ C ⠨⠫⠀⠠⠁⠠⠃⠠⠉ triangle down A B C ⬠ ⠫⠢ pentagon A ⬠ ⁡ ⁣ A ⠫⠢⠀⠠⠁ pentagon A A B C ⬠ ⁡ A ⁣ B ⁣ C ⠫⠢⠀⠠⠁⠠⠃⠠⠉ pentagon A B C ⌂ ⠫⠏⠛ general pentagon A ⌂ ⁡ ⁣ A ⠫⠏⠛⠀⠠⠁ general pentagon A A B C ⌂ ⁡ A ⁣ B ⁣ C ⠫⠏⠛⠀⠠⠁⠠⠃⠠⠉ general pentagon A B C ⬡ ⠫⠖ hexagon A ⬡ ⁡ ⁣ A ⠫⠖⠀⠠⠁ hexagon A A B C ⬡ ⁡ A ⁣ B ⁣ C ⠫⠖⠀⠠⠁⠠⠃⠠⠉ hexagon A B C ⌬ ⠫⠓⠭ general hexagon A ⌬ ⁡ ⁣ A ⠫⠓⠭⠀⠠⠁ general hexagon A A B C ⌬ ⁡ A ⁣ B ⁣ C ⠫⠓⠭⠀⠠⠁⠠⠃⠠⠉ general hexagon A B C ⊡ ⠫⠲ square A ⊡ ⁡ ⁣ A ⠫⠲⠀⠠⠁ square A A B C D ⊡ ⁡ A ⁣ B ⁣ C ⁣ D ⠫⠲⠀⠠⠁⠠⠃⠠⠉⠠⠙ square A B C D ▭ ⠫⠗ rectangle A ▭ ⁡ ⁣ A ⠫⠗⠀⠠⠁ rectangle A A B C D ▭ ⁡ A ⁣ B ⁣ C ⁣ D ⠫⠗⠀⠠⠁⠠⠃⠠⠉⠠⠙ rectangle A B C D < > ⠫⠓ rhombus A < > ⁡ ⁣ A ⠫⠓⠀⠠⠁ rhombus A A B C D < > ⁡ A ⁣ B ⁣ C ⁣ D ⠫⠓⠀⠠⠁⠠⠃⠠⠉⠠⠙ rhombus A B C D ▱ ⠫⠛ parallelogram A ▱ ⁡ ⁣ A ⠫⠛⠀⠠⠁ parallelogram A A B C D ▱ ⁡ A ⁣ B ⁣ C ⁣ D ⠫⠛⠀⠠⠁⠠⠃⠠⠉⠠⠙ parallelogram A B C D ⋄ ⠫⠙ diamond A ⋄ ⁡ ⁣ A ⠫⠙⠀⠠⠁ diamond A A B C D ⋄ ⁡ A ⁣ B ⁣ C ⁣ D ⠫⠙⠀⠠⠁⠠⠃⠠⠉⠠⠙ diamond A B C D ⭐ ⠫⠎ star A ⭐ ⁡ ⁣ A ⠫⠎⠀⠠⠁ star A A B C D ⭐ ⁡ A ⁣ B ⁣ C ⁣ D ⠫⠎⠀⠠⠁⠠⠃⠠⠉⠠⠙ star A B C D tz ⠫⠵ trapezoid A tz ⁡ ⁣ A ⠫⠵⠀⠠⠁ trapezoid A A B C D tz ⁡ A ⁣ B ⁣ C ⁣ D ⠫⠵⠀⠠⠁⠠⠃⠠⠉⠠⠙ trapezoid A B C D qd ⠫⠟ quadrilateral A qd ⁡ ⁣ A ⠫⠟⠀⠠⠁ quadrilateral A A B C D qd ⁡ A ⁣ B ⁣ C ⁣ D ⠫⠟⠀⠠⠁⠠⠃⠠⠉⠠⠙ quadrilateral A B C D ¯ ⠱ segment A ⁣ A ¯ ⠐⠠⠁⠣⠱⠻ segment A A B A ⁣ B ¯ ⠐⠠⠁⠠⠃⠣⠱⠻ segment A B ↔ ⠫⠪⠒⠒⠕ line A ⁣ A ↔ ⠐⠠⠁⠣⠫⠪⠒⠒⠕⠻ line A A B A ⁣ B ↔ ⠐⠠⠁⠠⠃⠣⠫⠪⠒⠒⠕⠻ line A B → ⠫⠕ ray A ⁣ A → ⠐⠠⠁⠣⠫⠕⠻ ray A A B A ⁣ B → ⠐⠠⠁⠠⠃⠣⠫⠕⠻ ray A B ⏜ ⠫⠁ arc A ⁣ A ⏜ ⠐⠠⠁⠣⠫⠁⠻ arc A A B A ⁣ B ⏜ ⠐⠠⠁⠠⠃⠣⠫⠁⠻ arc A B ⏝ ⠫⠄ arc down A ⁣ A ⏝ ⠐⠠⠁⠩⠫⠄⠻ arc down A A B A ⁣ B ⏝ ⠐⠠⠁⠠⠃⠩⠫⠄⠻ arc down A B ∥ ⠫⠇ parallel A B A ∥ B ⠠⠁⠀⠫⠇⠀⠠⠃ A parallel B ∦ ⠌⠫⠇ not parallel A B A ∦ B ⠠⠁⠀⠌⠫⠇⠀⠠⠃ A not parallel B ⊥ ⠫⠏ perpendicular A B A ⊥ B ⠠⠁⠀⠫⠏⠀⠠⠃ A perpendicular B ⊥̸ ⠌⠫⠏ not perpendicular A B A ⊥̸ B ⠠⠁⠀⠌⠫⠏⠀⠠⠃ A not perpendicular B × ⠫⠊ intersecting A B A × B ⠠⠁⠀⠫⠊⠀⠠⠃ A intersecting B ∠ ⠫⠪ angle A ∠ ⁡ ⁣ A ⠫⠪⠀⠠⠁ angle A A B C ∠ ⁡ A ⁣ B ⁣ C ⠫⠪⠀⠠⠁⠠⠃⠠⠉ angle A B C ∟ ⠫⠪⠨⠗⠻ right angle A ∟ ⁡ ⁣ A ⠫⠪⠨⠗⠻⠀⠠⠁ right angle A A B C ∟ ⁡ A ⁣ B ⁣ C ⠫⠪⠨⠗⠻⠀⠠⠁⠠⠃⠠⠉ right angle A B C ∡ ⠫⠪⠸⠫⠫⠁⠻ measured angle A ∡ ⁡ ⁣ A ⠫⠪⠸⠫⠫⠁⠻⠀⠠⠁ measured angle A A B C ∡ ⁡ A ⁣ B ⁣ C ⠫⠪⠸⠫⠫⠁⠻⠀⠠⠁⠠⠃⠠⠉ measured angle A B C ∢ ⠫⠐⠅⠸⠫⠫⠁⠻ spherical angle A ∢ ⁡ ⁣ A ⠫⠐⠅⠸⠫⠫⠁⠻⠀⠠⠁ spherical angle A A B C ∢ ⁡ A ⁣ B ⁣ C ⠫⠐⠅⠸⠫⠫⠁⠻⠀⠠⠁⠠⠃⠠⠉ spherical angle A B C m ⠍ angle measure A m ∠ ⁡ ⁣ A ⠍⠫⠪⠀⠠⠁ angle measure angle A A B C m ∠ ⁡ A ⁣ B ⁣ C ⠍⠫⠪⠀⠠⠁⠠⠃⠠⠉ angle measure angle A B C ← ⠫⠪⠒⠒ left arrow A B A ← B ⠠⠁⠀⠫⠪⠒⠒⠀⠠⠃ A left arrow B → ⠫⠕ right arrow A B A → B ⠠⠁⠀⠫⠕⠀⠠⠃ A right arrow B ↓ ⠫⠩⠒⠒⠕ down arrow A B A ↓ B ⠠⠁⠀⠫⠩⠒⠒⠕⠀⠠⠃ A down arrow B ↑ ⠫⠣⠒⠒⠕ up arrow A B A ↑ B ⠠⠁⠀⠫⠣⠒⠒⠕⠀⠠⠃ A up arrow B ⊕ ⠫⠉⠸⠫⠬⠻ circled plus A B A ⊕ B ⠠⠁⠫⠉⠸⠫⠬⠻⠠⠃ A circled plus B ⊖ ⠫⠉⠸⠫⠤⠻ circled minus A B A ⊖ B ⠠⠁⠫⠉⠸⠫⠤⠻⠠⠃ A circled minus B ⊗ ⠫⠉⠸⠫⠈⠡⠻ circled times A B A ⊗ B ⠠⠁⠫⠉⠸⠫⠈⠡⠻⠠⠃ A circled times B ⊘ ⠫⠉⠸⠫⠸⠌⠻ circled slash A B A ⊘ B ⠠⠁⠫⠉⠸⠫⠸⠌⠻⠠⠃ A circled slash B ⊙ ⠫⠉⠸⠫⠡⠻ circled dot A B A ⊙ B ⠠⠁⠫⠉⠸⠫⠡⠻⠠⠃ A circled dot B ⊚ ⠫⠉⠸⠫⠨⠡⠻ circled ring A B A ⊚ B ⠠⠁⠫⠉⠸⠫⠨⠡⠻⠠⠃ A circled ring B ⊛ ⠫⠉⠸⠫⠈⠼⠻ circled star A B A ⊛ B ⠠⠁⠫⠉⠸⠫⠈⠼⠻⠠⠃ A circled star B ⊜ ⠫⠉⠸⠫⠨⠅⠻ circled equals A B A ⊜ B ⠠⠁⠫⠉⠸⠫⠨⠅⠻⠠⠃ A circled equals B ←⃝ ⠫⠉⠸⠫⠫⠪⠒⠒⠻ circled left arrow A B A ←⃝ B ⠠⠁⠫⠉⠸⠫⠫⠪⠒⠒⠻⠠⠃ A circled left arrow B →⃝ ⠫⠉⠸⠫⠫⠒⠒⠕⠻ circled right arrow A B A →⃝ B ⠠⠁⠫⠉⠸⠫⠫⠒⠒⠕⠻⠠⠃ A circled right arrow B ↓⃝ ⠫⠉⠸⠫⠫⠩⠒⠒⠕⠻ circled down arrow A B A ↓⃝ B ⠠⠁⠫⠉⠸⠫⠫⠩⠒⠒⠕⠻⠠⠃ A circled down arrow B ↑⃝ ⠫⠉⠸⠫⠫⠣⠒⠒⠕⠻ circled up arrow A B A ↑⃝ B ⠠⠁⠫⠉⠸⠫⠫⠣⠒⠒⠕⠻⠠⠃ A circled up arrow B ⇆⃝ ⠫⠉⠸⠫⠫⠪⠒⠒⠫⠒⠒⠕⠻ circled left right arrow A B A ⇆⃝ B ⠠⠁⠫⠉⠸⠫⠫⠪⠒⠒⠫⠒⠒⠕⠻⠠⠃ A circled left right arrow B ⇄⃝ ⠫⠉⠸⠫⠫⠒⠒⠕⠫⠪⠒⠒⠻ circled right left arrow A B A ⇄⃝ B ⠠⠁⠫⠉⠸⠫⠫⠒⠒⠕⠫⠪⠒⠒⠻⠠⠃ A circled right left arrow B ⇵⃝ ⠫⠉⠸⠫⠫⠩⠒⠒⠕⠐⠫⠣⠒⠒⠕⠻ circled down up arrow A B A ⇵⃝ B ⠠⠁⠫⠉⠸⠫⠫⠩⠒⠒⠕⠐⠫⠣⠒⠒⠕⠻⠠⠃ A circled down up arrow B ⇅⃝ ⠫⠉⠸⠫⠫⠣⠒⠒⠕⠐⠫⠩⠒⠒⠕⠻ circled up down arrow A B A ⇅⃝ B ⠠⠁⠫⠉⠸⠫⠫⠣⠒⠒⠕⠐⠫⠩⠒⠒⠕⠻⠠⠃ A circled up down arrow B ⊞ ⠫⠲⠸⠫⠱⠈⠳⠻ squared plus A B A ⊞ B ⠠⠁⠫⠲⠸⠫⠱⠈⠳⠻⠠⠃ A squared plus B ⊟ ⠫⠲⠸⠫⠱⠻ squared minus A B A ⊟ B ⠠⠁⠫⠲⠸⠫⠱⠻⠠⠃ A squared minus B ⊠ ⠫⠲⠸⠫⠢⠈⠔⠻ squared times A B A ⊠ B ⠠⠁⠫⠲⠸⠫⠢⠈⠔⠻⠠⠃ A squared times B ⊡ ⠫⠲⠸⠫⠡⠻ squared dot A B A ⊡ B ⠠⠁⠫⠲⠸⠫⠡⠻⠠⠃ A squared dot B ⧅ ⠫⠲⠸⠫⠢⠻ squared back slash A B A ⧅ B ⠠⠁⠫⠲⠸⠫⠢⠻⠠⠃ A squared back slash B ⧄ ⠫⠲⠸⠫⠔⠻ squared slash A B A ⧄ B ⠠⠁⠫⠲⠸⠫⠔⠻⠠⠃ A squared slash B ⌷ ⌷ ⠫⠲⠸⠫⠳⠻ squared vertical bar A B A ⌷ ⌷ B ⠠⠁⠫⠲⠸⠫⠳⠻⠠⠃ A squared vertical bar B ⌸ ⠫⠲⠸⠫⠨⠅⠻ squared equals A B A ⌸ B ⠠⠁⠫⠲⠸⠫⠨⠅⠻⠠⠃ A squared equals B ⍇ ⠫⠲⠸⠫⠪⠒⠒⠻ squared left arrow A B A ⍇ B ⠠⠁⠫⠲⠸⠫⠪⠒⠒⠻⠠⠃ A squared left arrow B ⍈ ⠫⠲⠸⠫⠒⠒⠕⠻ squared right arrow A B A ⍈ B ⠠⠁⠫⠲⠸⠫⠒⠒⠕⠻⠠⠃ A squared right arrow B ⍗ ⠫⠲⠸⠫⠩⠒⠒⠕⠻ squared down arrow A B A ⍗ B ⠠⠁⠫⠲⠸⠫⠩⠒⠒⠕⠻⠠⠃ A squared down arrow B ⍐ ⠫⠲⠸⠫⠣⠒⠒⠕⠻ squared up arrow A B A ⍐ B ⠠⠁⠫⠲⠸⠫⠣⠒⠒⠕⠻⠠⠃ A squared up arrow B ▭ ⠫⠗ rectangle ⊙ ⠫⠉ circle ⊡ ⠫⠲ square ⬡ ⠫⠖ hexagon ∠ ⠫⠪ angle → ⠫⠕ right arrow x x □ ⠭⠘⠫⠲ x super square A B C D E F ∠ ⁡ A ⁣ B ⁣ C = ∠ ⁡ D ⁣ E ⁣ F ⠫⠪⠀⠠⠁⠠⠃⠠⠉⠀⠨⠅⠀⠫⠪⠀⠠⠙⠠⠑⠠⠋ angle A B C equals angle D E F ⊕ ⠫⠉⠸⠫⠬⠻ circled plus ⇵⃝ ⠫⠉⠸⠫⠫⠩⠒⠒⠕⠐⠫⠣⠒⠒⠕⠻ circled down up arrow ⇄⃝ ⠫⠉⠸⠫⠫⠒⠒⠕⠫⠪⠒⠒⠻ circled left right arrow 1 ∠ ⁡ ⁣ 1 ⠫⠪⠀⠼⠂ angle one A B C △ ⁡ A ⁣ B ⁣ C ⠫⠞⠀⠠⠁⠠⠃⠠⠉ triangle A B C R ⊙ ⁡ ⁣ R ⠫⠉⠀⠠⠗ circle R A 90 ∠ ⁡ ⁣ A = 90 ⁢ ° ⠫⠪⠀⠠⠁⠀⠨⠅⠀⠼⠔⠴⠘⠨⠡ angle A equals ninety degrees A ∟ ⁡ ⁣ A ⠫⠪⠨⠗⠻⠀⠠⠁ right angle A A B C ∡ ⁡ A ⁣ B ⁣ C ⠫⠪⠸⠫⠫⠁⠻⠀⠠⠁⠠⠃⠠⠉ measured angle A B C x y ∠ ⁡ ⁣ x + ∠ ⁡ ⁣ y ⠫⠪⠀⠭⠬⠫⠪⠀⠽ angle x plus angle y 1 2 3 ∠ ⁡ ⁣ 1 + 2 ⁢ ∠ ⁡ ⁣ 3 ⠫⠪⠀⠼⠂⠬⠆⠫⠪⠀⠼⠒ angle one plus two angle three A B C E F G △ ⁡ A ⁣ B ⁣ C △ ⁡ E ⁣ F ⁣ G ⠹⠫⠞⠀⠠⠁⠠⠃⠠⠉⠌⠫⠞⠀⠠⠑⠠⠋⠠⠛⠼ fraction triangle A B C over triangle D E F end fraction A B C m ∠ ⁡ A ⁣ B ⁣ C ⠍⠫⠪⠀⠠⠁⠠⠃⠠⠉ angle measure angle A B C 90 120 ∠ ⁡ ⁣ 90 ⁢ ° + ∠ ⁡ ⁣ 120 ⁢ ° ⠫⠪⠀⠼⠔⠴⠘⠨⠡⠐⠬⠫⠪⠀⠼⠂⠆⠴⠘⠨⠡ angle ninety degrees plus angle one twenty degrees □ ⁢ % ⠫⠲⠈⠴ square percent $ ⁢ △ ⠈⠎⠫⠞ dollar triangle 6 4 12 6 3 6 ⁤ 4 12 = 6 ⁤ △ 3 ⠼⠖⠸⠹⠲⠌⠂⠆⠸⠼⠀⠨⠅⠀⠼⠖⠸⠹⠫⠞⠌⠒⠸⠼ six and four twelfths equals six and triangle thirds 1 day 24 1 ⁢ ⁢ day = 24 ⁢ ⁢ ⋄ ⠼⠂⠀⠙⠁⠽⠀⠨⠅⠀⠼⠆⠲⠀⠫⠙ one day equals twenty four diamond x y y x x ⁢ ⊡ ⁢ y = y ⁢ ⊡ ⁢ x ⠭⠫⠲⠽⠀⠨⠅⠀⠽⠫⠲⠭ x square y equals y square x 2 4 7 2 + 4 ⁢ ⁢ △ ⁢ ⁢ 7 ⠼⠆⠬⠲⠀⠫⠞⠀⠼⠶ two plus four triangle seven 2 3 2 + 3 = ▽ ⠼⠆⠬⠒⠀⠨⠅⠀⠨⠫ two plus three equals triangle down f g f → g ⠋⠀⠫⠕⠀⠛ f right arrow g x x → ∞ ⠭⠀⠫⠕⠀⠠⠿ x right arrow infinity A B C D A ⁢ B ⊥ C ⁢ D ⠠⠁⠠⠃⠀⠫⠏⠀⠠⠉⠠⠙ A B perpendicular C D A B C D A ⁢ B ∦ C ⁢ D ⠠⠁⠠⠃⠀⠌⠫⠇⠀⠠⠉⠠⠙ A B not parallel C D x y x ⊕ y ⠭⠫⠉⠸⠫⠬⠻⠽ x circle plus y x y x ⊞ y ⠭⠫⠲⠸⠫⠱⠈⠳⠻⠽ x square plus y A B A ⁣ B → ⠐⠠⠁⠠⠃⠣⠫⠕⠻ ray A B 1101 1000 1101 ⋄ + 1000 ⋄ ⠼⠂⠂⠴⠂⠰⠫⠙⠐⠬⠂⠴⠴⠴⠰⠫⠙ one one zero one sub diamond plus one zero zero zero sub diamond x sin ⁡ x ⠎⠊⠝⠀⠭ sine x x cos ⁡ x ⠉⠕⠎⠀⠭ cosine x x tan ⁡ x ⠞⠁⠝⠀⠭ tangent x x sec ⁡ x ⠎⠑⠉⠀⠭ secant x x csc ⁡ x ⠉⠎⠉⠀⠭ cosecant x x cot ⁡ x ⠉⠕⠞⠀⠭ cotangent x x sin − 1 ⁡ x ⠁⠗⠉⠎⠊⠝⠀⠭ inverse sine x x cos − 1 ⁡ x ⠁⠗⠉⠉⠕⠎⠀⠭ inverse cosine x x tan − 1 ⁡ x ⠁⠗⠉⠞⠁⠝⠀⠭ inverse tangent x x sec − 1 ⁡ x ⠁⠗⠉⠎⠑⠉⠀⠭ inverse secant x x csc − 1 ⁡ x ⠁⠗⠉⠉⠎⠉⠀⠭ inverse cosecant x x cot − 1 ⁡ x ⠁⠗⠉⠉⠕⠞⠀⠭ inverse cotangent x x sinh ⁡ x ⠎⠊⠝⠓⠀⠭ hyperbolic sine x x cosh ⁡ x ⠉⠕⠎⠓⠀⠭ hyperbolic cosine x x tanh ⁡ x ⠞⠁⠝⠓⠀⠭ hyperbolic tangent x x sech ⁡ x ⠎⠑⠉⠓⠀⠭ hyperbolic secant x x csch ⁡ x ⠉⠎⠉⠓⠀⠭ hyperbolic cosecant x x coth ⁡ x ⠉⠕⠞⠓⠀⠭ hyperbolic cotangent x x sinh − 1 ⁡ x ⠁⠗⠉⠎⠊⠝⠓⠀⠭ inverse hyperbolic sine x x cosh − 1 ⁡ x ⠁⠗⠉⠉⠕⠎⠓⠀⠭ inverse hyperbolic cosine x x tanh − 1 ⁡ x ⠁⠗⠉⠞⠁⠝⠓⠀⠭ inverse hyperbolic tangent x x sech − 1 ⁡ x ⠁⠗⠉⠎⠑⠉⠓⠀⠭ inverse hyperbolic secant x x csch − 1 ⁡ x ⠁⠗⠉⠉⠎⠉⠓⠀⠭ inverse hyperbolic cosecant x x coth − 1 ⁡ x ⠁⠗⠉⠉⠕⠞⠓⠀⠭ inverse hyperbolic cotangent x x e x ⠑⠭⠏⠀⠭ exponential x x ln ⁡ x ⠇⠝⠀⠭ natural logarithm x x log ⁡ x ⠇⠕⠛⠀⠭ common logarithm x 2 x log 2 ⁡ x ⠇⠕⠛⠆⠀⠭ logarithm base two of x x arg ⁡ x ⠁⠗⠛⠀⠭ argument x x ℜ ⁡ x ⠗⠑⠀⠭ real part x x ℑ ⁡ x ⠊⠍⠀⠭ imaginary part x x max ⁡ x ⠍⠁⠭⠀⠭ maximum x x min ⁡ x ⠍⠊⠝⠀⠭ minimum x x sin ⁡ x ⠎⠊⠝⠀⠭ sine x x 2 cos 2 ⁡ x ⠉⠕⠎⠘⠆⠀⠭ cosine squared x x e sin ⁡ x ⠑⠭⠏⠀⠎⠊⠝⠀⠭ exponential of sine of x e x e sin ⁡ x ⠑⠘⠎⠊⠝⠀⠭ e super sine x A O B A ⁣ O ⁣ B ⏜ ⠐⠠⠁⠠⠕⠠⠃⠣⠫⠁⠻ arc A O B a x log a ⁡ x ⠇⠕⠛⠰⠁⠀⠭ log base a of x x sin − 1 ⁡ x ⠁⠗⠉⠎⠊⠝⠀⠭ inverse sine x x y sin ⁡ x + y ⠎⠊⠝⠀⠭⠬⠽ sine x plus y 3 sin ⁡ π ⁢ ⁄ ⁢ 3 ⠎⠊⠝⠀⠨⠏⠸⠌⠒ sine pi over three 3 sin ⁡ π ⁄ 3 ⠎⠊⠝⠀⠹⠨⠏⠸⠌⠒⠼ sine fraction pi slash three end fraction 30 45 30 45 sin ⁡ 30 ⁢ ° ⁢ cos ⁡ 45 ⁢ ° + cos ⁡ 30 ⁢ ° ⁢ sin ⁡ 45 ⁢ ° ⠎⠊⠝⠀⠼⠒⠴⠘⠨⠡⠐⠉⠕⠎⠀⠼⠲⠢⠘⠨⠡⠐⠬⠉⠕⠎⠀⠼⠒⠴⠘⠨⠡⠐⠎⠊⠝⠀⠼⠲⠢⠘⠨⠡ sine thirty degrees cosine forty five degrees plus cosine thirty degrees sine forty five degrees 2 x 3 y 2 ⁢ sin ⁡ x + 3 ⁢ cos ⁡ y ⠼⠆⠎⠊⠝⠀⠭⠬⠒⠉⠕⠎⠀⠽ two sine x plus 3 cosine y a y sin ⁡ a ⁢ cos ⁡ y ⠎⠊⠝⠀⠁⠉⠕⠎⠀⠽ sine a cosine y 1 x 1 − cos ⁡ x ⠜⠂⠤⠉⠕⠎⠀⠭⠻ root one minus cosine x end root 1 x x x x 1 cos ⁡ x − cos ⁡ x = tan ⁡ x ⋅ sin ⁡ x ⠹⠂⠌⠉⠕⠎⠀⠭⠼⠤⠉⠕⠎⠀⠭⠀⠨⠅⠀⠞⠁⠝⠀⠭⠡⠎⠊⠝⠀⠭ fraction one over cosine x end fraction minus cosine x equals tangent x dotted times sine x 1 x x x x 1 ⁄ cos ⁡ x − cos ⁡ x = tan ⁡ x ⋅ sin ⁡ x ⠹⠂⠸⠌⠉⠕⠎⠀⠭⠼⠤⠉⠕⠎⠀⠭⠀⠨⠅⠀⠞⠁⠝⠀⠭⠡⠎⠊⠝⠀⠭ fraction one slash cosine x end fraction minus cosine x equals tangent x dotted times sine x x ( x ) ⠷⠭⠾ open parenthesis x close parenthesis x [ x ] ⠈⠷⠭⠈⠾ open bracket x close bracket x { x } ⠨⠷⠭⠨⠾ open brace x close brace x ⦅ x ⦆ ⠸⠷⠭⠸⠾ open barred parenthesis x close barred parenthesis x ⟦ x ⟧ ⠈⠸⠷⠭⠈⠸⠾ open barred bracket x close barred bracket x ⦃ x ⦄ ⠨⠸⠷⠭⠨⠸⠾ open barred brace x close barred brace x | x | ⠳⠭⠳ absolute value of x x ∥ x ∥ ⠳⠳⠭⠳⠳ norm of x x y ( x , y ) ⠷⠭⠠⠀⠽⠾ open parenthesis x comma y close parenthesis x y [ x , y ] ⠈⠷⠭⠠⠀⠽⠈⠾ open bracket x comma y close bracket x y ( x , y ] ⠷⠭⠠⠀⠽⠈⠾ open parenthesis x comma y close bracket x y [ x , y ) ⠈⠷⠭⠠⠀⠽⠾ open bracket x comma y close parenthesis x ⌈ x ⌉ ⠈⠘⠷⠭⠈⠘⠾ open ceiling x close ceiling x ⌊ x ⌋ ⠈⠰⠷⠭⠈⠰⠾ open floor x close floor x ⟨ x ⟩ ⠨⠨⠷⠭⠨⠨⠾ open angle bracket x close angle bracket seven 2 1 ( ⁢ seven ) 2 + 1 ⠷⠎⠑⠧⠑⠝⠾⠘⠆⠐⠬⠂ open parenthesis seven close parenthesis squared plus one rate time distance ( ⁢ rate ) × ( ⁢ time ) = ( ⁢ distance ) ⠷⠗⠁⠞⠑⠾⠈⠡⠷⠞⠊⠍⠑⠾⠀⠨⠅⠀⠷⠙⠊⠎⠞⠁⠝⠉⠑⠾ open parenthesis rate close parenthesis times open parenthesis time close parenthesis equals open parenthesis distance close parenthesis x y x y ( x + y ) ⁢ ( x − y ) ⠷⠭⠬⠽⠾⠷⠭⠤⠽⠾ open parenthesis x plus y close parenthesis open parenthesis x minus y 3.5 3 ⌊ 3.5 ⌋ = 3 ⠈⠰⠷⠒⠨⠢⠈⠰⠾⠀⠨⠅⠀⠼⠒ open floor three point five close floor equals three 3.5 4 ⌈ 3.5 ⌉ = 4 ⠈⠘⠷⠒⠨⠢⠈⠘⠾⠀⠨⠅⠀⠼⠲ open ceiling three point five close ceiling equals four f ∥ f ∥ ⠳⠳⠋⠳⠳ norm of f x | x | ⠳⠭⠳ absolute value of x x y u v 2 ( x + y u + v ) 2 ⠷⠹⠭⠬⠽⠌⠥⠬⠧⠼⠾⠘⠆ open parenthesis begin fraction x plus y over u plus v close fraction close parenthesis squared x x ⠜⠨⠜⠭⠨⠻⠻ root root x end root end root x y x + y ⠭⠬⠽ x plus y x y x ± y ⠭⠬⠤⠽ x plus or minus y x y x +- y ⠭⠬⠐⠤⠽ x plus then minus y x + x ⠘⠬⠐⠭ positive x x y x − y ⠭⠤⠽ x minus y x y x ∓ y ⠭⠤⠬⠽ x minus or plus y x y x -+ y ⠭⠤⠐⠬⠽ x minus plus y x − x ⠘⠤⠐⠭ negative x x y x ⋅ y ⠭⠡⠽ x dotted times y x y x × y ⠭⠈⠡⠽ x times sign y x y x ∗ y ⠭⠈⠼⠽ x times asterisk y x y x ÷ y ⠹⠭⠨⠌⠽⠼ x divide sign y x y x ⁄ y ⠹⠭⠸⠌⠽⠼ fraction x slash y end fraction x y x ⁢ ⁄ ⁢ y ⠭⠸⠌⠽ x slash y x y x ∸ y ⠭⠨⠤⠽ x dot minus y @ ⠈⠁ at # ⠨⠼ hash $ ⠈⠎ dollar % ⠈⠴ percent ‰ ⠈⠴⠴ per mille ‱ ⠈⠴⠴⠴ per myriad \ ⠸⠡ back slash & ⠸⠯ ampsersand ¢ ⠈⠉ cent sign ° ⠘⠨⠡ degrees ¶ ⠈⠠⠏ paragraph sign

§ ⠈⠠⠎ section sign † ⠸⠻ dagger ‡ ⠸⠸⠻ double dagger x y x ∣ y ⠭⠳⠽ x divides y x y x ∤ y ⠭⠌⠳⠽ x not divides y x y x ∧ y ⠭⠈⠩⠽ x and y x y x ∨ y ⠭⠈⠬⠽ x or y x y x ⊕ y ⠭⠫⠉⠸⠫⠬⠻⠽ x exclusive or y x ∼ x ⠈⠱⠭ not x x y x ∩ y ⠭⠨⠩⠽ x intersect y x y x ∪ y ⠭⠨⠬⠽ x union y x y x ⊕ y ⠭⠫⠉⠸⠫⠬⠻⠽ x circle plus y x y x ⊖ y ⠭⠫⠉⠸⠫⠤⠻⠽ x circle minus y x y x ⊗ y ⠭⠫⠉⠸⠫⠈⠡⠻⠽ x circle times y x y x ⊘ y ⠭⠫⠉⠸⠫⠸⠌⠻⠽ x circle slash y x y x ⊙ y ⠭⠫⠉⠸⠫⠡⠻⠽ x circle dot y x y x ⨸ y ⠭⠫⠉⠸⠫⠨⠌⠻⠽ x circle divide y ∅ ⠸⠴ empty set A T T A ⁢ T ⁢ & ⁢ T ⠠⠁⠠⠞⠸⠯⠠⠞ A T ampersand T & ⠸⠯ ampersand A B A ⁢ & ⁢ B ⠠⠁⠸⠯⠠⠃ A ampersand B f g f ∗ g ⠋⠈⠼⠛ f asterisk g 3 4 3 ∗ 4 ⠼⠒⠈⠼⠼⠲ three asterisk four x x ∗ ⠭⠘⠈⠼ x super asterisk x y x ⁢ # ⁢ y ⠭⠨⠼⠽ x hash sign y 2 3 2 ⁢ # ⁢ 3 ⠼⠆⠨⠼⠼⠒ 2 hash sign 3 R R # ⠠⠗⠘⠨⠼ R super hash sign A B A ⁢ ¶ ⁢ B ⠠⠁⠈⠠⠏⠠⠃ A paragraph symbol B A

B A ⁢ § ⁢ B ⠠⠁⠈⠠⠎⠠⠃ A section symbol B A B A ⁢ ⭐ ⁢ B ⠠⠁⠫⠎⠠⠃ A star B A B A ∩ B ⠠⠁⠨⠩⠠⠃ A intersect B A B A ∪ B ⠠⠁⠨⠬⠠⠃ A union B x y x ∧ y ⠭⠈⠩⠽ x and y x y x ∨ y ⠭⠈⠬⠽ x or y 2 3 + 2 -+ 3 ⠬⠆⠤⠐⠬⠒ plus two minus plus three 3 5 − 3 +- 5 ⠤⠼⠒⠬⠐⠤⠢ minus three plus then minus 5 x y x ∓ y ⠭⠤⠬⠽ x minus or plus y x y x ± y ⠭⠬⠤⠽ x plus or minus y 3 10 3 × 10 ⠼⠒⠈⠡⠂⠴ three times sign ten x y x ⋅ y ⠭⠡⠽ x dotted times y and or and ⁢ ⁄ ⁢ or ⠁⠝⠙⠸⠌⠕⠗ and slash or rise run rise ⁢ ⁄ ⁢ run ⠗⠊⠎⠑⠸⠌⠗⠥⠝ rise slash run 1 watt 1 joule sec 1 ⁢ ⁢ watt = 1 ⁢ ⁢ joule ⁢ ⁄ ⁢ sec ⠼⠂⠀⠺⠁⠞⠞⠀⠨⠅⠀⠼⠂⠀⠚⠕⠥⠇⠑⠸⠌⠎⠑⠉ one watt equals one joule slash second c o c ⁢ ⁄ ⁢ o ⠉⠸⠌⠕ c slash o volt amp volt ⁢ ⁄ ⁢ amp ⠧⠕⠇⠞⠸⠌⠁⠍⠏ volt slash amp 60 mi hr 60 ⁢ ⁢ mi ⁢ ⁄ ⁢ hr ⠼⠖⠴⠀⠍⠊⠸⠌⠓⠗ sixty miles slash hour 7 4 76 7 ⁢ ⁄ ⁢ 4 ⁢ ⁄ ⁢ 76 ⠼⠶⠸⠌⠲⠸⠌⠶⠖ seven slash four slash seven six p ∼ p ⠈⠱⠏ not p p q r ∼ p ∨ ∼ q ∨ ∼ r ⠈⠱⠏⠈⠬⠈⠱⠟⠈⠬⠈⠱⠗ not p or not q or not r T R ∼ ∼ T ∨ R ⠈⠱⠐⠈⠱⠠⠞⠈⠬⠠⠗ not not T or R x y x = − y ⠭⠀⠨⠅⠀⠤⠽ x equals minus y x sin ⁡ − x ⠎⠊⠝⠀⠤⠭ sine of minus x 1 2 n 1 + 2 + … + n ⠼⠂⠬⠆⠬⠀⠄⠄⠄⠀⠬⠝ one plus two plus ellipsis plus n 10 8 10 − ⁢ — = 8 ⠼⠂⠴⠤⠀⠤⠤⠤⠤⠀⠨⠅⠀⠼⠦ ten minus long dash equals eight 1 yd 2 yd 3 yd 1 ⁢ ⁢ yd + 2 ⁢ ⁢ yd = 3 ⁢ ⁢ yd ⠼⠂⠀⠽⠙⠬⠆⠀⠽⠙⠀⠨⠅⠀⠼⠒⠀⠽⠙ one yard plus two yard equals three yard a b a ⁢ \ ⁢ b ⠁⠸⠡⠃ a back slash b x y x ⊕ y ⠭⠫⠉⠸⠫⠬⠻⠽ x circle plus y 12 3 12 ÷ 3 ⠹⠂⠆⠨⠌⠒⠼ twelve divide sign three f g f ⁢ ° ⁢ g ⠋⠘⠨⠡⠐⠛ f degrees g f g f ∘ g ⠋⠨⠡⠛ f compose g x y sin ⁡ x − sin ⁡ y ⠎⠊⠝⠀⠭⠤⠎⠊⠝⠀⠽ sine x minus sine y x y x ⁢ □ ⁢ y ⠭⠫⠲⠽ x square y □ + △ ⠫⠲⠬⠫⠞ square plus triangle rate time ⁢ rate × ⁢ time ⠗⠁⠞⠑⠈⠡⠞⠊⠍⠑ rate times sign time miles hour miles ⁢ ⁄ ⁢ hour ⠍⠊⠇⠑⠎⠸⠌⠓⠕⠥⠗ miles slash hour quotient divisor remainder dividend ⁢ quotient × ⁢ divisor + ⁢ remainder = ⁢ dividend ⠟⠥⠕⠞⠊⠑⠝⠞⠈⠡⠙⠊⠧⠊⠎⠕⠗⠬⠗⠑⠍⠁⠊⠝⠙⠑⠗⠀⠨⠅⠀⠙⠊⠧⠊⠙⠑⠝⠙ quotient times sign divisor plus remainder equals dividend 3 seven 2 4 seven 1 5 seven 0 345 seven 3 × ⁢ seven 2 + 4 × seven 1 + 5 × seven 0 = 345 seven ⠼⠒⠈⠡⠎⠑⠧⠑⠝⠘⠆⠐⠬⠲⠈⠡⠎⠑⠧⠑⠝⠘⠂⠐⠬⠢⠈⠡⠎⠑⠧⠑⠝⠘⠴⠀⠨⠅⠀⠼⠒⠲⠢⠰⠎⠑⠧⠑⠝ three times sign seven super two plus four times seven super one plus five times seven super zero equals three four five sub seven 2 n 3 3 ( 2 ⁢ n + 3 ) ∣ 3 ⠷⠆⠝⠬⠒⠾⠳⠒ open parenthesis two n plus three close parenthesis divides three 3 ft 2 3 ft 2 6 ft 2 3 ⁢ ⁢ ft 2 + 3 ⁢ ⁢ ft 2 = 6 ⁢ ⁢ ft 2 ⠼⠒⠀⠋⠞⠘⠆⠐⠬⠒⠀⠋⠞⠘⠆⠀⠨⠅⠀⠼⠖⠀⠋⠞⠘⠆ three feet squared plus three feet squared equals six feet squared A A A ∪ ∅ = A ⠠⠁⠨⠬⠸⠴⠀⠨⠅⠀⠠⠁ A union empty set equals A even integers odd integers { even ⁢ integers } ∩ { odd ⁢ integers } = { } ⠨⠷⠑⠧⠑⠝⠊⠝⠞⠑⠛⠑⠗⠎⠨⠾⠨⠩⠨⠷⠕⠙⠙⠊⠝⠞⠑⠛⠑⠗⠎⠨⠾⠀⠨⠅⠀⠨⠷⠀⠨⠾ open brace even integers close brace intersect open brace odd integers close brace equals empty set x y x = y ⠭⠀⠨⠅⠀⠽ x equals y x y x ≠ y ⠭⠀⠌⠨⠅⠀⠽ x not equals y x y x < y ⠭⠀⠐⠅⠀⠽ x less than y x y x > y ⠭⠀⠨⠂⠀⠽ x greater than y x y x ≤ y ⠭⠀⠐⠅⠱⠀⠽ x less than or equal to y x y x ≥ y ⠭⠀⠨⠂⠱⠀⠽ x greater than or equal to y x y x ≡ y ⠭⠀⠸⠇⠀⠽ x equivalent to y x y x ≢ y ⠭⠀⠌⠸⠇⠀⠽ x not equivalent to y x y x ∼ y ⠭⠀⠈⠱⠀⠽ x similar to y x y x ≁ y ⠭⠀⠌⠈⠱⠀⠽ x not similar to y x y x ≃ y ⠭⠀⠈⠱⠱⠀⠽ x similar or equal to y x y x ≄ y ⠭⠀⠌⠈⠱⠱⠀⠽ x not similar or equal to y x y x ≈ y ⠭⠀⠈⠱⠈⠱⠀⠽ x approximately equal to y x y x ≉ y ⠭⠀⠌⠈⠱⠈⠱⠀⠽ x not approximately equal to y x y x ≅ y ⠭⠀⠈⠱⠨⠅⠀⠽ x congruent to y x y x ≇ y ⠭⠀⠌⠈⠱⠨⠅⠀⠽ x not congruent to y x y x ≺ y ⠭⠀⠨⠐⠅⠀⠽ x precedes y x y x ≻ y ⠭⠀⠨⠨⠂⠀⠽ x succeeds y x y x ⪯ y ⠭⠀⠨⠐⠅⠱⠀⠽ x precedes or equal to y x y x ⪰ y ⠭⠀⠨⠨⠂⠱⠀⠽ x succeeds or equal to y x y x ≪ y ⠭⠀⠐⠅⠈⠐⠅⠻⠀⠽ x much less than y x y x ≫ y ⠭⠀⠨⠂⠈⠨⠂⠻⠀⠽ x much greater than y x y x ≐ y ⠭⠀⠐⠨⠅⠣⠡⠻⠀⠽ x dot equals y x y x ≑ y ⠭⠀⠐⠨⠅⠩⠡⠣⠡⠻⠀⠽ x dot equal dot y x y x ∶ y ⠭⠀⠐⠂⠀⠽ x ratio y x y x ∷ y ⠭⠀⠰⠆⠀⠽ x proportion y x y x ∝ y ⠭⠀⠸⠿⠀⠽ x varies as y x y x ∈ y ⠭⠀⠈⠑⠀⠽ x in y x y x ∉ y ⠭⠀⠌⠈⠑⠀⠽ x not in y x y x ⊂ y ⠭⠀⠸⠐⠅⠀⠽ x proper subset y x y x ⊃ y ⠭⠀⠸⠨⠂⠀⠽ x proper superset y x y x ⊆ y ⠭⠀⠸⠐⠅⠱⠀⠽ x subset or equal to y x y x ⊇ y ⠭⠀⠸⠨⠂⠱⠀⠽ x superset or equal to y x y x ⊄ y ⠭⠀⠌⠸⠐⠅⠀⠽ x not proper subset of y x y x ⊅ y ⠭⠀⠌⠸⠨⠂⠀⠽ x not proper superset of y x y x ⊈ y ⠭⠀⠌⠸⠐⠅⠱⠀⠽ x not subset of y x y x ⊉ y ⠭⠀⠌⠸⠨⠂⠱⠀⠽ x not superset of y x y x ∥ y ⠭⠀⠫⠇⠀⠽ x parallel y x y x ∦ y ⠭⠀⠌⠫⠇⠀⠽ x not parallel y x y x ⊥ y ⠭⠀⠫⠏⠀⠽ x perpendicular y x y x ⊥̸ y ⠭⠀⠌⠫⠏⠀⠽ x not perpendicular y ≠ ⠌⠨⠅ not equals ∉ ⠌⠈⠑ not in ∦ ⠌⠫⠇ not parallel B A B ← A ⠠⠃⠀⠫⠪⠒⠒⠀⠠⠁ B left arrow A A B A → B ⠠⠁⠀⠫⠕⠀⠠⠃ A right arrow B A B A ↔ B ⠠⠁⠀⠫⠪⠒⠒⠕⠀⠠⠃ A horizontal arrow B f x 0 f ⁢ ( x ) ≡ 0 ⠋⠷⠭⠾⠀⠸⠇⠀⠼⠴ f open parenthesis x close parenthesis equivalent zero x A x ∈ A ⠭⠀⠈⠑⠀⠠⠁ x in A x y x ∼ y ⠭⠀⠈⠱⠀⠽ x similar to y x y x = y ⠭⠀⠨⠅⠀⠽ x equals y x y x > y ⠭⠀⠨⠂⠀⠽ x greater than y X Y X ⊂ Y ⠠⠭⠀⠸⠐⠅⠀⠠⠽ X proper subset of Y 1 2 3 6 1 ∶ 2 ∷ 3 ∶ 6 ⠼⠂⠀⠐⠂⠀⠼⠆⠀⠰⠆⠀⠼⠒⠀⠐⠂⠀⠼⠖ one ratio two proportion three ratio six a b b c d d a + b ∶ b ∷ c + d ∶ d ⠁⠬⠃⠀⠐⠂⠀⠃⠀⠰⠆⠀⠉⠬⠙⠀⠐⠂⠀⠙ a plus b ratio b proportion c plus d ratio d x y x ∝ y ⠭⠀⠸⠿⠀⠽ x varies as y → ⠫⠕ right arrow ← ⠫⠪⠒⠒ left arrow ↔ ⠫⠪⠒⠒⠕ horizontal arrow ↑ ⠫⠣⠒⠒⠕ up arrow ↓ ⠫⠩⠒⠒⠕ down arrow ↕ ⠫⠣⠪⠒⠒⠕ vertical arrow ↗ ⠫⠘⠒⠒⠕ north east arrow ↖ ⠫⠘⠪⠒⠒ north west arrow ↘ ⠫⠰⠒⠒⠕ south east arrow ↙ ⠫⠰⠪⠒⠒ south west arrow ⤡ ⠫⠘⠪⠒⠒⠕ north west south east arrow ⤢ ⠫⠰⠪⠒⠒⠕ north east south west arrow a b a ← b ⠁⠀⠫⠪⠒⠒⠀⠃ a left arrow b a b a → b ⠁⠀⠫⠕⠀⠃ a right arrow b a b a ↓ b ⠁⠀⠫⠩⠒⠒⠕⠀⠃ a down arrow b a b a ↑ b ⠁⠀⠫⠣⠒⠒⠕⠀⠃ a up arrow b a b a ↗ b ⠁⠀⠫⠘⠒⠒⠕⠀⠃ a north east arrow b a b a ↖ b ⠁⠀⠫⠘⠪⠒⠒⠀⠃ a north west arrow b a b a ↙ b ⠁⠀⠫⠰⠪⠒⠒⠀⠃ a south west arrow b a b a ↘ b ⠁⠀⠫⠰⠒⠒⠕⠀⠃ a south east arrow b a b a ↔ b ⠁⠀⠫⠪⠒⠒⠕⠀⠃ a horizontal arrow b a b a ↕ b ⠁⠀⠫⠣⠪⠒⠒⠕⠀⠃ a vertical arrow b a b a ⤢ b ⠁⠀⠫⠰⠪⠒⠒⠕⠀⠃ a north east south west arrow a b a ⤡ b ⠁⠀⠫⠘⠪⠒⠒⠕⠀⠃ a north west south east arrow b Å ⠈⠠⠁ angstrom * ⠈⠼ asterisk @ ⠈⠁ at sign ^ ⠸⠣ caret sign £ ⠈⠇ pound sign ✓ ⠈⠜ check mark đ ⠈⠫ d with slash ℏ ⠈⠓ h with slash ℞ ⠈⠠⠗ crossed R ƛ ⠈⠨⠇ lambda with slash ∅ ⠸⠴ emptyset { } ⠨⠷⠀⠨⠾ open brace close brace x x ! ⠭⠯ x factorial π ⠨⠏ pi i ⠊ imaginary i e ⠑ exponential e ∞ ⠠⠿ infinity 1 10,000 1 1 ⁢ ⁄ ⁢ 10,000 = 1 ⁢ Å ⠼⠂⠸⠌⠂⠴⠠⠴⠴⠴⠀⠨⠅⠀⠼⠂⠀⠈⠠⠁ one slash one zero comma thousand equals one angstrom 3 boxes 27 3 ⁢ ⁢ boxes ⁢ @ ⁢ 27 ⁢ ¢ ⠼⠒⠀⠃⠕⠭⠑⠎⠀⠈⠁⠀⠼⠆⠶⠈⠉ three boxes at sign twenty seven cents .35 73 .35 ⁢ ^ ⁢ 73 ⠼⠨⠒⠢⠸⠣⠶⠒ point three five caret seven three 10 10 ⁢ ¢ ⠼⠂⠴⠈⠉ ten cent x x ⁢ ¢ ⠭⠈⠉ x cent 2.98 $ ⁢ 2.98 ⠈⠎⠆⠨⠔⠦ dollar two point nine eight x $ ⁢ x ⠈⠎⠭ dollar x 7 7 ⁢ % ⠼⠶⠈⠴ seven percent x x ⁢ % ⠭⠈⠴ x percent 5 £ ⁢ 5 ⠈⠇⠢ pound five x £ ⁢ x ⠈⠇⠭ pound x milk ✓ ⁢ milk ⠈⠜⠀⠍⠊⠇⠅ check milk eggs ( ✓ ) ⁢ eggs ⠷⠈⠜⠾⠀⠑⠛⠛⠎ open parenthesis check mark close parenthesis eggs bread ✓ ⁢ ✓ ⁢ bread ⠈⠜⠈⠜⠀⠃⠗⠑⠁⠙ check check bread P 1 P 2 P 3 P 4 ℞ ⁢ ( P 1 ⁢ P 2 , P 3 ⁢ P 4 ) ⠈⠠⠗⠷⠠⠏⠂⠠⠏⠆⠠⠀⠠⠏⠒⠠⠏⠲⠾ crossed R open parenthesis P one P two comma P three P four close parenthesis 90 90 180 90 ⁢ ° + 90 ⁢ ° = 180 ⁢ ° ⠼⠔⠴⠘⠨⠡⠐⠬⠔⠴⠘⠨⠡⠀⠨⠅⠀⠼⠂⠦⠴⠘⠨⠡ ninety degrees plus ninety degrees equals one eighty degrees n n ! ⠝⠯ n factorial n k ( n − k ) ! ⠷⠝⠤⠅⠾⠯ open parenthesis n minus k close parenthesis factorial x x ′ ⠭⠄ x prime x x ″ ⠭⠄⠄ x prime prime x x ‴ ⠭⠄⠄⠄ x prime prime prime x 2 x ′ 2 ⠭⠄⠘⠆ x prime squared x i x ′ i ⠭⠄⠰⠊ x prime sub i x 1 x ′ 1 ⠭⠄⠂ x prime sub one u v u v ( u + v ) ′ = u ′ + v ′ ⠷⠥⠬⠧⠾⠄⠀⠨⠅⠀⠥⠄⠬⠧⠄ open parenthesis u plus v close parenthesis prime equals u prime plus v prime x x ‾ ′ ⠭⠱⠄ x over bar prime 5 8 5 ′ ⁢ 8 ″ ⠼⠢⠄⠦⠄⠄ five prime eight prime prime 20 30 10 20 ⁢ ° ⁢ 30 ′ ⁢ 10 ″ ⠼⠆⠴⠘⠨⠡⠐⠒⠴⠄⠂⠴⠄⠄ twenty degrees thirty prime ten prime prime A B A C ∵ ⁢ A ⁢ B = A ⁢ C ⠈⠌⠀⠠⠁⠠⠃⠀⠨⠅⠀⠠⠁⠠⠉ because A B equals A C A B A C ∴ ⁢ A ⁢ B = A ⁢ C ⠠⠡⠀⠠⠁⠠⠃⠀⠨⠅⠀⠠⠁⠠⠉ therefore A B equals A C ς ⠨⠈⠎ greek lower case sigma symbol ϙ ⠨⠟ greek lower case qoph ϛ ⠨⠮ greek lower case stigma ϝ ⠨⠧ greek lower case digamma ϡ ⠨⠉ greek lower case sampi a ⠈⠰⠁ script lower case a b ⠈⠰⠃ script lower case b c ⠈⠰⠉ script lower case c d ⠈⠰⠙ script lower case d ℯ ⠈⠰⠑ script lower case e f ⠈⠰⠋ script lower case f ℊ ⠈⠰⠛ script lower case g h ⠈⠰⠓ script lower case h i ⠈⠰⠊ script lower case i j ⠈⠰⠚ script lower case j k ⠈⠰⠅ script lower case k l ⠈⠰⠇ script lower case l m ⠈⠰⠍ script lower case m n ⠈⠰⠝ script lower case n ℴ ⠈⠰⠕ script lower case o p ⠈⠰⠏ script lower case p q ⠈⠰⠟ script lower case q r ⠈⠰⠗ script lower case r s ⠈⠰⠎ script lower case s t ⠈⠰⠞ script lower case t u ⠈⠰⠥ script lower case u v ⠈⠰⠧ script lower case v w ⠈⠰⠺ script lower case w x ⠈⠰⠭ script lower case x y ⠈⠰⠽ script lower case y z ⠈⠰⠵ script lower case z A ⠈⠰⠠⠁ script upper case a ℬ ⠈⠰⠠⠃ script upper case b C ⠈⠰⠠⠉ script upper case c D ⠈⠰⠠⠙ script upper case d ℰ ⠈⠰⠠⠑ script upper case e ℱ ⠈⠰⠠⠋ script upper case f G ⠈⠰⠠⠛ script upper case g ℋ ⠈⠰⠠⠓ script upper case h ℐ ⠈⠰⠠⠊ script upper case i J ⠈⠰⠠⠚ script upper case j K ⠈⠰⠠⠅ script upper case k ℒ ⠈⠰⠠⠇ script upper case l ℳ ⠈⠰⠠⠍ script upper case m N ⠈⠰⠠⠝ script upper case n O ⠈⠰⠠⠕ script upper case o P ⠈⠰⠠⠏ script upper case p Q ⠈⠰⠠⠟ script upper case q ℛ ⠈⠰⠠⠗ script upper case r S ⠈⠰⠠⠎ script upper case s T ⠈⠰⠠⠞ script upper case t U ⠈⠰⠠⠥ script upper case u V ⠈⠰⠠⠧ script upper case v W ⠈⠰⠠⠺ script upper case w X ⠈⠰⠠⠭ script upper case x Y ⠈⠰⠠⠽ script upper case y Z ⠈⠰⠠⠵ script upper case z a ⠈⠸⠁ fraktur lower case a b ⠈⠸⠃ fraktur lower case b c ⠈⠸⠉ fraktur lower case c d ⠈⠸⠙ fraktur lower case d e ⠈⠸⠑ fraktur lower case e f ⠈⠸⠋ fraktur lower case f g ⠈⠸⠛ fraktur lower case g h ⠈⠸⠓ fraktur lower case h i ⠈⠸⠊ fraktur lower case i j ⠈⠸⠚ fraktur lower case j k ⠈⠸⠅ fraktur lower case k l ⠈⠸⠇ fraktur lower case l m ⠈⠸⠍ fraktur lower case m n ⠈⠸⠝ fraktur lower case n o ⠈⠸⠕ fraktur lower case o p ⠈⠸⠏ fraktur lower case p q ⠈⠸⠟ fraktur lower case q r ⠈⠸⠗ fraktur lower case r s ⠈⠸⠎ fraktur lower case s t ⠈⠸⠞ fraktur lower case t u ⠈⠸⠥ fraktur lower case u v ⠈⠸⠧ fraktur lower case v w ⠈⠸⠺ fraktur lower case w x ⠈⠸⠭ fraktur lower case x y ⠈⠸⠽ fraktur lower case y z ⠈⠸⠵ fraktur lower case z A ⠈⠸⠠⠁ fraktur upper case a B ⠈⠸⠠⠃ fraktur upper case b ℭ ⠈⠸⠠⠉ fraktur upper case c D ⠈⠸⠠⠙ fraktur upper case d E ⠈⠸⠠⠑ fraktur upper case e F ⠈⠸⠠⠋ fraktur upper case f G ⠈⠸⠠⠛ fraktur upper case g ℌ ⠈⠸⠠⠓ fraktur upper case h ℑ ⠈⠸⠠⠊ fraktur upper case i J ⠈⠸⠠⠚ fraktur upper case j K ⠈⠸⠠⠅ fraktur upper case k L ⠈⠸⠠⠇ fraktur upper case l M ⠈⠸⠠⠍ fraktur upper case m N ⠈⠸⠠⠝ fraktur upper case n O ⠈⠸⠠⠕ fraktur upper case o P ⠈⠸⠠⠏ fraktur upper case p Q ⠈⠸⠠⠟ fraktur upper case q ℜ ⠈⠸⠠⠗ fraktur upper case r S ⠈⠸⠠⠎ fraktur upper case s T ⠈⠸⠠⠞ fraktur upper case t U ⠈⠸⠠⠥ fraktur upper case u V ⠈⠸⠠⠧ fraktur upper case v W ⠈⠸⠠⠺ fraktur upper case w X ⠈⠸⠠⠭ fraktur upper case x Y ⠈⠸⠠⠽ fraktur upper case y ℨ ⠈⠸⠠⠵ fraktur upper case z 3 3 3 3 ⠜⠨⠣⠒⠜⠒⠨⠻⠻ square root of cube root of three 3 3 3 3 ⠣⠨⠜⠒⠨⠻⠜⠒⠻ root degree (root three end root) three end root 3 3 3 3 3 ⁢ 3 ⠣⠒⠨⠜⠒⠨⠻⠜⠒⠻ root degree (three times root three end root) three end root 3 3 3 3 ⠜⠨⠣⠨⠨⠜⠒⠨⠨⠻⠜⠒⠨⠻⠻ root root degree (three times root three end root) of three end root end root 10g 10g 20g 10g + 10g = 20g ⠼⠂⠴⠛⠬⠂⠴⠛⠀⠨⠅⠀⠼⠆⠴⠛ ten g plus ten g equals twenty g 1km 100m 1km = 100m ⠼⠂⠅⠍⠀⠨⠅⠀⠼⠂⠴⠴⠍ one km equals one hundred m 100cm 2 m 2 100cm 2 = ?m 2 ⠼⠂⠴⠴⠉⠍⠘⠆⠀⠨⠅⠀⠿⠍⠘⠆ one hundred cm squared equals omission m squared 1 . 1 ∗ . ⠼⠂⠈⠼⠨ one period asterisk x, y “ ⁢ x, ⁢ ⁢ y ⁢ ” ⠦⠭⠠⠀⠽⠴ open quote x comma y punctuation indicator close quote 1 3 4 1 3 5 1 ⁤ 3 4 1 ⁤ 3 5 ⠠⠹⠂⠸⠹⠒⠌⠲⠸⠼⠠⠌⠂⠸⠹⠒⠌⠢⠸⠼⠠⠼ begin fraction one and one fourth over one and three fifths x y x ≊ y ⠭⠀⠈⠱⠈⠱⠱⠀⠽ x approximately or equal to y x y x ⩰ y ⠭⠀⠈⠱⠈⠱⠨⠅⠀⠽ x approximately over equal to y x y x ≊̸ y ⠭⠀⠌⠈⠱⠈⠱⠱⠀⠽ x not approximately or equal to y x y x ⩰̸ y ⠭⠀⠌⠈⠱⠈⠱⠨⠅⠀⠽ x not approximately over equal to y x y x ≦ y ⠭⠀⠐⠅⠨⠅⠀⠽ x less than over equal to y x y x ≧ y ⠭⠀⠨⠂⠨⠅⠀⠽ x greater than over equal to y x y x ⫅ y ⠭⠀⠸⠐⠅⠨⠅⠀⠽ x subset over equal to y x y x ⫆ y ⠭⠀⠸⠨⠂⠨⠅⠀⠽ x superset over equal to y x y x ⫅̸ y ⠭⠀⠌⠸⠐⠅⠨⠅⠀⠽ x not subset over equal to y x y x ⫆̸ y ⠭⠀⠌⠸⠨⠂⠨⠅⠀⠽ x not superset over equal to y h7 ⠫⠶ heptagon A h7 ⁡ ⁣ A ⠫⠶⠀⠠⠁ heptagon A A B C h7 ⁡ A ⁣ B ⁣ C ⠫⠶⠀⠠⠁⠠⠃⠠⠉ heptagon A B C ih7 ⠫⠓⠏ general heptagon A ih7 ⁡ ⁣ A ⠫⠓⠏⠀⠠⠁ general heptagon A A B C ih7 ⁡ A ⁣ B ⁣ C ⠫⠓⠏⠀⠠⠁⠠⠃⠠⠉ general heptagon A B C o8 ⠫⠦ octagon A o8 ⁡ ⁣ A ⠫⠦⠀⠠⠁ octagon A A B C o8 ⁡ A ⁣ B ⁣ C ⠫⠦⠀⠠⠁⠠⠃⠠⠉ octagon A B C io8 ⠫⠕⠉ general octagon A io8 ⁡ ⁣ A ⠫⠕⠉⠀⠠⠁ general octagon A A B C io8 ⁡ A ⁣ B ⁣ C ⠫⠕⠉⠀⠠⠁⠠⠃⠠⠉ general octagon A B C x y x ⩟ y ⠭⠈⠩⠱⠽ x and y x y x ⩠ y ⠭⠈⠩⠨⠅⠽ x and y x y x ⩡ y ⠭⠈⠬⠱⠽ x or y x y x ⩣ y ⠭⠈⠬⠨⠅⠽ x or y x y x ∩̲ y ⠭⠨⠩⠱⠽ x intersect y x y x ∩̳ y ⠭⠨⠩⠨⠅⠽ x intersect y x y x ∪̲ y ⠭⠨⠬⠱⠽ x union y x y x ∪̳ y ⠭⠨⠬⠨⠅⠽ x union y x y x ∍ y ⠭⠀⠈⠢⠀⠽ x ni y ● ⠫⠸⠉ filled circle A ● ⁡ ⁣ A ⠫⠸⠉⠀⠠⠁ filled circle A A B C ● ⁡ A ⁣ B ⁣ C ⠫⠸⠉⠀⠠⠁⠠⠃⠠⠉ filled circle A B C ⬬ ⠫⠸⠑ filled ellipse A ⬬ ⁡ ⁣ A ⠫⠸⠑⠀⠠⠁ filled ellipse A A B C ⬬ ⁡ A ⁣ B ⁣ C ⠫⠸⠑⠀⠠⠁⠠⠃⠠⠉ filled ellipse A B C ▲ ⠫⠸⠞ filled triangle A ▲ ⁡ ⁣ A ⠫⠸⠞⠀⠠⠁ filled triangle A A B C ▲ ⁡ A ⁣ B ⁣ C ⠫⠸⠞⠀⠠⠁⠠⠃⠠⠉ filled triangle A B C ▼ ⠨⠫⠸ filled triangle down A ▼ ⁡ ⁣ A ⠨⠫⠸⠀⠠⠁ filled triangle down A A B C ▼ ⁡ A ⁣ B ⁣ C ⠨⠫⠸⠀⠠⠁⠠⠃⠠⠉ filled triangle down A B C ⬟ ⠫⠸⠢ filled pentagon A ⬟ ⁡ ⁣ A ⠫⠸⠢⠀⠠⠁ filled pentagon A A B C ⬟ ⁡ A ⁣ B ⁣ C ⠫⠸⠢⠀⠠⠁⠠⠃⠠⠉ filled pentagon A B C ⌂ ⠫⠸⠏⠛ filled general pentagon A ⌂ ⁡ ⁣ A ⠫⠸⠏⠛⠀⠠⠁ filled general pentagon A A B C ⌂ ⁡ A ⁣ B ⁣ C ⠫⠸⠏⠛⠀⠠⠁⠠⠃⠠⠉ filled general pentagon A B C ⬢ ⠫⠸⠖ filled hexagon A ⬢ ⁡ ⁣ A ⠫⠸⠖⠀⠠⠁ filled hexagon A A B C ⬢ ⁡ A ⁣ B ⁣ C ⠫⠸⠖⠀⠠⠁⠠⠃⠠⠉ filled hexagon A B C ⌬ ⠫⠸⠓⠭ filled general hexagon A ⌬ ⁡ ⁣ A ⠫⠸⠓⠭⠀⠠⠁ filled general hexagon A A B C ⌬ ⁡ A ⁣ B ⁣ C ⠫⠸⠓⠭⠀⠠⠁⠠⠃⠠⠉ filled general hexagon A B C h7 ⠫⠸⠶ filled heptagon A h7 ⁡ ⁣ A ⠫⠸⠶⠀⠠⠁ filled heptagon A A B C h7 ⁡ A ⁣ B ⁣ C ⠫⠸⠶⠀⠠⠁⠠⠃⠠⠉ filled heptagon A B C ih7 ⠫⠸⠓⠏ filled general heptagon A ih7 ⁡ ⁣ A ⠫⠸⠓⠏⠀⠠⠁ filled general heptagon A A B C ih7 ⁡ A ⁣ B ⁣ C ⠫⠸⠓⠏⠀⠠⠁⠠⠃⠠⠉ filled general heptagon A B C o8 ⠫⠸⠦ filled octagon A o8 ⁡ ⁣ A ⠫⠸⠦⠀⠠⠁ filled octagon A A B C o8 ⁡ A ⁣ B ⁣ C ⠫⠸⠦⠀⠠⠁⠠⠃⠠⠉ filled octagon A B C io8 ⠫⠸⠕⠉ filled general octagon A io8 ⁡ ⁣ A ⠫⠸⠕⠉⠀⠠⠁ filled general octagon A A B C io8 ⁡ A ⁣ B ⁣ C ⠫⠸⠕⠉⠀⠠⠁⠠⠃⠠⠉ filled general octagon A B C ■ ⠫⠸⠲ filled square A ■ ⁡ ⁣ A ⠫⠸⠲⠀⠠⠁ filled square A A B C D ■ ⁡ A ⁣ B ⁣ C ⁣ D ⠫⠸⠲⠀⠠⠁⠠⠃⠠⠉⠠⠙ filled square A B C D ▬ ⠫⠸⠗ filled rectangle A ▬ ⁡ ⁣ A ⠫⠸⠗⠀⠠⠁ filled rectangle A A B C D ▬ ⁡ A ⁣ B ⁣ C ⁣ D ⠫⠸⠗⠀⠠⠁⠠⠃⠠⠉⠠⠙ filled rectangle A B C D < > ⠫⠸⠓ filled rhombus A < > ⁡ ⁣ A ⠫⠸⠓⠀⠠⠁ filled rhombus A A B C D < > ⁡ A ⁣ B ⁣ C ⁣ D ⠫⠸⠓⠀⠠⠁⠠⠃⠠⠉⠠⠙ filled rhombus A B C D ▰ ⠫⠸⠛ filled parallelogram A ▰ ⁡ ⁣ A ⠫⠸⠛⠀⠠⠁ filled parallelogram A A B C D ▰ ⁡ A ⁣ B ⁣ C ⁣ D ⠫⠸⠛⠀⠠⠁⠠⠃⠠⠉⠠⠙ filled parallelogram A B C D ⬩ ⠫⠸⠙ filled diamond A ⬩ ⁡ ⁣ A ⠫⠸⠙⠀⠠⠁ filled diamond A A B C D ⬩ ⁡ A ⁣ B ⁣ C ⁣ D ⠫⠸⠙⠀⠠⠁⠠⠃⠠⠉⠠⠙ filled diamond A B C D ⭑ ⠫⠸⠎ filled star A ⭑ ⁡ ⁣ A ⠫⠸⠎⠀⠠⠁ filled star A A B C D ⭑ ⁡ A ⁣ B ⁣ C ⁣ D ⠫⠸⠎⠀⠠⠁⠠⠃⠠⠉⠠⠙ filled star A B C D tz ⠫⠸⠵ filled trapezoid A tz ⁡ ⁣ A ⠫⠸⠵⠀⠠⠁ filled trapezoid A A B C D tz ⁡ A ⁣ B ⁣ C ⁣ D ⠫⠸⠵⠀⠠⠁⠠⠃⠠⠉⠠⠙ filled trapezoid A B C D qd ⠫⠸⠟ filled quadrilateral A qd ⁡ ⁣ A ⠫⠸⠟⠀⠠⠁ filled quadrilateral A A B C D qd ⁡ A ⁣ B ⁣ C ⁣ D ⠫⠸⠟⠀⠠⠁⠠⠃⠠⠉⠠⠙ filled quadrilateral A B C D x 5 x ⋅ 5 ⠭⠐⠢ x times 5 x .6 x ⋅ .6 ⠭⠐⠨⠖ x times decimal point six 2 Σ ⁢ 2 ⠨⠠⠎⠐⠆ capital sigma times two T1E4 T1E4 ⠼⠞⠂⠑⠲ ten one eleven four c 0 10 2 c 1 10 c 2 c 0 ⁢ 10 2 + c 1 ⁢ 10 + c 2 ⠉⠴⠐⠂⠴⠘⠆⠐⠬⠉⠂⠐⠂⠴⠬⠉⠆ c sub zero ten squared plus c sub one ten plus c two 2 n 1 5 3 2 n 2 5 1 2 2 ⁢ n 1 ⁢ 5 − 3 ⁢ ⁄ ⁢ 2 − n 2 ⁢ 5 − 1 ⁢ ⁄ ⁢ 2 ⠼⠆⠝⠂⠐⠢⠘⠤⠒⠸⠌⠆⠐⠤⠝⠆⠐⠢⠘⠤⠂⠸⠌⠆ two n sub one five super minus three slash two minus n sub two five super minus one slash two 0. a 1 a 2 0. ⁢ a 1 ⁢ a 2 ⁢ … ⠼⠴⠨⠐⠁⠂⠁⠆⠀⠄⠄⠄ zero point a sub one a sub two ellipsis 0. 1 2 0. ⁢ α 1 ⁢ α 2 ⁢ … ⠼⠴⠨⠐⠨⠁⠂⠨⠁⠆⠀⠄⠄⠄ zero point alpha sub one alpha sub two ellipsis 1 3 . 1 3 = . ⁢ ? ⠹⠂⠌⠒⠼⠀⠨⠅⠀⠨⠐⠿ fraction one over three end fraction equals point omission 3. .4 3.4 3. + .4 = 3.4 ⠼⠒⠨⠐⠬⠨⠲⠀⠨⠅⠀⠼⠒⠨⠲ three point plus point four equals three point four 3. ( 3. ) ⠷⠒⠨⠐⠾ open parenthesis three point close parenthesis 1. 2. 1. 2. ⠹⠂⠨⠐⠌⠆⠨⠐⠼ fraction one point over two point end fraction x y | x | ⁢ | y | ⠳⠭⠳⠐⠳⠽⠳ absolute value of x times absolute value of y x y ∥ x ∥ ⁢ ∥ y ∥ ⠳⠳⠭⠳⠳⠐⠳⠳⠽⠳⠳ norm x times norm y x ∥ | x | ∥ ⠳⠳⠐⠳⠭⠳⠐⠳⠳ norm of absolute value of x 9 14 23 9 ⁢ □ ⁢ 14 = 23 ⠼⠔⠫⠲⠐⠂⠲⠀⠨⠅⠀⠼⠆⠒ nine square fourteen equals two three 9 7 13 7 9 7 ⁢ ■ ⁢ 13 7 ⠼⠔⠰⠶⠐⠫⠸⠲⠐⠂⠒⠰⠶ nine sub seven filled square one three sub seven T ∼ ∼ T ⠈⠱⠐⠈⠱⠠⠞ not not T x 1 x 1 ⠭⠂ x sub one x 1 x ⋅ 1 ⠭⠐⠂ x times one S 2 S ⋅ 2 ⠠⠎⠐⠆ capital s times two A x 1 A x 1 ⠠⠁⠰⠭⠰⠰⠂ capital a sub (x sub one) A x 1 A x ⋅ 1 ⠠⠁⠰⠭⠂ capital a sub (x times one) A x 1 A x ⁢ 1 ⠠⠁⠰⠭⠐⠂ (capital a sub x) times one 0. 1 2 0. ⁢ α 1 ⁢ α 2 ⁢ … ⠼⠴⠨⠐⠨⠁⠂⠨⠁⠆⠀⠄⠄⠄ zero point alpha sub one alpha sub two ellipsis 0. 1 2 0. ⁢ Γ 1 ⁢ Γ 2 ⁢ … ⠼⠴⠨⠐⠨⠠⠛⠂⠨⠠⠛⠆⠀⠄⠄⠄ zero point upper case gamma sub one upper case gamma sub two ellipsis 0. 1 2 0. ⁢ a 1 ⁢ a 2 ⁢ … ⠼⠴⠨⠐⠈⠸⠁⠂⠈⠸⠁⠆⠀⠄⠄⠄ zero point fraktur a sub one fraktur a sub two ellipsis 0. 1 2 0. ⁢ A 1 ⁢ A 2 ⁢ … ⠼⠴⠨⠐⠈⠸⠠⠁⠂⠈⠸⠠⠁⠆⠀⠄⠄⠄ zero point fraktur capital a sub one fraktur capital a sub two ellipsis 0. 1 2 0. ⁢ a 1 ⁢ a 2 ⁢ … ⠼⠴⠨⠐⠈⠰⠁⠂⠈⠰⠁⠆⠀⠄⠄⠄ zero point script a sub one script a sub two ellipsis 0. 1 2 0. ⁢ A 1 ⁢ A 2 ⁢ … ⠼⠴⠨⠐⠈⠰⠠⠁⠂⠈⠰⠠⠁⠆⠀⠄⠄⠄ zero point script capital a sub one script capital a sub two ellipsis a b | a | ⁢ | b | ⠳⠁⠳⠐⠳⠃⠳ absolute value of a times absolute value of b a b ∥ a ∥ ⁢ ∥ b ∥ ⠳⠳⠁⠳⠳⠐⠳⠳⠃⠳⠳ norm a times norm b a ∥ | a | ∥ ⠳⠳⠐⠳⠁⠳⠐⠳⠳ norm of absolute value of a a | ∥ a ∥ | ⠳⠐⠳⠳⠁⠳⠳⠐⠳ absolute value of norm of a a b a ∣ | b | ⠁⠳⠐⠳⠃⠳ a divides absolute value of b a b a ∣ ∥ b ∥ ⠁⠳⠐⠳⠳⠃⠳⠳ a divides norm of b a b a ∤ | b | ⠁⠌⠳⠐⠳⠃⠳ a does not divide absolute value of b a b a ∤ ∥ b ∥ ⠁⠌⠳⠐⠳⠳⠃⠳⠳ a does not divide norm of b