Arithmetic operations

Operation Symbols used Result's name Notes
addition a+b sum commutative: a+b=b+a
associative: (a+b)+c=a+(b+c)
0 is identity: a+0=a
a, -a inverses: a+-a=0
a,b terms added or subtracted
subtraction a-b difference a-b≠b-a
(a-b)-c≠a-(b-c)
"difference of/between a and b"
multiplication a×b
a·b
ab (juxtaposition) 5a 5x (5)(6)
a*b
product a,b factors
commutative: ab=ba
associative: (ab)c=a(bc)
1 is identity: a·1=a
a, 1/a inverses: a·1/a=1
shortcut repeated addition
distributes over addition: a(b+c)=ab+ac
division a÷b

a/b
quotient a/b≠b/a
(a/b)/c≠a/(b/c)
shortcut repeated subtraction
"quotient of a and b"
exponentiation bp (superscript)
b^p
power b is base, p is exponent or power.
shortcut repeated multiplication
"b to the pth power"
b2 "squared"    b3 "cubed"     b0=1
Laws: xmxn=xm+n    (xm)n=xmn
   xm/xn=xm-n    x-n=1/xn
square root √a
sqrt()
root a≥0
positive root
√a2=a
√a√a=a
√of non-perfect square integer is irrational
√(ab)=√a√b