Number-related Problems

Addition
Expressions that can be translated to addition, ( + ): sum, plus, added to, in addition, increased by, and more than.

Verbal expression Algebraic equivalent
the sum of x and y x + y or y + x
x plus y x + y
x increased by y x + y
x added to y y + x
x in addition to y y + x
x more than y y + x

 

Subtraction
Expressions that can be translated to subtraction, ( - ): difference, minus, subtract, subtract from, less, less than, decreased by, diminished by, lowered by, and exceed.

Verbal expression Algebraic equivalent
the difference between x and y x - y
x minus y x - y
x decreased by y x - y
x diminished by y x - y
x lowered by y x - y
x exceeds y x - y
x less y x - y
x less than y y - x
subtract x from y y - x

 

Multiplication
Expressions that can be translated to multiplication, ( × ): product, times, and of. Expressions in multiple of a number are also worth noting: double, twice, triple, thrice, quadruple, four times, etcetera.

Verbal expression Algebraic equivalent
the product of x and y xy
x times y xy
x of y xy
double a number x 2x
twice a number y 2y

 

Division
Expressions that can be translated to division, ( ÷ ): quotient of, divided by, and over.

Verbal expression Algebraic equivalent
the quotient of x and y x/y
x divided by y x/y
x over y x/y

 

Equality
The words ‘is’ and ‘by’ denotes equality, ( = ).

Verbal expression Algebraic equivalent
the sum of x and y is z x + y = z
x exceeds y by z x - y = z

 

Other expressions

  • The reciprocal of x is 1/x and the reciprocal of x/y is y/x.
  • Divide 100 into two parts, if x is one part, the other part is (100 - x)
  • For two consecutive numbers, if the first number is x then the second number is (x + 1)
  • For two consecutive even or odd numbers, if the first number is x then the second number is (x + 2)
  • The square of a number x is x2
  • The cube of a number x is x3
  • The ratio of x to y is x/y

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