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| or |y - x|
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 numbers, if the first number is 2x then the second number is (2x + 2)
• For two consecutive odd numbers, if the first number is (2x + 1) then the second number is (2x + 3)
• 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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