# 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 2
*x*then the second number is (2*x*+ 2) - For two consecutive odd numbers, if the first number is (2
*x*+ 1) then the second number is (2*x*+ 3) - The square of a number
*x*is*x*^{2} - The cube of a number
*x*is*x*^{3} - The ratio of
*x*to*y*is*x*/*y*

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