**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 one is x then the other number is (x + 1)
- For two consecutive even or odd numbers, if one is x then the other number is (x + 2)
- 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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