## Mathematical Expressions used in Math Word Problems

To solve any mathematical problem, it is important to understand and know the mathematical meaning of the words used in the problem. Many mathematical expressions or even general expressions have the same meaning and may indicate a relationship between quantities or a mathematical operation (such as addition, subtraction, multiplication, and division).

**Equality Expressions**

All of the following expressions represents that two quantities are equal (=).

- is equal to (or equals)
- is the same as
- the result is
- yields
- gives

For example, 2+5 is equal to 7.

Note: The word “is” is also used to mean “equals”. For example, 8 is 5 more than 3, or 8 equal 5 + 3.

**Addition** **Expressions**

All of the following expression shows that the number $X$ and $Y$ are added

Expression Description |
Example |

$X+Y$ | $2+3$ |

The sum of $X$ and $Y$ | The sum of 2 and 3 |

The total of $X$ and $Y$ | The total of 2 and 3 |

$X$ added to $Y$ | 2 added to 3 |

$X$ increased by $Y$ | 2 increased by 3 |

$X$ more than $Y$ | 2 more than 3 |

$X$ greater than $Y$ | 2 greater than 3 |

**Subtraction Expressions**

All of the following expressions show that the number $Y$ is to be subtracted from the number $X$

Expression Description |
Example |

$X-Y$ | $7-2$ |

$X$ minus $Y$ | 7 minus 3 |

$X$ less $Y$ | 7 less 3 |

The difference of $X$ and $Y$ | The difference between 7 and 3 |

from $X$ subtract $Y$ | from 7 subtract 3 |

$X$ take away $Y$ | 7 take away 3 |

$X$ decreased by $Y$ | 7 decreased by 3 |

$X$ diminished by $Y$ | 7 diminished by 3 |

$Y$ is subtracted from $X$ | 7 is subtracted from 3 |

$Y$ less than $X$ | 3 less than 7 |

**Multiplication Expressions**

The following expression can be used if the numbers $X$ and $Y$ need to be multiplied.

Expression Description |
Example |

$X \times Y$ | $2\times 3$ |

$X$ multiplied by $Y$ | 2 multiplied by 3 |

The product of $X$ and $Y$ | The product of 2 and 3 |

$X$ times $Y$ | 2 times 3 |

For multiplication of two or more numbers symbol $\times$ or $\cdot$ is used. In algebra, a number before a variable is a coefficient, such as $4Y$ means 4 times $Y$, where 4 is coefficient.

**Division Expressions**

All of the following expression indicate the division of the numbers $X$ and $Y$ (in the order $X \div Y$.

Expression |
Example |

$X \div Y$ | $10 \div 2$ |

$X$ divided by $Y$ | 10 divided by 2 |

The quotient of $X$ and $Y$ | The quotient of 10 and 2 |

Read about Significant Figures