### Theory:

Do you know the difference between the

**verbal statement**and**algebraic statements?**Let's see an example to understand this clearly.Example:

Kathir is twice taller than Kumar. That is Kathir height is two times larger than Kumar's height. Now, this is known as a verbal statement. If you write the above verbal statement in an algebraic statement we get,

Let the height of the Kumar is \(x\)

Therefore Kathir height \(=\) $2\times \mathit{Height}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{Kumar}\phantom{\rule{0.147em}{0ex}}=2x$.

In the above example, we understood that normally we use the verbal statement to mention any mathematical operation, then we translate this verbal statement to an algebraic statement to find the unknown value.

Now let's see a few examples of how we are using the verbal and algebraic statement in the mathematical operation.

**[Note**: Here the unknown value \(x\) is represented in verbal statement as some number or a number].

**Addition**keywords: Sum, total, added, increased, more than, etc.Operation | Phrase | Example -Verbal statement | Algebraic statements |

Addition (+) | The sum of | The sum of a number and three. | $x\phantom{\rule{0.147em}{0ex}}+3$ |

Plus | A number plus three. | $x\phantom{\rule{0.147em}{0ex}}+3$ | |

Increased by | three increased by some number. | $3+x$ |

**Subtraction**keywords: Minus, Decreased by, less than, the difference of, subtracted, etc.Operation | Phrase | Phrase example- Verbal statement | Algebraic statements |

Subtraction (-) | Subtracted from | Eight subtracted from a number. | $x-8$ |

Decreased by | Eight decreased by some number. | $x-8$ | |

The difference of | The difference between Eight and some number. | $8\phantom{\rule{0.147em}{0ex}}-x$ |

**keywords: Multiplied by, The product of, Times, Thrice, Twice etc.****Multiplication**

Operation | Phrase | Phrase example -Verbal statement | Algebraic statements |

Multiplication | Multiplied by | Some number multiplied by fifteen. | $15x$ |

The product of | The product of negative fifteen. | $-15x$ | |

Times | Fifteen times a number. | $15x$ |

**Division**keywords: Divided by, The ratio of, The quotient of, etc.

Operation | Phrase | Phrase example -Verbal statement | Algebraic statements |

Division | Divided by | Twelve divided by some number. | $\frac{x}{12}$ |

The ratio of | The ratio of Twelve to a number. | $\frac{12}{x}$ |

Using these above, we can also make another operation that is,

**Equals****keywords**

**: Equals, Is the same as, yields.**

Operation | Phrase | Phrase example -Verbal statement | Algebraic statements |

Equals | Equals | Eight equals to less than three number. | $8=3-x$ |

Is the same as | Eight is the same as thrice the number. | $8=3x$ |