# Number sentence

A number sentence is a "mathematical sentence" used to express various mathematical relationships, namely equality and inequality. Number sentences are made up of:

- Numerals
- Operations (addition, subtraction, multiplication, division, etc.)
- Equality / inequality symbols

Below are some examples of number sentences.

Examples

Addition sentence | : | 5 + 3 = 8 |

Subtraction sentence | : | 6 - 4 = 2 |

Multiplication sentence | : | 7 × 8 = 56 |

Division sentence | : | 8 ÷ 2 = 4 |

Number sentences can also be written with fractions, decimals, negative numbers, with powers, and more. We can identify all the examples above as equations based on the use of the "=" sign. It is worth nothing that number sentences do not necessarily have to be true. For example, 2 - 3 = 5 is still a number sentence, albeit a false one. False number sentences can be used to test our understanding of basic arithmetic and all the symbols involved. For example, one thing we could change about the false number sentence is the minus sign. If we changed the minus sign to a plus sign, the number sentence would be true:

2 + 3 = 5

Number sentences can also take the form of inequalities. The key inequality symbols that we should recognize are:

- less than: <
- greater than: >
- less than or equal to: ≤
- greater than or equal to: ≥
- is not equal to: ≠

In the false number sentence above, 2 - 3 = 5, instead of changing the minus sign, we could also instead use various inequality signs. 2 - 3 = -1, so we could also write 2 - 3 < 5, and the number sentence would be true. Alternatively, we could write 2 - 3 ≠ 5, and this would also be true.

Examples

Change the following false number sentences such that they become true.

1. 2 + 8 < 10:

2 + 8 = 10

2 + 8 ≤ 10

2 + 8 ≥ 10

2. 5 ≥ 12:

5 ≠ 12

5 < 12

5 ≤ 12

5 + 7 = 12

Note that the above solutions are not all the possible solutions, just a few. There are many different ways to solve them.