With basic arithmetic operations we’ve solved problems like the ones below:

Problem | Solution |

2 + 3 = __ | 2 + 3 = 5 |

4 x 6 = __ | 4 x 6 = 24 |

28 ÷ 4 = __ | 28 ÷ 4 = 7 |

In these problems we have spaces next to the equal sign instead of the answer e.g. = __

In equations we use letters instead of empty spaces. We can write and solve the problems above by using letters like this:

Problem | Solution |

2 + 3 = n | n = 5 |

4 x 6 = a | a = 24 |

28 ÷ 4 = b | b = 7 |

The above problems use n , a , and b but any letters can be used.

The letters are just placeholders – like a blank. We nearly always use letters but you could use anything!

5 + 6 = n

n = 11

OR

5 + 6 =

= 11

What really matters is what it represents – the answer – in this case 11

Ensure your child is not confused by the use of letters. This is probably the first time he or she has used letters outside of written or spoken language.

**Why Use Letters**

Using letters as placeholders can really help with some number problems because they let us write the problem out as an equation. When we solve the equation we find the answer to the problem.

Solving equations means finding what the letter represents or what it is equal to.

### Examples

Problem | Equation | Solution |

I want to buy a shirt costing $25. I have $8. How much more do I need? | n + 8 = 25 | n = 17 |

My Dad has lost 35 lbs and now weighs 175 lbs. How much did he weigh before he lost weight? | n – 35 = 175 | n = 210 |

In 8 weeks I’ll be going on holiday and I’d like to have $160 when I go. How much do I have to save every week? | n x 8 = 160 | n = 20 |

The next page in this section will start to show how to solve equations like the ones above.