# Year 5 Maths

# Letters That Stand for Numbers

Sometimes in maths we use a letter to stand for a number. Here’s an example:

### A = 6 + (8 × 5)

In an equation like this, A stands for a mystery number and your job as a maths detective is to work out what A equals. In this case, you can solve the mystery by multiplying and then adding:

### A = 6 + (8 × 5)

= 6 + 40

= 46

So A = 46. See if you can work out the mystery number in this equation:

### B = (8 × 3) – 4

## Equality Properties

Equality properties are rules that can help you solve equations like the ones above. One equality property says that equals added to equals are equal. This property can help you work out the mystery number in the following equation.

### Y - 25 = 15

This equality property says that, if you add an equal quantity to both sides of any equation, it will still be an equation. Look what happens if we add 25 to both sides of this equation.

### Y - 25 = 15

(Y - 25) + 25 = 15 + 25

Y = 40

If you subtract 25 from Y and then add 25, the addition and subtraction cancel each other out, and you are left with just Y on the left side of the equation. On the right side of the equation, you add 25 to 15 and get 40. So you know that Y = 40.

Use the same technique to solve Z - 12 = 17 and P - 29 = 17.

Now let’s learn another equality property: equals added to equals are equal. This is also very useful for solving equations. Here’s an example:

### Y ÷ 2 = 37

This equality property tells us that we can multiply both sides of an equation by the same number and we will still have an equation. Look what happens when we multiply by 2.

Do you remember learning this equality property first in Year 3 in our example of making orange juice?

### Y ÷ 2 = 37

(Y ÷ 2) × 2 = 37 × 2

Y = 74

If we divide Y by 2 and then multiply it by 2, the multiplication undoes the division, and we are left with just Y on the left side of the equation. Meanwhile, on the right side of the equation, we multiply 37 by 2 and get 74. So Y = 74.

Try to solve another problem of this sort on your own: Z ÷ 6 = 23

Remembering these equality properties will help you as you begin to study the kind of maths called algebra.

This activity is adapted from pages 234-236 of What Your Year 5 Child Needs to Know, which can be purchased here.

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