Missing Numbers and Equalities

What you will learn

• Say what the equals sign means.
• Check whether two sides are equal.
• Find a missing number in an addition, a subtraction or an equality.

Before you start: you should be able to add and subtract within $20$. See Adding Within 20 and Subtracting Within 20.

The idea

Many people think the equals sign means “the answer comes next”. It really means the same as. In $3 + 4 = 7$, the left side and the right side have the same value. Think of a balance: if both pans hold the same amount, the balance sits level.

Equal sides

The two sides do not have to look alike. $6 + 2$ and $4 + 4$ are both $8$, so $6 + 2 = 4 + 4$ is a true equality.

When the two sides are not the same, the balance tips and we cannot use the equals sign.

Finding a missing number

Sometimes a box or a gap $\square$ stands for a number you do not know. You find it by making both sides balance.

For $5 + \square = 9$: the total is $9$, and you have $5$ already. How many more make $9$? Use subtraction: $9 - 5 = 4$.

For $\square - 3 = 6$: a number was reduced by $3$ and became $6$. Go back by adding: $6 + 3 = 9$.

Always check by putting your number back in the gap and seeing if the two sides are equal.

Worked examples

Example 1: Missing in an addition

Find $\square$ in $7 + \square = 15$.

1. The total is $15$ and we have $7$.
2. Subtract: $15 - 7 = 8$.
3. Check: $7 + 8 = 15$.

Answer: $8$.

Example 2: Missing in a subtraction

Find $\square$ in $14 - \square = 9$.

1. We start at $14$ and reach $9$.
2. The amount taken away is $14 - 9 = 5$.
3. Check: $14 - 5 = 9$.

Answer: $5$.

Example 3: Balance both sides

Find $\square$ in $3 + 6 = \square + 4$.

1. The left side is $3 + 6 = 9$.
2. The right side must also be $9$, so $\square + 4 = 9$.
3. $9 - 4 = 5$.
4. Check: $5 + 4 = 9$.

Answer: $5$.

Do not read $=$ as “the answer is”. In $6 + 2 = 4 + 4$ there is no single answer on the right. It just says both sides are the same.

Why it matters

Finding a missing number is the beginning of algebra. Later you will use a letter such as $x$ instead of a box, and solve $x + 5 = 9$ in the same way. The idea of keeping both sides balanced is the idea behind every equation you will solve. See Equations when you are ready.