Equivalent number sentences
Theory
Equivalent number sentences are a Year 4 maths number and algebra skill: understanding that the equals sign means both sides have the same value, deciding whether a number sentence is true or false, and finding the missing number that makes two sides balance. This page explains the balance idea and how to complete sentences with multiplication, division, addition and subtraction. Curriculum: VC2M4A01 / AC9M4A01.
A number sentence is a maths statement with an equals sign, like \(5 \times 3 = 15\). The equals sign \(=\) means the same value as. Both sides must be worth exactly the same, so it works like a balance.
Two number sentences are equivalent when both sides have the same value, even if the numbers look different. \(3 \times 6 = 9 \times 2\) is true because each side is worth \(18\). If the sides are not the same value, the sentence is false.
When a number is missing we show it with a box \(\square\). To fill the box, work out the side you already know, then choose the number that makes the other side equal to the same value.
Number sentences do not need formulas, but these facts help you keep both sides equal.
The same balance idea works for addition and subtraction.
How to complete an equivalent number sentence
- Work out the side you know. Add, subtract, multiply or divide to find its value.
- Match the other side. Find the number that makes the other side equal to that same value.
- Check both sides. Work out each side on its own. They must be the same value for the sentence to be true.
| \(4 \times 4\) | \(=\) | \(16\) |
| \(\square \times 2\) | \(=\) | \(16\) |
| \(8 \times 2\) | \(=\) | \(16\) |
The box is \(8\).
| \(4 \times 5\) | \(=\) | \(20\) |
| \(12 + 9\) | \(=\) | \(21\) |
| \(20\) | \(\neq\) | \(21\) |
The sides are \(20\) and \(21\), which are not the same, so the sentence is false.
| \(5 \times 5\) | \(=\) | \(25\) |
| \(40 - \square\) | \(=\) | \(25\) |
| \(40 - 15\) | \(=\) | \(25\) |
The box is \(15\).
| \(24 \div 6\) | \(=\) | \(4\) |
| \(\square \div 3\) | \(=\) | \(4\) |
| \(12 \div 3\) | \(=\) | \(4\) |
The box is \(12\).
| \(46 + 28\) | \(=\) | \(74\) |
| \(50 + \square\) | \(=\) | \(74\) |
| \(\square\) | \(=\) | \(74 - 50 = 24\) |
Shortcut: \(50\) is \(4\) more than \(46\), so the box is \(4\) less than \(28\), which is \(24\).
| \(71 - 39\) | \(=\) | \(32\) |
| \(72 - \square\) | \(=\) | \(32\) |
| \(\square\) | \(=\) | \(72 - 32 = 40\) |
\(72\) is \(1\) more than \(71\), so take away \(1\) more as well: \(39 + 1 = 40\). Adding the same amount to both numbers keeps the difference the same.
Common pitfalls
Frequently asked questions
What does the equals sign mean?
The equals sign means "the same value as". It works like a balance: whatever is on the left must be worth exactly the same as whatever is on the right. It does not mean "write the answer next".
What is an equivalent number sentence?
Two number sentences are equivalent when both sides have the same value, even if the numbers look different. For example, \(3 \times 6 = 9 \times 2\) because each side is worth \(18\).
How do you find a missing number in a number sentence?
Work out the side you know first. Then find the number that makes the other side equal to the same value. In \(2 \times 9 = \square \times 3\), the left side is \(18\), so the box is \(6\) because \(6 \times 3 = 18\).
Does the order of the numbers matter in multiplication?
No. Swapping the order of the factors keeps the same product, so \(7 \times 5 = 5 \times 7\). Both are worth \(35\).
What does the box or blank mean in a number sentence?
The box \(\square\) stands for a missing number you have to find. You choose the number that makes both sides of the sentence have the same value.
How do you know if a number sentence is true or false?
Work out the value of each side on its own, then compare them. If both sides are the same value the sentence is true. If they are different it is false.