Equivalent number sentences
Theory
Two number sentences are equivalent when both sides have the same value. If one number goes up, another must go down by the same amount to keep the balance.
Equivalent number sentences have the same value on each side, even if they look different.
In \(36 + 28 = 40 + \square\), both sides must make \(64\).
Because \(36\) rose by \(4\) to make \(40\), the \(28\) must drop by \(4\) to \(24\).
Keeping both sides equal
| Side | Value |
|---|---|
| \(36 + 28\) | \(64\) |
| \(40 + 24\) | \(64\) |
How to complete an equivalent sentence
- Work out the side you know fully.
- Make the other side reach the same total.
- Check both sides are equal.
Left side: \(36 + 28 = 64\).
| \(64 - 40\) | \(=\) | \(24\) |
\(15\) rose by \(5\), so \(9\) must fall by \(5\).
| \(9 - 5\) | \(=\) | \(4\) |
Left side: \(3 \times 8 = 24\).
| \(24 \div 6\) | \(=\) | \(4\) |
\(6 \times 10 = 60\), then \(60 \div 4 = 15\).
| \(60 \div 4\) | \(=\) | \(15\) |
Common pitfalls
Frequently asked questions
What makes two sentences equivalent?
Both sides have the same value. \(36 + 28\) and \(40 + 24\) both equal \(64\), so they are equivalent.
What is compensation?
Raising one number and lowering another by the same amount, so the total stays the same. Up by \(4\), down by \(4\).
Can I use it with multiplication?
Yes. \(3 \times 8 = 6 \times 4\) because both sides equal \(24\).
Why can't I write \(15 = 18\)?
The equals sign only joins equal values. Two different totals are not equal, so each step needs its own sentence.