Concept 4 of 5
Compare Two Expressions
Today's big idea
Work out both sides completely before choosing which sign belongs between them.
Guessing from the size of the numbers fails, since both sides must be worked.
How it works
👀 What's going on?
Two sums sit either side of an empty box, and you have to say which is bigger. The numbers themselves look like a clue and they are not, because a longer-looking sum is often the smaller one.
💡 Here's the trick
Look at the two sides above. Each is worked out completely and separately, and only the two answers are compared. The sign then follows: the smaller side takes the point of the less-than sign, and two equal sides take an equals.
🪄 How to do it
- 1.Work out the left side of the sum above on its own.
- 2.Work out the right side the same way.
- 3.Compare the two answers and choose the sign that points at the smaller one.
✍️ Try it
Which sign belongs in 18 + 22 against 5 times 8? Then: which sign belongs in 9 times 4 against 50 take away 12?
The first gives 40 on the left and 40 on the right, so the sign is =. The second gives 36 against 38, so the left is smaller and the sign is <.
⚠️ Watch out
You might be thinking you can judge from the size of the numbers on show. You cannot. 5 times 8 uses two small numbers and reaches 40, while 50 take away 12 uses a big one and only reaches 38.
🌟 Why this matters
Deciding which of two amounts is larger, when neither is written plainly, is what comparing prices or offers actually involves. Both sides have to be worked out first.
Exam tip: Write both answers above the box before choosing, since the sign is then obvious.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Which sign makes it true? 24 + 16 ▢ 30 + 8”
- 1
Solve the left side
24 + 16 = 40.
- 2
Solve the right side
30 + 8 = 38.
- 3
Compare
40 is bigger than 38, so the sign is >.
- 4
Answer ✓
Sign = >
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Solve the left side and the right side, then compare the two totals.
SIGN · ROUND 1 OF 3
9 + 6 ▢ 30 − 15
Which sign fits?
Quick check
✅ VERIFICATION
Both sides of a comparison work out to 45. Which sign belongs between them?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Number Groups
Check every statement against the real set.