🔢 Comparing Numerical Expressions 🔢
Let's learn which numbers are bigger, smaller, or the same!
🎯 What is Comparing Expressions?
When we compare expressions, we find out:
- ✅ Which one is GREATER (bigger)
- ✅ Which one is LESSER (smaller)
- ✅ If they are EQUAL (the same)
3 + 5 or 4 × 2
📝 The Three Comparison Signs
>
Greater Than
The open side faces the BIGGER number
<
Less Than
The pointy side faces the SMALLER number
=
Equal To
Both sides have the SAME value
How to read the sign
Read from left to right, in the same order as the numbers:
- 3 < 7 — "three is less than seven"
- 8 > 5 — "eight is greater than five"
- 6 = 6 — "six equals six"
On the number line, the bigger number is further to the right. 7 is to the right of 3, so 7 > 3, and 3 < 7.
Why does this work? The numbers on the line go in counting order: each next number is one more than the one before.
What does the sign "=" mean?
Solve: 8 + 4 = □ + 5. Which number goes in the box?
How to solve
- Work out the left side: 8 + 4 = 12.
- The sign "=" says: the right side must also be 12.
- Which number plus 5 makes 12? It is 7, because 7 + 5 = 12.
- Answer: □ = 7.
Check: 8 + 4 = 12 and 7 + 5 = 12. Left 12, right 12. True.
Why 12 and 17 do not work
Put the number in the box and work out both sides.
Write 12. Right side: 12 + 5 = 17. Left side: 12. We get 12 = 17. This is false.
Write 17. Right side: 17 + 5 = 22. Left side: 12. We get 12 = 22. This is false.
Why? The sign "=" does not mean "write the answer". It says that the left side and the right side are the same number.
The balance scale
Imagine a balance scale with two pans. The left pan holds 8 + 4. The right pan holds □ + 5. The scale is level only when both pans hold the same amount. The left side is 12, so the right side must be 12 too.
Left: 8 + 4 = 12. Right: 7 + 5 = 12. The same, so the scale is level.
Practice
1) 9 + 6 = □ + 10
Answer: 5
Check: 9 + 6 = 15 and 5 + 10 = 15.
2) 7 + 8 = 10 + □
Answer: 5
Check: 7 + 8 = 15 and 10 + 5 = 15.
3) 20 − 5 = □ − 3
Answer: 18
Check: 20 − 5 = 15 and 18 − 3 = 15.
4) True or false: 7 = 3 + 4
Answer: true
Check: 3 + 4 = 7. Left 7, right 7.