Let’s go step by step to compare each pair of fractions. We’ll use the circles to help us see which fraction is bigger, smaller, or if they’re equal.
---
First Pair: 1/4 vs 1/2
- The first circle is split into 4 parts, and we shade 1 → that’s 1/4.
- The second circle is split into 2 parts, and we shade 1 → that’s 1/2.
- Visually, 1/2 covers more area than 1/4.
→ So,
1/4 < 1/2
---
Second Pair: 5/12 vs 4/8
- First circle: 12 slices, shade 5 → 5/12
- Second circle: 8 slices, shade 4 → 4/8 = 1/2 (since half of 8 is 4)
- Is 5/12 less than, greater than, or equal to 1/2?
→ Half of 12 is 6, so 5/12 is less than 6/12 (which is 1/2).
→ So,
5/12 < 4/8
---
Third Pair: 7/16 vs 7/8
- Both have numerator 7, but different denominators.
- 7/16 means 7 out of 16 pieces — very small pieces.
- 7/8 means 7 out of 8 pieces — much bigger pieces.
→ Since 8 is smaller than 16, each piece in 7/8 is bigger → so 7/8 is larger.
→
7/16 < 7/8
---
Fourth Pair: 3/5 vs 10/14
- Let’s simplify 10/14 → divide top and bottom by 2 → 5/7
- Now compare 3/5 and 5/7
- Cross-multiply: 3×7 = 21, 5×5 = 25 → since 21 < 25, then 3/5 < 5/7
→ So,
3/5 < 10/14
*(Alternatively, think: 3/5 is a little over half, 10/14 is almost all — definitely bigger)*
---
Fifth Pair: 6/16 vs 8/16
- Same denominator! Just compare numerators: 6 vs 8
→ 6 is less than 8 → so
6/16 < 8/16
---
Sixth Pair: 5/5 vs 1/5
- 5/5 = whole thing = 1
- 1/5 = just one part
→ Clearly,
5/5 > 1/5
---
Seventh Pair: 4/6 vs 8/16
- Simplify both:
- 4/6 = 2/3
- 8/16 = 1/2
- Compare 2/3 and 1/2 → cross multiply: 2×2=4, 3×1=3 → 4>3 → so 2/3 > 1/2
→
4/6 > 8/16
---
Eighth Pair: 2/2 vs 4/4
- 2/2 = 1 whole
- 4/4 = 1 whole
→ They are equal →
2/2 = 4/4
---
Final Answer:
1/4 < 1/2
5/12 < 4/8
7/16 < 7/8
3/5 < 10/14
6/16 < 8/16
5/5 > 1/5
4/6 > 8/16
2/2 = 4/4
Parent Tip: Review the logic above to help your child master the concept of simple equivalent fractions worksheet.
