Explanation:
We need to find the fraction represented by each shaded circle diagram, then compare the two fractions using >, <, or =.
Each circle is divided into equal parts. The numerator is the number of shaded parts; the denominator is the total number of parts.
Let’s go one pair at a time:
1) Already done:
Left: 2 out of 5 → 2/5
Right: 3 out of 7 → 3/7
2/5 = 0.4, 3/7 ≈ 0.4286 → 2/5 < 3/7
✔
2) Left: circle divided into 3 parts, 1 shaded → 1/3
Right: circle divided into 12 parts, 3 shaded → 3/12 = 1/4
Compare 1/3 vs 1/4: 1/3 ≈ 0.333, 1/4 = 0.25 → 1/3 > 1/4
So: 1/3 > 1/4
3) Left: circle divided into 8 parts, 3 shaded → 3/8
Right: circle divided into 8 parts, 5 shaded → 5/8
Same denominator → compare numerators: 3 < 5 → 3/8 < 5/8
4) Left: circle divided into 12 parts, 2 shaded → 2/12 = 1/6
Right: circle divided into 6 parts, 1 shaded → 1/6
So: 1/6 = 1/6
5) Left: circle divided into 8 parts, 5 shaded → 5/8
Right: circle divided into 10 parts, 6 shaded → 6/10 = 3/5
Compare 5/8 vs 3/5:
Cross-multiply: 5×5 = 25, 3×8 = 24 → 25 > 24 → 5/8 > 3/5
So: 5/8 > 3/5
6) Left: circle divided into 5 parts, 3 shaded → 3/5
Right: circle divided into 8 parts, 5 shaded → 5/8
We just compared these in #5 (reverse): 3/5 < 5/8
Because 3×8 = 24, 5×5 = 25 → 24 < 25 → 3/5 < 5/8
So: 3/5 < 5/8
7) Left: circle divided into 8 parts, 3 shaded → 3/8
Right: circle divided into 10 parts, 4 shaded → 4/10 = 2/5
Compare 3/8 and 2/5:
3×5 = 15, 2×8 = 16 → 15 < 16 → 3/8 < 2/5
So: 3/8 < 2/5
8) Left: circle divided into 5 parts, 3 shaded → 3/5
Right: circle divided into 8 parts, 3 shaded → 3/8
Same numerator, larger denominator means smaller fraction → 3/5 > 3/8
Or cross-multiply: 3×8 = 24, 3×5 = 15 → 24 > 15 → 3/5 > 3/8
So: 3/5 > 3/8
9) Left: circle divided into 4 parts, 3 shaded → 3/4
Right: circle divided into 8 parts, 5 shaded → 5/8
Compare: 3/4 = 6/8, so 6/8 > 5/8 → 3/4 > 5/8
So: 3/4 > 5/8
10) Left: circle divided into 10 parts, 3 shaded → 3/10
Right: circle divided into 5 parts, 2 shaded → 2/5 = 4/10
So 3/10 < 4/10 → 3/10 < 2/5
So: 3/10 < 2/5
Now write all answers clearly:
2) 1/3 > 1/4
3) 3/8 < 5/8
4) 1/6 = 1/6
5) 5/8 > 3/5
6) 3/5 < 5/8
7) 3/8 < 2/5
8) 3/5 > 3/8
9) 3/4 > 5/8
10) 3/10 < 2/5
Final Answer:
2) 1/3 > 1/4
3) 3/8 < 5/8
4) 1/6 = 1/6
5) 5/8 > 3/5
6) 3/5 < 5/8
7) 3/8 < 2/5
8) 3/5 > 3/8
9) 3/4 > 5/8
10) 3/10 < 2/5
Parent Tip: Review the logic above to help your child master the concept of comparing fractions worksheet with pictures.
