Let’s go through each problem one by one. We’ll compare the fractions by thinking about how much of each circle is shaded — even if we don’t shade them, we can imagine it!
Remember:
- The bottom number (denominator) tells us how many equal parts the whole is split into.
- The top number (numerator) tells us how many of those parts are shaded.
- Bigger fraction = more shaded area.
We’ll use > (greater than), < (less than), or = (equal to).
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1) Already done:
½ > ⅓ → because half a circle is bigger than one-third.
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2) Compare ⅓ and ¼
Imagine splitting a pizza into 3 slices vs 4 slices. One slice from the 3-slice pizza is BIGGER than one slice from the 4-slice pizza.
So:
⅓ > ¼
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3) Compare ⅕ and ⅓
One-fifth means 1 out of 5 pieces — very small piece.
One-third means 1 out of 3 pieces — bigger piece.
So:
⅕ < ⅓
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4) Compare ½ and ²⁄₄
Half a circle is the same as two-fourths — because if you split a circle into 4, two of them make half.
So:
½ = ²⁄
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5) Compare ¾ and ⅔
Three-fourths: almost the whole circle (only 1 part missing out of 4).
Two-thirds: also big, but let’s think:
If we split both circles into 12 parts (common denominator):
¾ = 9/12
⅔ = 8/12
So 9/12 > 8/12 →
¾ > ⅔
*(Alternatively: draw it mentally — 3 out of 4 is more than 2 out of 3.)*
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6) Compare ²⁄₅ and ½
Two-fifths: less than half (because half of 5 is 2.5, so 2 is less than that).
Half is exactly half.
So:
²⁄₅ < ½
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7) Compare ⅓ and ²⁄₆
Two-sixths simplifies to ⅓ (divide top and bottom by 2).
So they’re equal!
⅓ = ²⁄₆
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8) Compare ¼ and ⅕
One-fourth is bigger than one-fifth — because when you divide something into fewer pieces, each piece is bigger.
So:
¼ > ⅕
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9) Compare ³⁄₅ and ¾
Three-fifths vs three-fourths. Same numerator? Then look at denominators: smaller denominator = bigger pieces.
Fourth is bigger than fifth → so ¾ > ³⁄₅
Or convert:
³⁄₅ = 12/20
¾ = 15/20 → so ¾ is bigger.
Thus:
³⁄₅ < ¾
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10) Compare ⁵⁄ and ²⁄₂
Five-sixths is almost the whole thing — just one piece missing.
Two-halves is the WHOLE thing (since 2 ÷ 2 = 1).
So ⁵⁄₆ is less than 1, and ²⁄₂ equals 1.
Therefore:
⁵⁄₆ < ²⁄₂
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Final Answer:
1) ½ > ⅓
2) ⅓ > ¼
3) ⅕ < ⅓
4) ½ = ²⁄₄
5) ¾ > ⅔
6) ²⁄₅ < ½
7) ⅓ = ²⁄₆
8) ¼ > ⅕
9) ³⁄₅ < ¾
10) ⁵⁄ < ²⁄₂
Parent Tip: Review the logic above to help your child master the concept of fractions worksheet for 2nd grade.
