Explanation:
We are comparing pairs of fractions and deciding whether to use
<,
>, or
=.
To compare two fractions, we can either:
- Find a common denominator and compare numerators, or
- Convert them to decimals (if easy), or
- Cross-multiply: for fractions a/b and c/d, compare a·d vs b·c.
- If a·d < b·c → a/b < c/d
- If a·d > b·c → a/b > c/d
- If a·d = b·c → a/b = c/d
Let’s go one by one:
---
A. 4/9 vs 5/6
Cross-multiply:
4 × 6 = 24
9 × 5 = 45
24 < 45 → so 4/9 < 5/6
✔ Answer:
<
B. 4/5 vs 3/6
Simplify 3/6 = 1/2
Now compare 4/5 and 1/2
Cross-multiply: 4×2 = 8, 5×1 = 5 → 8 > 5 → 4/5 > 1/2
✔ Answer:
>
C. 5/7 vs 5/5
5/5 = 1
5/7 < 1 → so 5/7 < 5/5
✔ Answer:
<
D. 1/3 vs 3/9
3/9 simplifies to 1/3
So 1/3 = 3/9
✔ Answer:
=
E. 3/6 vs 2/5
Simplify 3/6 = 1/2
Compare 1/2 and 2/5
Cross-multiply: 1×5 = 5, 2×2 = 4 → 5 > 4 → 1/2 > 2/5
So 3/6 > 2/5
✔ Answer:
>
F. 3/9 vs 2/7
Simplify 3/9 = 1/3
Compare 1/3 and 2/7
Cross-multiply: 1×7 = 7, 3×2 = 6 → 7 > 6 → 1/3 > 2/7
So 3/9 > 2/7
✔ Answer:
>
G. 2/5 vs 1/2
Cross-multiply: 2×2 = 4, 5×1 = 5 → 4 < 5 → 2/5 < 1/2
✔ Answer:
<
H. 1/2 vs 2/7
Cross-multiply: 1×7 = 7, 2×2 = 4 → 7 > 4 → 1/2 > 2/7
✔ Answer:
>
I. 1/5 vs 5/8
Cross-multiply: 1×8 = 8, 5×5 = 25 → 8 < 25 → 1/5 < 5/8
✔ Answer:
<
J. 1/3 vs 3/8
Cross-multiply: 1×8 = 8, 3×3 = 9 → 8 < 9 → 1/3 < 3/8
✔ Answer:
<
Let me double-check each quickly:
A. 4/9 ≈ 0.444, 5/6 ≈ 0.833 → < ✔
B. 4/5 = 0.8, 3/6 = 0.5 → > ✔
C. 5/7 ≈ 0.714, 5/5 = 1 → < ✔
D. 1/3 = 3/9 → = ✔
E. 3/6 = 0.5, 2/5 = 0.4 → > ✔
F. 3/9 = 0.333, 2/7 ≈ 0.286 → > ✔
G. 2/5 = 0.4, 1/2 = 0.5 → < ✔
H. 1/2 = 0.5, 2/7 ≈ 0.286 → > ✔
I. 1/5 = 0.2, 5/8 = 0.625 → < ✔
J. 1/3 ≈ 0.333, 3/8 = 0.375 → < ✔
All correct.
Final Answer:
A: <
B: >
C: <
D: =
E: >
F: >
G: <
H: >
I: <
J: <
Parent Tip: Review the logic above to help your child master the concept of ordering fractions worksheet 5th grade.
