Let’s go through each problem one by one. I’ll solve them step by step so you can follow along easily.
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Part 1: GCF (Greatest Common Factor)
We need to find the biggest number that divides both numbers in each pair.
A. 32 and 48
Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Common factors: 1, 2, 4, 8, 16 → Greatest is
16
B. 9 and 27
Factors of 9: 1, 3, 9
Factors of 27: 1, 3, 9, 27
Common factors: 1, 3, 9 → Greatest is
9
C. 12 and 20
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 20: 1, 2, 4, 5, 10, 20
Common factors: 1, 2, 4 → Greatest is
4
D. 15 and 35
Factors of 15: 1, 3, 5, 15
Factors of 35: 1, 5, 7, 35
Common factors: 1, 5 → Greatest is
5
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Part 2: LCM (Least Common Multiple)
We need the smallest number that both numbers divide into evenly.
E. 4 and 6
Multiples of 4: 4, 8, 12, 16...
Multiples of 6: 6, 12, 18...
First common multiple:
12
F. 10 and 15
Multiples of 10: 10, 20, 30...
Multiples of 15: 15, 30...
First common multiple:
30
G. 9 and 12
Multiples of 9: 9, 18, 27, 36...
Multiples of 12: 12, 24, 36...
First common multiple:
36
H. 5 and 7
These are both prime — no common factors except 1. So LCM = 5 × 7 =
35
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Part 3: List all factors
I. 29 → It’s a prime number! Only factors:
1, 29
J. 44 → Let’s list pairs:
1×44, 2×22, 4×11 → Factors:
1, 2, 4, 11, 22, 44
K. 96 → This has many! Let’s go step by step:
1×96, 2×48, 3×32, 4×24, 6×16, 8×12 → Factors:
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
L. 72 → Pairs:
1×72, 2×36, 3×24, 4×18, 6×12, 8×9 → Factors:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
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Part 4: LCD (Least Common Denominator) for fractions
M. 4/9 and 2/3
LCD is the LCM of denominators 9 and 3.
Multiples of 9: 9, 18...
Multiples of 3: 3, 6, 9...
So LCD =
9
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Part 5: Equivalent Fractions
N. 4/10 → Multiply numerator and denominator by same number.
Try ×2: 8/20 → Or simplify first? But question says “at least 1 equivalent”, so we can also do:
Divide by 2: 2/5 → That’s simpler! So
2/5 is equivalent.
(You could also write 8/20, 12/30, etc.)
O. 6/9 → Divide top and bottom by 3 →
2/3
P. 2/5 → Multiply by 2 →
4/10 (or 6/15, 8/20, etc.)
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Part 6: Improper Fraction to Mixed Number
Q. 10/4 → How many times does 4 go into 10? 2 times (8), remainder 2 → So
2 2/4, which simplifies to
2 1/2
R. 7/6 → 6 goes into 7 once, remainder 1 →
1 1/6
S. 12/5 → 5 goes into 12 twice (10), remainder 2 →
2 2/5
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Part 7: Mixed Number to Improper Fraction
T. 7 1/2 → Multiply whole number by denominator: 7×2=14, add numerator: 14+1=15 →
15/2
U. 4 1/3 → 4×3=12, +1=13 →
13/3
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Final Answer:
A. 16
B. 9
C. 4
D. 5
E. 12
F. 30
G. 36
H. 35
I. 1, 29
J. 1, 2, 4, 11, 22, 44
K. 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
L. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
M. 9
N. 2/5 (or 8/20, etc.)
O. 2/3
P. 4/10 (or 6/15, etc.)
Q. 2 1/2
R. 1 1/6
S. 2 2/5
T. 15/2
U. 13/3
Parent Tip: Review the logic above to help your child master the concept of improper fractions worksheet 5th grade.
