Adding and Subtracting Fractions with Unlike Denominators Review ... - Free Printable

Let’s go through each problem one by one, step by step, and solve them carefully.

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Problem 1:
To add the fractions 5/12 and 3/4, what must first be done?
→ To add fractions, they need to have the same denominator (bottom number). So we find a common denominator.
Answer: c) find a common denominator

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Problem 2:
Find the sum: 1/2 + 1/4
→ Convert 1/2 to fourths: 1/2 = 2/4
→ Now add: 2/4 + 1/4 = 3/4
Answer: 3/4

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Problem 3:
Find the difference: 2/3 - 1/9
→ Convert 2/3 to ninths: 2/3 = 6/9
→ Subtract: 6/9 - 1/9 = 5/9
Answer: 5/9

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Problem 4:
Find the sum: 2 1/8 + 6 1/2
→ Add whole numbers: 2 + 6 = 8
→ Add fractions: 1/8 + 1/2 → convert 1/2 to eighths: 1/2 = 4/8
→ 1/8 + 4/8 = 5/8
→ Total: 8 + 5/8 = 8 5/8
Answer: 8 5/8

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Problem 5:
Find the difference: 5 2/4 - 2 1/3
→ First simplify 2/4 to 1/2 → so it’s 5 1/2 - 2 1/3
→ Whole numbers: 5 - 2 = 3
→ Fractions: 1/2 - 1/3 → common denominator is 6
→ 1/2 = 3/6, 1/3 = 2/6 → 3/6 - 2/6 = 1/6
→ Total: 3 + 1/6 = 3 1/6
Answer: 3 1/6

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Problem 6:
Find the sum: 3/4 + 1 7/12
→ Write as mixed number addition: 0 3/4 + 1 7/12
→ Whole numbers: 0 + 1 = 1
→ Fractions: 3/4 + 7/12 → common denominator is 12
→ 3/4 = 9/12 → 9/12 + 7/12 = 16/12 = 1 4/12 = 1 1/3
→ Total: 1 + 1 1/3 = 2 1/3
Answer: 2 1/3

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Problem 7:
Find the difference: 3 4/10 - 2/5
→ Simplify 4/10 to 2/5 → so it’s 3 2/5 - 2/5
→ Subtract fractions: 2/5 - 2/5 = 0
→ Whole number stays: 3
Answer: 3

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Problem 8:
Find the sum of three sixths and nine twelves.
→ “Three sixths” = 3/6 = 1/2
→ “Nine twelves” = 9/12 = 3/4
→ Add: 1/2 + 3/4 → common denominator 4 → 2/4 + 3/4 = 5/4 = 1 1/4
Answer: 1 1/4

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Problem 9:
Find the difference of six eighths and three fourths.
→ Six eighths = 6/8 = 3/4
→ Three fourths = 3/4
→ Difference: 3/4 - 3/4 = 0
Answer: 0

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Problem 10:
Find the sum of five and five eights plus one and one fourth.
→ “Five and five eights” = 5 5/8
→ “One and one fourth” = 1 1/4
→ Add: 5 + 1 = 6
→ Fractions: 5/8 + 1/4 → 1/4 = 2/8 → 5/8 + 2/8 = 7/8
→ Total: 6 7/8
Answer: 6 7/8

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Problem 11:
Find the difference of three and two eights minus two and one forth.
→ “Three and two eights” = 3 2/8 = 3 1/4
→ “Two and one forth” = 2 1/4
→ Subtract: 3 1/4 - 2 1/4 = 1
Answer: 1

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Problem 12:
Find the missing fraction: 4 1/4 + ___ = 7 1/2
→ Subtract: 7 1/2 - 4 1/4
→ Whole numbers: 7 - 4 = 3
→ Fractions: 1/2 - 1/4 = 2/4 - 1/4 = 1/4
→ Total: 3 1/4
Answer: 3 1/4

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Problem 13:
Find the missing fraction: 6 3/4 - ___ = 2 1/4
→ Subtract: 6 3/4 - 2 1/4
→ Whole numbers: 6 - 2 = 4
→ Fractions: 3/4 - 1/4 = 2/4 = 1/2
→ Total: 4 1/2
Answer: 4 1/2

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Problem 14:
Find the missing fraction: ___ + 8 1/2 = 10 3/8
→ Subtract: 10 3/8 - 8 1/2
→ Whole numbers: 10 - 8 = 2
→ Fractions: 3/8 - 1/2 → 1/2 = 4/8 → 3/8 - 4/8 = -1/8 → borrow 1 from 2 → becomes 1 + 8/8 = 1 8/8
→ So: 1 8/8 + 3/8 = 1 11/8? Wait — better way:

Actually:
10 3/8 - 8 1/2
Convert both to eighths:
10 3/8 = 83/8
8 1/2 = 8 4/8 = 68/8
Subtract: 83/8 - 68/8 = 15/8 = 1 7/8
Answer: 1 7/8

Wait — let me double-check that:

10 3/8 minus 8 1/2
= (10 - 8) + (3/8 - 1/2)
= 2 + (3/8 - 4/8)
= 2 - 1/8
= 1 7/8 ✔

Yes, correct.

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Now, compiling all answers in order:

Final Answer:
1. c
2. 3/4
3. 5/9
4. 8 5/8
5. 3 1/6
6. 2 1/3
7. 3
8. 1 1/4
9. 0
10. 6 7/8
11. 1
12. 3 1/4
13. 4 1/2
14. 1 7/8