Math worksheet for converting improper fractions to mixed numbers and mixed numbers to improper fractions.

Let’s solve each problem step by step. We’ll start with converting improper fractions to mixed numbers, then move to converting mixed numbers to improper fractions.

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Part 1: Converting Improper Fractions to Mixed Numbers

To convert an improper fraction (top number bigger than bottom) to a mixed number:
- Divide the top number by the bottom number.
- The whole number part is how many times the bottom goes into the top evenly.
- The remainder becomes the new top number (numerator), and the bottom stays the same.

Let’s go one by one:

1) 29 ÷ 4 = 7 with remainder 1 → 7 1/4
2) 13 ÷ 6 = 2 with remainder 1 → 2 1/6
3) 73 ÷ 9 = 8 with remainder 1 → 8 1/9
4) 65 ÷ 8 = 8 with remainder 1 → 8 1/8
5) 17 ÷ 2 = 8 with remainder 1 → 8 1/2
6) 5 ÷ 2 = 2 with remainder 1 → 2 1/2
7) 25 ÷ 4 = 6 with remainder 1 → 6 1/4
8) 43 ÷ 7 = 6 with remainder 1 → 6 1/7
9) 29 ÷ 4 = 7 with remainder 1 → 7 1/4
10) 73 ÷ 9 = 8 with remainder 1 → 8 1/9
11) 19 ÷ 3 = 6 with remainder 1 → 6 1/3
12) 43 ÷ 7 = 6 with remainder 1 → 6 1/7
13) 11 ÷ 5 = 2 with remainder 1 → 2 1/5
14) 91 ÷ 10 = 9 with remainder 1 → 9 1/10
15) 37 ÷ 6 = 6 with remainder 1 → 6 1/6

Wait — let me double-check a few that might have different remainders.

Check #3: 9 × 8 = 72, 73 - 72 = 1 → correct → 8 1/9
Check #8: 7 × 6 = 42, 43 - 42 = 1 → correct → 6 1/7
Check #14: 10 × 9 = 90, 91 - 90 = 1 → correct → 9 1/10
Check #15: 6 × 6 = 36, 37 - 36 = 1 → correct → 6 1/6

Actually, looking again — some of these are repeating patterns because the numerator is always 1 more than a multiple of the denominator? Not all, but many. Let’s verify #5: 17 ÷ 2 = 8 R1 → yes. #6: 5 ÷ 2 = 2 R1 → yes. All seem correct.

But wait — let’s check #1: 4×7=28, 29-28=1 → 7 1/4 ✔️
#2: 6×2=12, 13-12=1 → 2 1/6 ✔️
All good so far.

Now Part 2:

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Part 2: Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction:
- Multiply the whole number by the denominator.
- Add the numerator.
- Put that result over the original denominator.

Example: 2 1/3 → (2×3 + 1)/3 = 7/3

Let’s do each:

1) 7 1/3 → (7×3 + 1)/3 = (21+1)/3 = 22/3
2) 7 9/10 → (7×10 + 9)/10 = (70+9)/10 = 79/10
3) 7 3/4 → (7×4 + 3)/4 = (28+3)/4 = 31/4
4) 2 1/2 → (2×2 + 1)/2 = (4+1)/2 = 5/2
5) 8 4/7 → (8×7 + 4)/7 = (56+4)/7 = 60/7
6) 2 3/5 → (2×5 + 3)/5 = (10+3)/5 = 13/5
7) 3 5/8 → (3×8 + 5)/8 = (24+5)/8 = 29/8
8) 6 7/9 → (6×9 + 7)/9 = (54+7)/9 = 61/9
9) 9 1/8 → (9×8 + 1)/8 = (72+1)/8 = 73/8
10) 6 2/5 → (6×5 + 2)/5 = (30+2)/5 = 32/5
11) 4 1/3 → (4×3 + 1)/3 = (12+1)/3 = 13/3
12) 2 2/3 → (2×3 + 2)/3 = (6+2)/3 = 8/3
13) 8 1/2 → (8×2 + 1)/2 = (16+1)/2 = 17/2
14) 4 3/10 → (4×10 + 3)/10 = (40+3)/10 = 43/10
15) 8 4/5 → (8×5 + 4)/5 = (40+4)/5 = 44/5

Double-checking a few:

#2: 7×10=70 +9=79 → 79/10 ✔️
#5: 8×7=56 +4=60 → 60/7 ✔️
#9: 9×8=72 +1=73 → 73/8 ✔️
#15: 8×5=40 +4=44 → 44/5 ✔️

All calculations checked.

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Final Answer:

Converting Improper Fractions to Mixed Numbers:

1) 7 1/4
2) 2 1/6
3) 8 1/9
4) 8 1/8
5) 8 1/2
6) 2 1/2
7) 6 1/4
8) 6 1/7
9) 7 1/4
10) 8 1/9
11) 6 1/3
12) 6 1/7
13) 2 1/5
14) 9 1/10
15) 6 1/6

Converting Mixed Numbers to Improper Fractions:

1) 22/3
2) 79/10
3) 31/4
4) 5/2
5) 60/7
6) 13/5
7) 29/8
8) 61/9
9) 73/8
10) 32/5
11) 13/3
12) 8/3
13) 17/2
14) 43/10
15) 44/5