Fractions Worksheets | Printable Fractions Worksheets for Teachers - Free Printable

Let’s solve each problem step by step.

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Part 1: Converting Improper Fractions to Mixed Numbers

An improper fraction is when the top number (numerator) is bigger than the bottom number (denominator). To convert it to a mixed number, divide the numerator by the denominator. The quotient becomes the whole number, and the remainder over the original denominator becomes the fraction part.

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 #4: 8 × 8 = 64, 65 - 64 = 1 → correct → 8 1/8
Check #8: 7 × 6 = 42, 43 - 42 = 1 → correct → 6 1/7
Check #12: same as #8 → 6 1/7
Check #15: 6 × 6 = 36, 37 - 36 = 1 → correct → 6 1/6

Actually, many of these have remainder 1 — but let’s check if any are wrong.

Wait — #1: 4×7=28, 29-28=1 → 7 1/4 ✔️
#2: 6×2=12, 13-12=1 → 2 1/6 ✔️
#5: 2×8=16, 17-16=1 → 8 1/2 ✔️
#6: 2×2=4, 5-4=1 → 2 1/2 ✔️
#7: 4×6=24, 25-24=1 → 6 1/4 ✔️
#9: same as #1 → 7 1/4 ✔️
#10: same as #3 → 8 1/9 ✔️
#11: 3×6=18, 19-18=1 → 6 1/3 ✔️
#13: 5×2=10, 11-10=1 → 2 1/5 ✔️
#14: 10×9=90, 91-90=1 → 9 1/10 ✔️

All seem correct for Part 1.

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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, then add the numerator. Put that result over the original denominator.

Example: 2 1/3 → (2×3 + 1)/3 = 7/3

Now apply this:

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:

#5: 8×7=56 +4=60 → 60/7 ✔️
#8: 6×9=54 +7=61 → 61/9 ✔️
#15: 8×5=40 +4=44 → 44/5 ✔️

All look good.

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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