Let’s solve each problem step by step. To convert a mixed number to an improper fraction:
1. Multiply the whole number by the denominator.
2. Add the numerator to that result.
3. Keep the same denominator.
4. Simplify if needed (but most of these are already in simplest form).
We’ll go one by one.
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1) 3 2/3
→ 3 × 3 = 9
→ 9 + 2 = 11
→ Answer:
11/3
2) 4 1/4
→ 4 × 4 = 16
→ 16 + 1 = 17
→ Answer:
17/4
3) 2 3/7
→ 2 × 7 = 14
→ 14 + 3 = 17
→ Answer:
17/7
4) 9 1/2
→ 9 × 2 = 18
→ 18 + 1 = 19
→ Answer:
19/2
5) 5 3/4
→ 5 × 4 = 20
→ 20 + 3 = 23
→ Answer:
23/4
6) 7 1/5
→ 7 × 5 = 35
→ 35 + 1 = 36
→ Answer:
36/5
7) 4 5/6
→ 4 × 6 = 24
→ 24 + 5 = 29
→ Answer:
29/6
8) 2 6/9
→ First, simplify 6/9 → divide top and bottom by 3 → 2/3
So now it’s 2 2/3
→ 2 × 3 = 6
→ 6 + 2 = 8
→ Answer:
8/3
*(Note: You could also do 2×9=18+6=24 → 24/9 → simplify to 8/3 — same answer)*
9) 3 9/10
→ 3 × 10 = 30
→ 30 + 9 = 39
→ Answer:
39/10
10) 6 5/7
→ 6 × 7 = 42
→ 42 + 5 = 47
→ Answer:
47/7
11) 8 3/10
→ 8 × 10 = 80
→ 80 + 3 = 83
→ Answer:
83/10
12) 4 7/8
→ 4 × 8 = 32
→ 32 + 7 = 39
→ Answer:
39/8
13) 9 5/8
→ 9 × 8 = 72
→ 72 + 5 = 77
→ Answer:
77/8
14) 3 4/15
→ 3 × 15 = 45
→ 45 + 4 = 49
→ Answer:
49/15
15) 11 2/3
→ 11 × 3 = 33
→ 33 + 2 = 35
→ Answer:
35/3
16) 7 4/6
→ Simplify 4/6 → 2/3
Now it’s 7 2/3
→ 7 × 3 = 21
→ 21 + 2 = 23
→ Answer:
23/3
*(Or: 7×6=42+4=46 → 46/6 → simplify to 23/3)*
17) 6 2/11
→ 6 × 11 = 66
→ 66 + 2 = 68
→ Answer:
68/11
18) 12 3/4
→ 12 × 4 = 48
→ 48 + 3 = 51
→ Answer:
51/4
19) 14 2/5
→ 14 × 5 = 70
→ 70 + 2 = 72
→ Answer:
72/5
20) 8 4/9
→ 8 × 9 = 72
→ 72 + 4 = 76
→ Answer:
76/9
21) 7 3/12
→ Simplify 3/12 → 1/4
Now it’s 7 1/4
→ 7 × 4 = 28
→ 28 + 1 = 29
→ Answer:
29/4
*(Or: 7×12=84+3=87 → 87/12 → divide by 3 → 29/4)*
22) 23 1/3
→ 23 × 3 = 69
→ 69 + 1 = 70
→ Answer:
70/3
23) 11 5/8
→ 11 × 8 = 88
→ 88 + 5 = 93
→ Answer:
93/8
24) 4 3/14
→ 4 × 14 = 56
→ 56 + 3 = 59
→ Answer:
59/14
25) 20 3/4
→ 20 × 4 = 80
→ 80 + 3 = 83
→ Answer:
83/4
26) 12 3/6
→ Simplify 3/6 → 1/2
Now it’s 12 1/2
→ 12 × 2 = 24
→ 24 + 1 = 25
→ Answer:
25/2
*(Or: 12×6=72+3=75 → 75/6 → divide by 3 → 25/2)*
27) 30 2/3
→ 30 × 3 = 90
→ 90 + 2 = 92
→ Answer:
92/3
28) 9 2/7
→ 9 × 7 = 63
→ 63 + 2 = 65
→ Answer:
65/7
29) 6 9/10
→ 6 × 10 = 60
→ 60 + 9 = 69
→ Answer:
69/10
30) 25 2/3
→ 25 × 3 = 75
→ 75 + 2 = 77
→ Answer:
77/3
31) 16 4/5
→ 16 × 5 = 80
→ 80 + 4 = 84
→ Answer:
84/5
32) 8 6/11
→ 8 × 11 = 88
→ 88 + 6 = 94
→ Answer:
94/11
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Final Answer:
1) 11/3
2) 17/4
3) 17/7
4) 19/2
5) 23/4
6) 36/5
7) 29/6
8) 8/3
9) 39/10
10) 47/7
11) 83/10
12) 39/8
13) 77/8
14) 49/15
15) 35/3
16) 23/3
17) 68/11
18) 51/4
19) 72/5
20) 76/9
21) 29/4
22) 70/3
23) 93/8
24) 59/14
25) 83/4
26) 25/2
27) 92/3
28) 65/7
29) 69/10
30) 77/3
31) 84/5
32) 94/11
Parent Tip: Review the logic above to help your child master the concept of improper fractions to mixed numbers worksheets.
