Fractions Worksheets | Printable Fractions Worksheets for Teachers - Free Printable

Here are the solutions to the problems on the worksheet.

Part 1: Converting Improper Fractions to Mixed Numbers

To solve these, divide the top number (numerator) by the bottom number (denominator). The answer is the whole number, the remainder becomes the new top number, and the bottom number stays the same.

1) 29 ÷ 4 = 7 with a remainder of 1.
Answer: $7 \frac{1}{4}$

2) 13 ÷ 6 = 2 with a remainder of 1.
Answer: $2 \frac{1}{6}$

3) 73 ÷ 9 = 8 with a remainder of 1 ($9 \times 8 = 72$).
Answer: $8 \frac{1}{9}$

4) 65 ÷ 8 = 8 with a remainder of 1 ($8 \times 8 = 64$).
Answer: $8 \frac{1}{8}$

5) 17 ÷ 2 = 8 with a remainder of 1.
Answer: $8 \frac{1}{2}$

6) 5 ÷ 2 = 2 with a remainder of 1.
Answer: $2 \frac{1}{2}$

7) 25 ÷ 4 = 6 with a remainder of 1 ($4 \times 6 = 24$).
Answer: $6 \frac{1}{4}$

8) 43 ÷ 7 = 6 with a remainder of 1 ($7 \times 6 = 42$).
Answer: $6 \frac{1}{7}$

9) 29 ÷ 4 = 7 with a remainder of 1.
Answer: $7 \frac{1}{4}$

10) 73 ÷ 9 = 8 with a remainder of 1.
Answer: $8 \frac{1}{9}$

11) 19 ÷ 3 = 6 with a remainder of 1 ($3 \times 6 = 18$).
Answer: $6 \frac{1}{3}$

12) 43 ÷ 7 = 6 with a remainder of 1.
Answer: $6 \frac{1}{7}$

13) 11 ÷ 5 = 2 with a remainder of 1.
Answer: $2 \frac{1}{5}$

14) 91 ÷ 10 = 9 with a remainder of 1.
Answer: $9 \frac{1}{10}$

15) 37 ÷ 6 = 6 with a remainder of 1 ($6 \times 6 = 36$).
Answer: $6 \frac{1}{6}$

***

Part 2: Converting Mixed Numbers to Improper Fractions

To solve these, multiply the whole number by the denominator, then add the numerator. Keep the denominator the same.
*(Formula: Whole $\times$ Bottom + Top = New Top)*

1) $7 \frac{1}{3}$: $(7 \times 3) + 1 = 21 + 1 = 22$.
Answer: $\frac{22}{3}$

2) $7 \frac{9}{10}$: $(7 \times 10) + 9 = 70 + 9 = 79$.
Answer: $\frac{79}{10}$

3) $7 \frac{3}{4}$: $(7 \times 4) + 3 = 28 + 3 = 31$.
Answer: $\frac{31}{4}$

4) $2 \frac{1}{2}$: $(2 \times 2) + 1 = 4 + 1 = 5$.
Answer: $\frac{5}{2}$

5) $8 \frac{4}{7}$: $(8 \times 7) + 4 = 56 + 4 = 60$.
Answer: $\frac{60}{7}$

6) $2 \frac{3}{5}$: $(2 \times 5) + 3 = 10 + 3 = 13$.
Answer: $\frac{13}{5}$

7) $3 \frac{5}{8}$: $(3 \times 8) + 5 = 24 + 5 = 29$.
Answer: $\frac{29}{8}$

8) $6 \frac{7}{9}$: $(6 \times 9) + 7 = 54 + 7 = 61$.
Answer: $\frac{61}{9}$

9) $9 \frac{1}{8}$: $(9 \times 8) + 1 = 72 + 1 = 73$.
Answer: $\frac{73}{8}$

10) $6 \frac{2}{5}$: $(6 \times 5) + 2 = 30 + 2 = 32$.
Answer: $\frac{32}{5}$

11) $4 \frac{1}{3}$: $(4 \times 3) + 1 = 12 + 1 = 13$.
Answer: $\frac{13}{3}$

12) $2 \frac{2}{3}$: $(2 \times 3) + 2 = 6 + 2 = 8$.
Answer: $\frac{8}{3}$

13) $8 \frac{1}{2}$: $(8 \times 2) + 1 = 16 + 1 = 17$.
Answer: $\frac{17}{2}$

14) $4 \frac{3}{10}$: $(4 \times 10) + 3 = 40 + 3 = 43$.
Answer: $\frac{43}{10}$

15) $8 \frac{4}{5}$: $(8 \times 5) + 4 = 40 + 4 = 44$.
Answer: $\frac{44}{5}$

Final Answer:
Converting Improper Fractions to Mixed Numbers:
1) $7 \frac{1}{4}$
2) $2 \frac{1}{6}$
3) $8 \frac{1}{9}$
4) $8 \frac{1}{8}$
5) $8 \frac{1}{2}$
6) $2 \frac{1}{2}$
7) $6 \frac{1}{4}$
8) $6 \frac{1}{7}$
9) $7 \frac{1}{4}$
10) $8 \frac{1}{9}$
11) $6 \frac{1}{3}$
12) $6 \frac{1}{7}$
13) $2 \frac{1}{5}$
14) $9 \frac{1}{10}$
15) $6 \frac{1}{6}$

Converting Mixed Numbers to Improper Fractions:
1) $\frac{22}{3}$
2) $\frac{79}{10}$
3) $\frac{31}{4}$
4) $\frac{5}{2}$
5) $\frac{60}{7}$
6) $\frac{13}{5}$
7) $\frac{29}{8}$
8) $\frac{61}{9}$
9) $\frac{73}{8}$
10) $\frac{32}{5}$
11) $\frac{13}{3}$
12) $\frac{8}{3}$
13) $\frac{17}{2}$
14) $\frac{43}{10}$
15) $\frac{44}{5}$