Multiplying Mixed Numbers with Whole Numbers Worksheets - Free Printable

Let's solve each problem step by step. The task is to multiply mixed numbers and whole numbers.

We'll follow these steps for each problem:

1. Convert the mixed number into an improper fraction.
2. Multiply the improper fraction by the whole number.
3. Simplify the result and convert back to a mixed number if needed.

---

1) $ 6\frac{2}{3} \times 9 $

Convert $ 6\frac{2}{3} $ to improper fraction:
$$
6\frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{18 + 2}{3} = \frac{20}{3}
$$

Now multiply:
$$
\frac{20}{3} \times 9 = \frac{20 \times 9}{3} = \frac{180}{3} = 60
$$

✔ Answer: 60

---

2) $ 7 \times 1\frac{2}{9} $

Convert $ 1\frac{2}{9} $:
$$
1\frac{2}{9} = \frac{9 \times 1 + 2}{9} = \frac{11}{9}
$$

Multiply:
$$
7 \times \frac{11}{9} = \frac{77}{9}
$$

Convert to mixed number:
$$
\frac{77}{9} = 8\frac{5}{9} \quad (\text{since } 9 \times 8 = 72, \; 77 - 72 = 5)
$$

✔ Answer: $ 8\frac{5}{9} $

---

3) $ 11 \times 2\frac{2}{7} $

Convert $ 2\frac{2}{7} $:
$$
2\frac{2}{7} = \frac{2 \times 7 + 2}{7} = \frac{14 + 2}{7} = \frac{16}{7}
$$

Multiply:
$$
11 \times \frac{16}{7} = \frac{176}{7}
$$

Convert:
$$
\frac{176}{7} = 25\frac{1}{7} \quad (7 \times 25 = 175, \; 176 - 175 = 1)
$$

✔ Answer: $ 25\frac{1}{7} $

---

4) $ 2\frac{1}{4} \times 8 $

Convert $ 2\frac{1}{4} $:
$$
2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4}
$$

Multiply:
$$
\frac{9}{4} \times 8 = \frac{72}{4} = 18
$$

✔ Answer: 18

---

5) $ 10\frac{9}{10} \times 10 $

Convert $ 10\frac{9}{10} $:
$$
10\frac{9}{10} = \frac{10 \times 10 + 9}{10} = \frac{109}{10}
$$

Multiply:
$$
\frac{109}{10} \times 10 = \frac{1090}{10} = 109
$$

✔ Answer: 109

---

6) $ 6 \times 1\frac{7}{12} $

Convert $ 1\frac{7}{12} $:
$$
1\frac{7}{12} = \frac{12 \times 1 + 7}{12} = \frac{19}{12}
$$

Multiply:
$$
6 \times \frac{19}{12} = \frac{114}{12} = \frac{19}{2} \quad (\text{divide numerator and denominator by 6})
$$

Convert:
$$
\frac{19}{2} = 9\frac{1}{2}
$$

✔ Answer: $ 9\frac{1}{2} $

---

7) $ 2 \times 3\frac{2}{9} $

Convert $ 3\frac{2}{9} $:
$$
3\frac{2}{9} = \frac{3 \times 9 + 2}{9} = \frac{27 + 2}{9} = \frac{29}{9}
$$

Multiply:
$$
2 \times \frac{29}{9} = \frac{58}{9}
$$

Convert:
$$
\frac{58}{9} = 6\frac{4}{9} \quad (9 \times 6 = 54, \; 58 - 54 = 4)
$$

✔ Answer: $ 6\frac{4}{9} $

---

8) $ 2\frac{3}{5} \times 15 $

Convert $ 2\frac{3}{5} $:
$$
2\frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{13}{5}
$$

Multiply:
$$
\frac{13}{5} \times 15 = \frac{195}{5} = 39
$$

✔ Answer: 39

---

9) $ 2\frac{5}{6} \times 12 $

Convert $ 2\frac{5}{6} $:
$$
2\frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{17}{6}
$$

Multiply:
$$
\frac{17}{6} \times 12 = \frac{204}{6} = 34
$$

✔ Answer: 34

---

10) $ 4 \times 7\frac{1}{2} $

Convert $ 7\frac{1}{2} $:
$$
7\frac{1}{2} = \frac{7 \times 2 + 1}{2} = \frac{15}{2}
$$

Multiply:
$$
4 \times \frac{15}{2} = \frac{60}{2} = 30
$$

✔ Answer: 30

---

11) $ 5 \times 3\frac{7}{8} $

Convert $ 3\frac{7}{8} $:
$$
3\frac{7}{8} = \frac{3 \times 8 + 7}{8} = \frac{24 + 7}{8} = \frac{31}{8}
$$

Multiply:
$$
5 \times \frac{31}{8} = \frac{155}{8}
$$

Convert:
$$
\frac{155}{8} = 19\frac{3}{8} \quad (8 \times 19 = 152, \; 155 - 152 = 3)
$$

✔ Answer: $ 19\frac{3}{8} $

---

12) $ 1\frac{10}{11} \times 2 $

Convert $ 1\frac{10}{11} $:
$$
1\frac{10}{11} = \frac{1 \times 11 + 10}{11} = \frac{21}{11}
$$

Multiply:
$$
\frac{21}{11} \times 2 = \frac{42}{11}
$$

Convert:
$$
\frac{42}{11} = 3\frac{9}{11} \quad (11 \times 3 = 33, \; 42 - 33 = 9)
$$

✔ Answer: $ 3\frac{9}{11} $

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✔ Final Answers:

1) 60
2) $ 8\frac{5}{9} $
3) $ 25\frac{1}{7} $
4) 18
5) 109
6) $ 9\frac{1}{2} $
7) $ 6\frac{4}{9} $
8) 39
9) 34
10) 30
11) $ 19\frac{3}{8} $
12) $ 3\frac{9}{11} $

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