Multiplying mixed numbers worksheets | Worsheets library - Free Printable

To solve these problems, we need to multiply mixed numbers. Here is the step-by-step method for each one:

1. Convert mixed numbers to improper fractions.
* Multiply the whole number by the denominator.
* Add the numerator.
* Place the result over the original denominator.
2. Multiply the fractions.
* Multiply the top numbers (numerators) together.
* Multiply the bottom numbers (denominators) together.
3. Simplify and convert back to a mixed number.
* If possible, simplify the fraction before or after multiplying.
* Divide the numerator by the denominator to get the whole number part. The remainder becomes the new numerator.

Let's solve each problem:

1. $1 \frac{1}{2} \times 3 \frac{3}{5}$
* Convert: $1 \frac{1}{2} = \frac{3}{2}$ and $3 \frac{3}{5} = \frac{18}{5}$
* Multiply: $\frac{3}{2} \times \frac{18}{5} = \frac{3 \times 18}{2 \times 5} = \frac{54}{10}$
* Simplify: $\frac{54}{10} = \frac{27}{5}$
* Convert back: $27 \div 5 = 5$ with a remainder of $2$. So, $5 \frac{2}{5}$.

2. $1 \frac{1}{6} \times 2 \frac{6}{13}$
* Convert: $1 \frac{1}{6} = \frac{7}{6}$ and $2 \frac{6}{13} = \frac{32}{13}$
* Multiply: $\frac{7}{6} \times \frac{32}{13}$
* Simplify before multiplying: $6$ and $32$ are both divisible by $2$. $\frac{7}{3} \times \frac{16}{13} = \frac{112}{39}$
* Convert back: $112 \div 39 = 2$ with a remainder of $34$ ($39 \times 2 = 78$, $112 - 78 = 34$). So, $2 \frac{34}{39}$.

3. $2 \frac{1}{3} \times 3 \frac{3}{5}$
* Convert: $2 \frac{1}{3} = \frac{7}{3}$ and $3 \frac{3}{5} = \frac{18}{5}$
* Multiply: $\frac{7}{3} \times \frac{18}{5}$
* Simplify before multiplying: $3$ and $18$ are divisible by $3$. $\frac{7}{1} \times \frac{6}{5} = \frac{42}{5}$
* Convert back: $42 \div 5 = 8$ with a remainder of $2$. So, $8 \frac{2}{5}$.

4. $3 \frac{1}{5} \times 1 \frac{5}{16}$
* Convert: $3 \frac{1}{5} = \frac{16}{5}$ and $1 \frac{5}{16} = \frac{21}{16}$
* Multiply: $\frac{16}{5} \times \frac{21}{16}$
* Simplify before multiplying: The $16$s cancel out. $\frac{1}{5} \times \frac{21}{1} = \frac{21}{5}$
* Convert back: $21 \div 5 = 4$ with a remainder of $1$. So, $4 \frac{1}{5}$.

5. $3 \frac{1}{2} \times 3 \frac{3}{5}$
* Convert: $3 \frac{1}{2} = \frac{7}{2}$ and $3 \frac{3}{5} = \frac{18}{5}$
* Multiply: $\frac{7}{2} \times \frac{18}{5}$
* Simplify before multiplying: $2$ and $18$ are divisible by $2$. $\frac{7}{1} \times \frac{9}{5} = \frac{63}{5}$
* Convert back: $63 \div 5 = 12$ with a remainder of $3$. So, $12 \frac{3}{5}$.

6. $3 \frac{5}{9} \times 2 \frac{1}{3}$
* Convert: $3 \frac{5}{9} = \frac{32}{9}$ and $2 \frac{1}{3} = \frac{7}{3}$
* Multiply: $\frac{32}{9} \times \frac{7}{3} = \frac{224}{27}$
* Convert back: $224 \div 27$. Let's estimate. $27 \times 10 = 270$ (too high). $27 \times 8 = 216$. $224 - 216 = 8$. So, $8 \frac{8}{27}$.

7. $1 \frac{1}{2} \times 3 \frac{1}{2}$
* Convert: $1 \frac{1}{2} = \frac{3}{2}$ and $3 \frac{1}{2} = \frac{7}{2}$
* Multiply: $\frac{3}{2} \times \frac{7}{2} = \frac{21}{4}$
* Convert back: $21 \div 4 = 5$ with a remainder of $1$. So, $5 \frac{1}{4}$.

8. $1 \frac{8}{12} \times 3 \frac{2}{10}$
* Simplify fractions first: $1 \frac{8}{12} = 1 \frac{2}{3}$ and $3 \frac{2}{10} = 3 \frac{1}{5}$
* Convert: $1 \frac{2}{3} = \frac{5}{3}$ and $3 \frac{1}{5} = \frac{16}{5}$
* Multiply: $\frac{5}{3} \times \frac{16}{5}$
* Simplify before multiplying: The $5$s cancel out. $\frac{1}{3} \times \frac{16}{1} = \frac{16}{3}$
* Convert back: $16 \div 3 = 5$ with a remainder of $1$. So, $5 \frac{1}{3}$.

9. $3 \frac{2}{5} \times 3 \frac{1}{3}$
* Convert: $3 \frac{2}{5} = \frac{17}{5}$ and $3 \frac{1}{3} = \frac{10}{3}$
* Multiply: $\frac{17}{5} \times \frac{10}{3}$
* Simplify before multiplying: $5$ and $10$ are divisible by $5$. $\frac{17}{1} \times \frac{2}{3} = \frac{34}{3}$
* Convert back: $34 \div 3 = 11$ with a remainder of $1$. So, $11 \frac{1}{3}$.

10. $3 \frac{4}{5} \times 2 \frac{2}{3}$
* Convert: $3 \frac{4}{5} = \frac{19}{5}$ and $2 \frac{2}{3} = \frac{8}{3}$
* Multiply: $\frac{19}{5} \times \frac{8}{3} = \frac{152}{15}$
* Convert back: $152 \div 15$. $15 \times 10 = 150$. Remainder is $2$. So, $10 \frac{2}{15}$.

11. $1 \frac{3}{4} \times 1 \frac{1}{4}$
* Convert: $1 \frac{3}{4} = \frac{7}{4}$ and $1 \frac{1}{4} = \frac{5}{4}$
* Multiply: $\frac{7}{4} \times \frac{5}{4} = \frac{35}{16}$
* Convert back: $35 \div 16 = 2$ with a remainder of $3$ ($16 \times 2 = 32$). So, $2 \frac{3}{16}$.

12. $2 \frac{4}{5} \times 1 \frac{1}{12}$
* Convert: $2 \frac{4}{5} = \frac{14}{5}$ and $1 \frac{1}{12} = \frac{13}{12}$
* Multiply: $\frac{14}{5} \times \frac{13}{12}$
* Simplify before multiplying: $14$ and $12$ are divisible by $2$. $\frac{7}{5} \times \frac{13}{6} = \frac{91}{30}$
* Convert back: $91 \div 30 = 3$ with a remainder of $1$ ($30 \times 3 = 90$). So, $3 \frac{1}{30}$.

13. $1 \frac{5}{9} \times 2 \frac{2}{5}$
* Convert: $1 \frac{5}{9} = \frac{14}{9}$ and $2 \frac{2}{5} = \frac{12}{5}$
* Multiply: $\frac{14}{9} \times \frac{12}{5}$
* Simplify before multiplying: $12$ and $9$ are divisible by $3$. $\frac{14}{3} \times \frac{4}{5} = \frac{56}{15}$
* Convert back: $56 \div 15 = 3$ with a remainder of $11$ ($15 \times 3 = 45$, $56 - 45 = 11$). So, $3 \frac{11}{15}$.

14. $3 \frac{2}{5} \times 1 \frac{1}{2}$
* Convert: $3 \frac{2}{5} = \frac{17}{5}$ and $1 \frac{1}{2} = \frac{3}{2}$
* Multiply: $\frac{17}{5} \times \frac{3}{2} = \frac{51}{10}$
* Convert back: $51 \div 10 = 5$ with a remainder of $1$. So, $5 \frac{1}{10}$.

Final Answer:
1. $5 \frac{2}{5}$
2. $2 \frac{34}{39}$
3. $8 \frac{2}{5}$
4. $4 \frac{1}{5}$
5. $12 \frac{3}{5}$
6. $8 \frac{8}{27}$
7. $5 \frac{1}{4}$
8. $5 \frac{1}{3}$
9. $11 \frac{1}{3}$
10. $10 \frac{2}{15}$
11. $2 \frac{3}{16}$
12. $3 \frac{1}{30}$
13. $3 \frac{11}{15}$
14. $5 \frac{1}{10}$