Grade 6 Multiplying Fractions Worksheets | Free Worksheets ... - Free Printable

Problem: Solving the Multiplying Fractions Worksheet

The worksheet involves multiplying fractions. The general rule for multiplying fractions is:

\[
\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}
\]

After multiplying, simplify the resulting fraction if possible.

Let's solve each problem step by step.

---

Section 1: First Set of Problems

#### 1. $\frac{1}{2} \times \frac{1}{2}$
\[
\frac{1}{2} \times \frac{1}{2} = \frac{1 \times 1}{2 \times 2} = \frac{1}{4}
\]
Answer: $\frac{1}{4}$

#### 2. $\frac{3}{4} \times \frac{1}{5}$
\[
\frac{3}{4} \times \frac{1}{5} = \frac{3 \times 1}{4 \times 5} = \frac{3}{20}
\]
Answer: $\frac{3}{20}$

#### 3. $\frac{9}{10} \times \frac{5}{6}$
\[
\frac{9}{10} \times \frac{5}{6} = \frac{9 \times 5}{10 \times 6} = \frac{45}{60}
\]
Simplify $\frac{45}{60}$ by dividing numerator and denominator by their greatest common divisor (GCD), which is 15:
\[
\frac{45 \div 15}{60 \div 15} = \frac{3}{4}
\]
Answer: $\frac{3}{4}$

#### 4. $\frac{1}{5} \times \frac{10}{11}$
\[
\frac{1}{5} \times \frac{10}{11} = \frac{1 \times 10}{5 \times 11} = \frac{10}{55}
\]
Simplify $\frac{10}{55}$ by dividing numerator and denominator by their GCD, which is 5:
\[
\frac{10 \div 5}{55 \div 5} = \frac{2}{11}
\]
Answer: $\frac{2}{11}$

#### 5. $\frac{3}{7} \times \frac{1}{9}$
\[
\frac{3}{7} \times \frac{1}{9} = \frac{3 \times 1}{7 \times 9} = \frac{3}{63}
\]
Simplify $\frac{3}{63}$ by dividing numerator and denominator by their GCD, which is 3:
\[
\frac{3 \div 3}{63 \div 3} = \frac{1}{21}
\]
Answer: $\frac{1}{21}$

#### 6. $\frac{4}{9} \times \frac{3}{8}$
\[
\frac{4}{9} \times \frac{3}{8} = \frac{4 \times 3}{9 \times 8} = \frac{12}{72}
\]
Simplify $\frac{12}{72}$ by dividing numerator and denominator by their GCD, which is 12:
\[
\frac{12 \div 12}{72 \div 12} = \frac{1}{6}
\]
Answer: $\frac{1}{6}$

#### 7. $\frac{5}{6} \times \frac{10}{15}$
\[
\frac{5}{6} \times \frac{10}{15} = \frac{5 \times 10}{6 \times 15} = \frac{50}{90}
\]
Simplify $\frac{50}{90}$ by dividing numerator and denominator by their GCD, which is 10:
\[
\frac{50 \div 10}{90 \div 10} = \frac{5}{9}
\]
Answer: $\frac{5}{9}$

#### 8. $\frac{9}{10} \times \frac{8}{9}$
\[
\frac{9}{10} \times \frac{8}{9} = \frac{9 \times 8}{10 \times 9} = \frac{72}{90}
\]
Simplify $\frac{72}{90}$ by dividing numerator and denominator by their GCD, which is 18:
\[
\frac{72 \div 18}{90 \div 18} = \frac{4}{5}
\]
Answer: $\frac{4}{5}$

#### 9. $\frac{4}{9} \times \frac{1}{8}$
\[
\frac{4}{9} \times \frac{1}{8} = \frac{4 \times 1}{9 \times 8} = \frac{4}{72}
\]
Simplify $\frac{4}{72}$ by dividing numerator and denominator by their GCD, which is 4:
\[
\frac{4 \div 4}{72 \div 4} = \frac{1}{18}
\]
Answer: $\frac{1}{18}$

#### 10. $\frac{6}{7} \times \frac{4}{5}$
\[
\frac{6}{7} \times \frac{4}{5} = \frac{6 \times 4}{7 \times 5} = \frac{24}{35}
\]
Answer: $\frac{24}{35}$

#### 11. $\frac{14}{20} \times \frac{10}{12}$
\[
\frac{14}{20} \times \frac{10}{12} = \frac{14 \times 10}{20 \times 12} = \frac{140}{240}
\]
Simplify $\frac{140}{240}$ by dividing numerator and denominator by their GCD, which is 20:
\[
\frac{140 \div 20}{240 \div 20} = \frac{7}{12}
\]
Answer: $\frac{7}{12}$

#### 12. $\frac{5}{7} \times \frac{1}{2}$
\[
\frac{5}{7} \times \frac{1}{2} = \frac{5 \times 1}{7 \times 2} = \frac{5}{14}
\]
Answer: $\frac{5}{14}$

---

Section 2: Second Set of Problems

#### 1. $\frac{12}{15} \times \frac{5}{6}$
\[
\frac{12}{15} \times \frac{5}{6} = \frac{12 \times 5}{15 \times 6} = \frac{60}{90}
\]
Simplify $\frac{60}{90}$ by dividing numerator and denominator by their GCD, which is 30:
\[
\frac{60 \div 30}{90 \div 30} = \frac{2}{3}
\]
Answer: $\frac{2}{3}$

#### 2. $\frac{8}{9} \times \frac{9}{10}$
\[
\frac{8}{9} \times \frac{9}{10} = \frac{8 \times 9}{9 \times 10} = \frac{72}{90}
\]
Simplify $\frac{72}{90}$ by dividing numerator and denominator by their GCD, which is 18:
\[
\frac{72 \div 18}{90 \div 18} = \frac{4}{5}
\]
Answer: $\frac{4}{5}$

#### 3. $\frac{1}{2} \times \frac{3}{4}$
\[
\frac{1}{2} \times \frac{3}{4} = \frac{1 \times 3}{2 \times 4} = \frac{3}{8}
\]
Answer: $\frac{3}{8}$

#### 4. $\frac{7}{8} \times \frac{2}{5}$
\[
\frac{7}{8} \times \frac{2}{5} = \frac{7 \times 2}{8 \times 5} = \frac{14}{40}
\]
Simplify $\frac{14}{40}$ by dividing numerator and denominator by their GCD, which is 2:
\[
\frac{14 \div 2}{40 \div 2} = \frac{7}{20}
\]
Answer: $\frac{7}{20}$

#### 5. $\frac{6}{7} \times \frac{1}{7}$
\[
\frac{6}{7} \times \frac{1}{7} = \frac{6 \times 1}{7 \times 7} = \frac{6}{49}
\]
Answer: $\frac{6}{49}$

#### 6. $\frac{8}{10} \times \frac{5}{7}$
\[
\frac{8}{10} \times \frac{5}{7} = \frac{8 \times 5}{10 \times 7} = \frac{40}{70}
\]
Simplify $\frac{40}{70}$ by dividing numerator and denominator by their GCD, which is 10:
\[
\frac{40 \div 10}{70 \div 10} = \frac{4}{7}
\]
Answer: $\frac{4}{7}$

#### 7. $\frac{1}{10} \times \frac{1}{5}$
\[
\frac{1}{10} \times \frac{1}{5} = \frac{1 \times 1}{10 \times 5} = \frac{1}{50}
\]
Answer: $\frac{1}{50}$

#### 8. $\frac{7}{8} \times \frac{2}{5}$
\[
\frac{7}{8} \times \frac{2}{5} = \frac{7 \times 2}{8 \times 5} = \frac{14}{40}
\]
Simplify $\frac{14}{40}$ by dividing numerator and denominator by their GCD, which is 2:
\[
\frac{14 \div 2}{40 \div 2} = \frac{7}{20}
\]
Answer: $\frac{7}{20}$

#### 9. $\frac{8}{11} \times \frac{3}{4}$
\[
\frac{8}{11} \times \frac{3}{4} = \frac{8 \times 3}{11 \times 4} = \frac{24}{44}
\]
Simplify $\frac{24}{44}$ by dividing numerator and denominator by their GCD, which is 4:
\[
\frac{24 \div 4}{44 \div 4} = \frac{6}{11}
\]
Answer: $\frac{6}{11}$

#### 10. $\frac{5}{9} \times \frac{3}{4}$
\[
\frac{5}{9} \times \frac{3}{4} = \frac{5 \times 3}{9 \times 4} = \frac{15}{36}
\]
Simplify $\frac{15}{36}$ by dividing numerator and denominator by their GCD, which is 3:
\[
\frac{15 \div 3}{36 \div 3} = \frac{5}{12}
\]
Answer: $\frac{5}{12}$

#### 11. $\frac{3}{4} \times \frac{3}{4}$
\[
\frac{3}{4} \times \frac{3}{4} = \frac{3 \times 3}{4 \times 4} = \frac{9}{16}
\]
Answer: $\frac{9}{16}$

#### 12. $\frac{4}{5} \times \frac{8}{10}$
\[
\frac{4}{5} \times \frac{8}{10} = \frac{4 \times 8}{5 \times 10} = \frac{32}{50}
\]
Simplify $\frac{32}{50}$ by dividing numerator and denominator by their GCD, which is 2:
\[
\frac{32 \div 2}{50 \div 2} = \frac{16}{25}
\]
Answer: $\frac{16}{25}$

---

Final Answers:

#### First Set:
1. $\frac{1}{4}$
2. $\frac{3}{20}$
3. $\frac{3}{4}$
4. $\frac{2}{11}$
5. $\frac{1}{21}$
6. $\frac{1}{6}$
7. $\frac{5}{9}$
8. $\frac{4}{5}$
9. $\frac{1}{18}$
10. $\frac{24}{35}$
11. $\frac{7}{12}$
12. $\frac{5}{14}$

#### Second Set:
1. $\frac{2}{3}$
2. $\frac{4}{5}$
3. $\frac{3}{8}$
4. $\frac{7}{20}$
5. $\frac{6}{49}$
6. $\frac{4}{7}$
7. $\frac{1}{50}$
8. $\frac{7}{20}$
9. $\frac{6}{11}$
10. $\frac{5}{12}$
11. $\frac{9}{16}$
12. $\frac{16}{25}$

---

Boxed Final Answer:

\[
\boxed{
\begin{array}{ccc}
\text{First Set:} & & \text{Second Set:} \\
1. \frac{1}{4} & 5. \frac{1}{21} & 9. \frac{1}{18} \\
2. \frac{3}{20} & 6. \frac{1}{6} & 10. \frac{24}{35} \\
3. \frac{3}{4} & 7. \frac{5}{9} & 11. \frac{7}{12} \\
4. \frac{2}{11} & 8. \frac{4}{5} & 12. \frac{5}{14} \\
& & \\
1. \frac{2}{3} & 5. \frac{6}{49} & 9. \frac{6}{11} \\
2. \frac{4}{5} & 6. \frac{4}{7} & 10. \frac{5}{12} \\
3. \frac{3}{8} & 7. \frac{1}{50} & 11. \frac{9}{16} \\
4. \frac{7}{20} & 8. \frac{7}{20} & 12. \frac{16}{25} \\
\end{array}
}
\]