301 Moved Permanently - Free Printable

Problem: Solve the multiplication of fractions and mixed numbers as given in the worksheet.

We will solve each problem step by step. Let's begin!

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#### 1. \( 5 \frac{6}{7} \times \frac{5}{8} \)

Step 1: Convert the mixed number \( 5 \frac{6}{7} \) to an improper fraction.
\[
5 \frac{6}{7} = \frac{5 \times 7 + 6}{7} = \frac{35 + 6}{7} = \frac{41}{7}
\]

Step 2: Multiply the fractions.
\[
\frac{41}{7} \times \frac{5}{8} = \frac{41 \times 5}{7 \times 8} = \frac{205}{56}
\]

Step 3: Convert the improper fraction \( \frac{205}{56} \) back to a mixed number.
\[
205 \div 56 = 3 \text{ remainder } 37 \quad \Rightarrow \quad \frac{205}{56} = 3 \frac{37}{56}
\]

Answer: \( \boxed{D} \)

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#### 2. \( 1 \frac{7}{12} \times 7 \frac{7}{12} \)

Step 1: Convert both mixed numbers to improper fractions.
\[
1 \frac{7}{12} = \frac{1 \times 12 + 7}{12} = \frac{19}{12}
\]
\[
7 \frac{7}{12} = \frac{7 \times 12 + 7}{12} = \frac{84 + 7}{12} = \frac{91}{12}
\]

Step 2: Multiply the fractions.
\[
\frac{19}{12} \times \frac{91}{12} = \frac{19 \times 91}{12 \times 12} = \frac{1729}{144}
\]

Step 3: Convert the improper fraction \( \frac{1729}{144} \) back to a mixed number.
\[
1729 \div 144 = 12 \text{ remainder } 1 \quad \Rightarrow \quad \frac{1729}{144} = 12 \frac{1}{144}
\]

Answer: \( \boxed{B} \)

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#### 3. \( 4 \frac{5}{6} \times \frac{10}{9} \)

Step 1: Convert the mixed number \( 4 \frac{5}{6} \) to an improper fraction.
\[
4 \frac{5}{6} = \frac{4 \times 6 + 5}{6} = \frac{24 + 5}{6} = \frac{29}{6}
\]

Step 2: Multiply the fractions.
\[
\frac{29}{6} \times \frac{10}{9} = \frac{29 \times 10}{6 \times 9} = \frac{290}{54}
\]

Step 3: Simplify the fraction \( \frac{290}{54} \).
\[
\text{GCD of 290 and 54 is 2} \quad \Rightarrow \quad \frac{290 \div 2}{54 \div 2} = \frac{145}{27}
\]

Step 4: Convert the improper fraction \( \frac{145}{27} \) back to a mixed number.
\[
145 \div 27 = 5 \text{ remainder } 10 \quad \Rightarrow \quad \frac{145}{27} = 5 \frac{10}{27}
\]

Answer: \( \boxed{D} \)

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#### 4. \( 10 \times \frac{16}{11} \)

Step 1: Write 10 as a fraction.
\[
10 = \frac{10}{1}
\]

Step 2: Multiply the fractions.
\[
\frac{10}{1} \times \frac{16}{11} = \frac{10 \times 16}{1 \times 11} = \frac{160}{11}
\]

Step 3: Convert the improper fraction \( \frac{160}{11} \) back to a mixed number.
\[
160 \div 11 = 14 \text{ remainder } 6 \quad \Rightarrow \quad \frac{160}{11} = 14 \frac{6}{11}
\]

Answer: \( \boxed{D} \)

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#### 5. \( \frac{7}{11} \times \frac{3}{5} \)

Step 1: Multiply the fractions.
\[
\frac{7}{11} \times \frac{3}{5} = \frac{7 \times 3}{11 \times 5} = \frac{21}{55}
\]

Answer: \( \boxed{B} \)

---

#### 6. \( 5 \frac{3}{4} \times \frac{14}{11} \)

Step 1: Convert the mixed number \( 5 \frac{3}{4} \) to an improper fraction.
\[
5 \frac{3}{4} = \frac{5 \times 4 + 3}{4} = \frac{20 + 3}{4} = \frac{23}{4}
\]

Step 2: Multiply the fractions.
\[
\frac{23}{4} \times \frac{14}{11} = \frac{23 \times 14}{4 \times 11} = \frac{322}{44}
\]

Step 3: Simplify the fraction \( \frac{322}{44} \).
\[
\text{GCD of 322 and 44 is 2} \quad \Rightarrow \quad \frac{322 \div 2}{44 \div 2} = \frac{161}{22}
\]

Step 4: Convert the improper fraction \( \frac{161}{22} \) back to a mixed number.
\[
161 \div 22 = 7 \text{ remainder } 7 \quad \Rightarrow \quad \frac{161}{22} = 7 \frac{7}{22}
\]

Answer: \( \boxed{B} \)

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#### 7. \( 3 \frac{4}{5} \times \frac{17}{12} \)

Step 1: Convert the mixed number \( 3 \frac{4}{5} \) to an improper fraction.
\[
3 \frac{4}{5} = \frac{3 \times 5 + 4}{5} = \frac{15 + 4}{5} = \frac{19}{5}
\]

Step 2: Multiply the fractions.
\[
\frac{19}{5} \times \frac{17}{12} = \frac{19 \times 17}{5 \times 12} = \frac{323}{60}
\]

Step 3: Convert the improper fraction \( \frac{323}{60} \) back to a mixed number.
\[
323 \div 60 = 5 \text{ remainder } 23 \quad \Rightarrow \quad \frac{323}{60} = 5 \frac{23}{60}
\]

Answer: \( \boxed{A} \)

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#### 8. \( 2 \times \frac{5}{4} \)

Step 1: Write 2 as a fraction.
\[
2 = \frac{2}{1}
\]

Step 2: Multiply the fractions.
\[
\frac{2}{1} \times \frac{5}{4} = \frac{2 \times 5}{1 \times 4} = \frac{10}{4}
\]

Step 3: Simplify the fraction \( \frac{10}{4} \).
\[
\text{GCD of 10 and 4 is 2} \quad \Rightarrow \quad \frac{10 \div 2}{4 \div 2} = \frac{5}{2}
\]

Step 4: Convert the improper fraction \( \frac{5}{2} \) back to a mixed number.
\[
\frac{5}{2} = 2 \frac{1}{2}
\]

Answer: \( \boxed{B} \)

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Final Answers:

1. \( \boxed{D} \)
2. \( \boxed{B} \)
3. \( \boxed{D} \)
4. \( \boxed{D} \)
5. \( \boxed{B} \)
6. \( \boxed{B} \)
7. \( \boxed{A} \)
8. \( \boxed{B} \)