Multiplying Mixed Numbers Worksheets - Free Printable

Problem Analysis:

The worksheet involves solving problems related to multiplication and division of fractions. Let's break down each part step by step.

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Part A: Find the value of \( x \)

#### 1) \( \frac{3}{4} \times \frac{1}{2} = x \)

To solve for \( x \):
- Multiply the numerators: \( 3 \times 1 = 3 \)
- Multiply the denominators: \( 4 \times 2 = 8 \)
- The product is: \( \frac{3}{8} \)

Thus, \( x = \frac{3}{8} \).

#### 2) \( \frac{5}{11} + \frac{7}{11} = x \)

This is an addition problem, not multiplication. To solve for \( x \):
- Add the numerators since the denominators are the same: \( 5 + 7 = 12 \)
- The denominator remains \( 11 \)
- The sum is: \( \frac{12}{11} \)

Thus, \( x = \frac{12}{11} \).

#### 3) \( x \div 6 = \frac{4}{5} \)

To solve for \( x \):
- Rewrite the division as multiplication by the reciprocal: \( x = \frac{4}{5} \times 6 \)
- Convert \( 6 \) to a fraction: \( 6 = \frac{6}{1} \)
- Multiply: \( \frac{4}{5} \times \frac{6}{1} = \frac{4 \times 6}{5 \times 1} = \frac{24}{5} \)

Thus, \( x = \frac{24}{5} \).

#### 4) \( x \times \frac{1}{2} = \frac{7}{10} \)

To solve for \( x \):
- Isolate \( x \) by multiplying both sides by the reciprocal of \( \frac{1}{2} \), which is \( 2 \):
\[
x = \frac{7}{10} \times 2
\]
- Convert \( 2 \) to a fraction: \( 2 = \frac{2}{1} \)
- Multiply: \( \frac{7}{10} \times \frac{2}{1} = \frac{7 \times 2}{10 \times 1} = \frac{14}{10} \)
- Simplify \( \frac{14}{10} \) by dividing numerator and denominator by their greatest common divisor (GCD), which is 2:
\[
\frac{14}{10} = \frac{7}{5}
\]

Thus, \( x = \frac{7}{5} \).

#### 5) \( 2 \times \frac{2}{3} = x \)

To solve for \( x \):
- Multiply the whole number \( 2 \) by the fraction \( \frac{2}{3} \):
\[
2 \times \frac{2}{3} = \frac{2 \times 2}{3} = \frac{4}{3}
\]

Thus, \( x = \frac{4}{3} \).

#### 6) \( x \times 1 \frac{3}{11} = 8 \frac{3}{4} \)

First, convert the mixed numbers to improper fractions:
- \( 1 \frac{3}{11} = \frac{11 \times 1 + 3}{11} = \frac{14}{11} \)
- \( 8 \frac{3}{4} = \frac{4 \times 8 + 3}{4} = \frac{35}{4} \)

Now, solve for \( x \):
- Rewrite the equation: \( x \times \frac{14}{11} = \frac{35}{4} \)
- Isolate \( x \) by multiplying both sides by the reciprocal of \( \frac{14}{11} \), which is \( \frac{11}{14} \):
\[
x = \frac{35}{4} \times \frac{11}{14}
\]
- Multiply the fractions:
\[
x = \frac{35 \times 11}{4 \times 14} = \frac{385}{56}
\]
- Simplify \( \frac{385}{56} \) by finding the GCD of 385 and 56, which is 7:
\[
\frac{385}{56} = \frac{385 \div 7}{56 \div 7} = \frac{55}{8}
\]

Thus, \( x = \frac{55}{8} \).

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Part B: The product of two fractions is \( 6 \frac{2}{7} \). If one of the fractions is \( 3 \frac{5}{7} \), what is the other fraction?

First, convert the mixed numbers to improper fractions:
- \( 6 \frac{2}{7} = \frac{7 \times 6 + 2}{7} = \frac{44}{7} \)
- \( 3 \frac{5}{7} = \frac{7 \times 3 + 5}{7} = \frac{26}{7} \)

Let the other fraction be \( x \). The equation is:
\[
x \times \frac{26}{7} = \frac{44}{7}
\]

Solve for \( x \):
- Isolate \( x \) by multiplying both sides by the reciprocal of \( \frac{26}{7} \), which is \( \frac{7}{26} \):
\[
x = \frac{44}{7} \times \frac{7}{26}
\]
- Multiply the fractions:
\[
x = \frac{44 \times 7}{7 \times 26} = \frac{44}{26}
\]
- Simplify \( \frac{44}{26} \) by finding the GCD of 44 and 26, which is 2:
\[
\frac{44}{26} = \frac{44 \div 2}{26 \div 2} = \frac{22}{13}
\]

Thus, the other fraction is \( \frac{22}{13} \).

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Part C: What is the product of the fractions \( 4 \frac{2}{9} \) and \( 4 \frac{2}{9} \)?

First, convert the mixed numbers to improper fractions:
- \( 4 \frac{2}{9} = \frac{9 \times 4 + 2}{9} = \frac{38}{9} \)

Now, find the product:
\[
\left( \frac{38}{9} \right) \times \left( \frac{38}{9} \right) = \frac{38 \times 38}{9 \times 9} = \frac{1444}{81}
\]

Convert \( \frac{1444}{81} \) to a mixed number:
- Divide 1444 by 81: \( 1444 \div 81 = 17 \) remainder \( 77 \)
- Write as a mixed number: \( 17 \frac{77}{81} \)

Thus, the product is \( 17 \frac{77}{81} \).

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Final Answers:

Part A:
1. \( x = \frac{3}{8} \)
2. \( x = \frac{12}{11} \)
3. \( x = \frac{24}{5} \)
4. \( x = \frac{7}{5} \)
5. \( x = \frac{4}{3} \)
6. \( x = \frac{55}{8} \)

Part B:
The other fraction is \( \frac{22}{13} \).

Part C:
The product is \( 17 \frac{77}{81} \).

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Boxed Final Answer:
\[
\boxed{\frac{22}{13}, 17 \frac{77}{81}}
\]