Question

1. 2 4/5 x 4 1/4

119/10

1. 2 7/10 x 3 1/3

your answer

1. 3 3/4 x 3 1/2

your answer
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Explanation:

Problem 9: \( 2\frac{7}{10} \times 3\frac{1}{3} \)

Step 1: Convert mixed numbers to improper fractions

First, convert \( 2\frac{7}{10} \) to an improper fraction. Multiply the whole number (2) by the denominator (10) and add the numerator (7): \( 2 \times 10 + 7 = 27 \), so \( 2\frac{7}{10} = \frac{27}{10} \).

Next, convert \( 3\frac{1}{3} \) to an improper fraction. Multiply the whole number (3) by the denominator (3) and add the numerator (1): \( 3 \times 3 + 1 = 10 \), so \( 3\frac{1}{3} = \frac{10}{3} \).

Step 2: Multiply the improper fractions

Now, multiply \( \frac{27}{10} \times \frac{10}{3} \). The 10 in the numerator and denominator cancels out: \( \frac{27 \times \cancel{10}}{\cancel{10} \times 3} = \frac{27}{3} \).

Step 3: Simplify the result

Simplify \( \frac{27}{3} \) by dividing 27 by 3: \( 27 \div 3 = 9 \).

Step 1: Convert mixed numbers to improper fractions

First, convert \( 3\frac{3}{4} \) to an improper fraction. Multiply the whole number (3) by the denominator (4) and add the numerator (3): \( 3 \times 4 + 3 = 15 \), so \( 3\frac{3}{4} = \frac{15}{4} \).

Next, convert \( 3\frac{1}{2} \) to an improper fraction. Multiply the whole number (3) by the denominator (2) and add the numerator (1): \( 3 \times 2 + 1 = 7 \), so \( 3\frac{1}{2} = \frac{7}{2} \).

Step 2: Multiply the improper fractions

Now, multiply \( \frac{15}{4} \times \frac{7}{2} \). Multiply the numerators together and the denominators together: \( \frac{15 \times 7}{4 \times 2} = \frac{105}{8} \).

Step 3: Convert back to a mixed number (optional)

Convert \( \frac{105}{8} \) to a mixed number. Divide 105 by 8: \( 8 \times 13 = 104 \), so \( \frac{105}{8} = 13\frac{1}{8} \).

Answer:

\( 9 \)

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Problem 10: \( 3\frac{3}{4} \times 3\frac{1}{2} \)