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4i) Divide. \( 22 \frac{1}{2} \div 1 \frac{2}{3}=\square \)

Ask by Schofield Burgess. in the United States
Feb 26,2025

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Answer

The answer is 13 1/2.

Solution

Step 1: Convert the mixed numbers to improper fractions.  • 22 1/2 = (22 × 2 + 1) / 2 = 45/2  • 1 2/3 = (1 × 3 + 2) / 3 = 5/3 Step 2: Divide by multiplying by the reciprocal.  (45/2) ÷ (5/3) = (45/2) × (3/5) Step 3: Multiply the numerators and denominators.  = (45 × 3) / (2 × 5) = 135/10 Step 4: Simplify the fraction.  Divide both numerator and denominator by 5:  = (135 ÷ 5) / (10 ÷ 5) = 27/2 Step 5: Convert 27/2 into a mixed number if desired.  27/2 = 13 1/2 Thus, the answer is: □ = 13 1/2

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To divide mixed numbers, first convert them to improper fractions. \( 22 \frac{1}{2} \) becomes \( \frac{45}{2} \) and \( 1 \frac{2}{3} \) becomes \( \frac{5}{3} \). The division of fractions is the same as multiplying by the reciprocal, so you do \( \frac{45}{2} \div \frac{5}{3} \), which is the same as \( \frac{45}{2} \times \frac{3}{5} \). This simplifies to \( \frac{135}{10} \), which can be reduced to \( 13 \frac{5}{10} \) or \( 13 \frac{1}{2} \). The result of \( 22 \frac{1}{2} \div 1 \frac{2}{3} \) is \( 13 \frac{1}{2} \).

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