4. [tex]$\frac{1}{4} \div 3 \frac{4}{5}$[/tex]
5. [tex]$1 \frac{3}{6} \div 2 \frac{1}{2}$[/tex]
6. [tex]$2 \frac{1}{3} \div 1 \frac{3}{6}$[/tex]
7. [tex]$4 \frac{2}{4} \div 2 \frac{1}{3}$[/tex]
Answer (2)
Convert each mixed number to an improper fraction.
Divide the first improper fraction by the second improper fraction by multiplying by the reciprocal.
Simplify the resulting fraction to its lowest terms.
The answers are: 76 45 , 5 3 , 9 14 , and 14 27 respectively. 76 45 , 5 3 , 9 14 , 14 27
Explanation
Understanding the Problem We are given four division problems involving mixed numbers. Our goal is to evaluate each division problem and express the answer as a simplified fraction or mixed number.
Problem 4: Convert to Improper Fractions and Divide For problem 4, we have 2 4 1 ÷ 3 5 4 . First, we convert the mixed numbers to improper fractions: 2 4 1 = 4 9 and 3 5 4 = 5 19 . Then, we divide the fractions: 4 9 ÷ 5 19 = 4 9 × 19 5 = 76 45 .
Problem 5: Convert to Improper Fractions and Divide For problem 5, we have 1 6 3 ÷ 2 2 1 . Converting to improper fractions: 1 6 3 = 1 2 1 = 2 3 and 2 2 1 = 2 5 . Dividing the fractions: 2 3 ÷ 2 5 = 2 3 × 5 2 = 10 6 = 5 3 .
Problem 6: Convert to Improper Fractions and Divide For problem 6, we have 2 3 1 ÷ 1 6 3 . Converting to improper fractions: 2 3 1 = 3 7 and 1 6 3 = 1 2 1 = 2 3 . Dividing the fractions: 3 7 ÷ 2 3 = 3 7 × 3 2 = 9 14 .
Problem 7: Convert to Improper Fractions and Divide For problem 7, we have 4 4 2 ÷ 2 3 1 . Converting to improper fractions: 4 4 2 = 4 2 1 = 2 9 and 2 3 1 = 3 7 . Dividing the fractions: 2 9 ÷ 3 7 = 2 9 × 7 3 = 14 27 .
Final Answers Therefore, the solutions are:
Problem 4: 76 45
Problem 5: 5 3
Problem 6: 9 14
Problem 7: 14 27
Examples
Understanding fraction division is essential in many real-life scenarios, such as cooking, where you might need to halve or quarter a recipe. For example, if a recipe calls for 2 2 1 cups of flour, but you only want to make half the recipe, you would divide 2 2 1 by 2. This gives you 2 2 1 ÷ 2 = 2 5 ÷ 2 = 2 5 × 2 1 = 4 5 = 1 4 1 cups of flour. Similarly, dividing fractions is crucial in construction, where you might need to cut materials into precise fractional lengths.
To solve the division of mixed numbers, first convert them into improper fractions. Then, divide by multiplying by the reciprocal of the divisor. The results are 76 5 , 5 3 , 9 14 , and 14 27 respectively.
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