(4.) $2 \frac{1}{4} \div 3 \frac{4}{5}=$
(5) $1 \frac{3}{4} \div 2 \frac{1}{5}=$
Answer (2)
Convert mixed numbers to improper fractions.
Divide the improper fractions in each problem.
Problem (4): 2 4 1 ÷ 3 5 4 = 4 9 ÷ 5 19 = 76 45 .
Problem (5): 1 4 3 ÷ 2 5 1 = 4 7 ÷ 5 11 = 44 35 .
The answers are 76 45 and 44 35 .
Explanation
Problem Setup and Conversion to Improper Fractions We are asked to evaluate two division problems involving mixed numbers. Let's tackle them one at a time. The problems are:
(4.) 2 4 1 ÷ 3 5 4 = (5) 1 4 3 ÷ 2 5 1 =
First, we need to convert the mixed numbers to improper fractions.
Converting Mixed Numbers to Improper Fractions (Problem 4) For problem (4), we convert 2 4 1 and 3 5 4 to improper fractions:
2 4 1 = 4 2 × 4 + 1 = 4 8 + 1 = 4 9
3 5 4 = 5 3 × 5 + 4 = 5 15 + 4 = 5 19
Dividing Improper Fractions (Problem 4) Now we divide the improper fractions for problem (4):
4 9 ÷ 5 19 = 4 9 × 19 5 = 4 × 19 9 × 5 = 76 45
Converting Mixed Numbers to Improper Fractions (Problem 5) For problem (5), we convert 1 4 3 and 2 5 1 to improper fractions:
1 4 3 = 4 1 × 4 + 3 = 4 4 + 3 = 4 7
2 5 1 = 5 2 × 5 + 1 = 5 10 + 1 = 5 11
Dividing Improper Fractions (Problem 5) Now we divide the improper fractions for problem (5):
4 7 ÷ 5 11 = 4 7 × 11 5 = 4 × 11 7 × 5 = 44 35
Final Answer Therefore, the solutions are:
(4.) 2 4 1 ÷ 3 5 4 = 76 45 (5) 1 4 3 ÷ 2 5 1 = 44 35
Examples
Understanding division of fractions is crucial in many real-life scenarios. For instance, if you're baking and need to divide a recipe in half, or if you're splitting a pizza among friends, you're using division of fractions. Imagine you have 2 4 1 cups of flour and each cookie requires 3 5 4 cups. The result 76 45 tells you that you can't even make one whole cookie. Similarly, if you have 1 4 3 of a pizza and each person eats 2 5 1 of a pizza, the result 44 35 tells you what fraction of a person's serving you have.
To solve the given division problems, we converted the mixed numbers to improper fractions and then divided them. The answers are 76 45 for the first problem and 44 35 for the second problem. This shows how to handle mixed number divisions step by step.
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