\(\begin{array}{l}6 \frac{2}{4} \div 7 \frac{1}{5}= \\ 1 \frac{3}{6} \div 2 \frac{1}{2}= \\ 1 \frac{3}{4} \div 2 \frac{1}{7}=\end{array}\)
Answer (2)
Convert mixed numbers to improper fractions.
Divide the first improper fraction by the second improper fraction by multiplying by its reciprocal.
Simplify the resulting fraction.
The solutions are: 72 65 , 5 3 , and 60 49 . 72 65 , 5 3 , 60 49
Explanation
Convert mixed numbers to improper fractions First, we need to convert the mixed numbers to improper fractions. Let's start with the first problem: 6 4 2 ÷ 7 5 1 .
6 4 2 = 6 + 4 2 = 6 + 2 1 = 2 12 + 2 1 = 2 13
7 5 1 = 7 + 5 1 = 5 35 + 5 1 = 5 36
Divide the improper fractions Now, we divide the improper fractions:
2 13 ÷ 5 36 = 2 13 × 36 5 = 2 × 36 13 × 5 = 72 65
Convert mixed numbers to improper fractions Next, let's solve the second problem: 1 6 3 ÷ 2 2 1 .
1 6 3 = 1 + 6 3 = 1 + 2 1 = 2 2 + 2 1 = 2 3
2 2 1 = 2 + 2 1 = 2 4 + 2 1 = 2 5
Divide the improper fractions Now, we divide the improper fractions:
2 3 ÷ 2 5 = 2 3 × 5 2 = 2 × 5 3 × 2 = 10 6 = 5 3
Convert mixed numbers to improper fractions Finally, let's solve the third problem: 1 4 3 ÷ 2 7 1 .
1 4 3 = 1 + 4 3 = 4 4 + 4 3 = 4 7
2 7 1 = 2 + 7 1 = 7 14 + 7 1 = 7 15
Divide the improper fractions Now, we divide the improper fractions:
4 7 ÷ 7 15 = 4 7 × 15 7 = 4 × 15 7 × 7 = 60 49
Final Answer Therefore, the solutions are:
6 4 2 ÷ 7 5 1 = 72 65
1 6 3 ÷ 2 2 1 = 5 3
1 4 3 ÷ 2 7 1 = 60 49
Examples
Understanding fraction division is essential in many real-life scenarios, such as cooking, where you might need to divide ingredient quantities. For instance, 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 to find the adjusted amount of flour needed. This skill also applies to calculating distances on maps, determining proportions in construction projects, and managing time effectively by dividing tasks into smaller intervals. Mastering fraction division allows for accurate scaling and proportional reasoning in various practical applications.
To solve the divisions of mixed numbers, first convert them to improper fractions, then divide by multiplying by the reciprocal of the second fraction. The results are 72 65 , 5 3 , and 60 49 .
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