6. [tex]$\frac{1}{3} \div 1 \frac{3}{6}=[/tex]
7. [tex]$4 \frac{2}{4} \div 2 \frac{1}{3}=[/tex]
8. [tex]$1 \frac{3}{4} \div 2 \frac{1}{2}=[/tex]
9. [tex]$2 \frac{1}{7} \div 1 \frac{3}{4}=[/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.
Convert the simplified improper fraction back to a mixed number or a proper fraction: 6. 1 9 5 , 7. 1 14 13 , 8. 10 7 , 9. 1 49 11 .
1 9 5 , 1 14 13 , 10 7 , 1 49 11
Explanation
Understanding the Problem We are given four division problems involving mixed numbers and asked to evaluate them. A mixed number is a whole number and a fraction combined into one. To divide mixed numbers, we first convert them to improper fractions, then perform the division by multiplying by the reciprocal of the second fraction, and finally simplify the result.
Problem 6: 2 3 1 ÷ 1 6 3 For problem 6, we have 2 3 1 ÷ 1 6 3 . First, we convert the mixed numbers to improper fractions:
2 3 1 = 3 2 × 3 + 1 = 3 7
1 6 3 = 6 1 × 6 + 3 = 6 9 = 2 3
Now we divide the fractions:
3 7 ÷ 2 3 = 3 7 × 3 2 = 3 × 3 7 × 2 = 9 14
Converting back to a mixed number:
9 14 = 1 9 5
Problem 7: 4 4 2 ÷ 2 3 1 For problem 7, we have 4 4 2 ÷ 2 3 1 . First, we convert the mixed numbers to improper fractions:
4 4 2 = 4 4 × 4 + 2 = 4 18 = 2 9
2 3 1 = 3 2 × 3 + 1 = 3 7
Now we divide the fractions:
2 9 ÷ 3 7 = 2 9 × 7 3 = 2 × 7 9 × 3 = 14 27
Converting back to a mixed number:
14 27 = 1 14 13
Problem 8: 1 4 3 ÷ 2 2 1 For problem 8, we have 1 4 3 ÷ 2 2 1 . First, we convert the mixed numbers to improper fractions:
1 4 3 = 4 1 × 4 + 3 = 4 7
2 2 1 = 2 2 × 2 + 1 = 2 5
Now we divide the fractions:
4 7 ÷ 2 5 = 4 7 × 5 2 = 4 × 5 7 × 2 = 20 14 = 10 7
Problem 9: 2 7 1 ÷ 1 4 3 For problem 9, we have 2 7 1 ÷ 1 4 3 . First, we convert the mixed numbers to improper fractions:
2 7 1 = 7 2 × 7 + 1 = 7 15
1 4 3 = 4 1 × 4 + 3 = 4 7
Now we divide the fractions:
7 15 ÷ 4 7 = 7 15 × 7 4 = 7 × 7 15 × 4 = 49 60
Converting back to a mixed number:
49 60 = 1 49 11
Final Answers Therefore, the solutions are:
2 3 1 ÷ 1 6 3 = 1 9 5
4 4 2 ÷ 2 3 1 = 1 14 13
1 4 3 ÷ 2 2 1 = 10 7
2 7 1 ÷ 1 4 3 = 1 49 11
Examples
Understanding division of mixed numbers is crucial in everyday situations, such as when you're adjusting a recipe. For instance, if a recipe calls for 2 2 1 cups of flour and you only want to make half the recipe, you need to divide 2 2 1 by 2. Converting this to 2 5 ÷ 2 = 2 5 × 2 1 = 4 5 = 1 4 1 , you'll know you need 1 4 1 cups of flour. This skill ensures accuracy in cooking, baking, and various measurement-related tasks.
To solve the division of mixed numbers, convert each mixed number to an improper fraction, then multiply by the reciprocal of the second fraction. After dividing and simplifying, convert back to a mixed number if needed. The answers are: 6. 9 2 , 7. 1 14 13 , 8. 10 7 , 9. 1 49 11 .
;
