Choose the correct method to find the answer.
8. [tex]$\frac{1}{3} \div \frac{6}{11}$[/tex]
A. [tex]$\frac{1}{3} \times \frac{6}{11}$[/tex]
B. [tex]$\frac{3}{1} \times \frac{11}{6}$[/tex]
C. [tex]$\frac{1}{3} \div \frac{11}{6}$[/tex]
D. [tex]$\frac{1}{3} \times \frac{11}{6}$[/tex]
Answer (2)
To divide fractions, multiply by the reciprocal of the second fraction.
The reciprocal of 11 6 is 6 11 .
Rewrite the division as multiplication: 3 1 ÷ 11 6 = 3 1 × 6 11 .
The correct method is D .
Explanation
Understanding the Problem We are given the division problem 3 1 ÷ 11 6 and asked to choose the correct equivalent expression from the options provided.
Finding the Reciprocal To divide by a fraction, we multiply by its reciprocal. The reciprocal of 11 6 is 6 11 .
Rewriting the Division as Multiplication Therefore, 3 1 ÷ 11 6 is equivalent to 3 1 × 6 11 .
Identifying the Correct Option Comparing this with the options, we see that option D, 3 1 × 6 11 , is the correct one.
Examples
When you're baking and a recipe calls for dividing a fraction of an ingredient, like flour, it's easier to multiply by the reciprocal. For instance, if you need to divide 3 1 cup of flour into portions of 11 6 cup each, you would calculate 3 1 ÷ 11 6 , which is the same as 3 1 × 6 11 . This tells you how many portions you can make. Understanding reciprocals makes cooking and baking much simpler!
To divide the fraction 3 1 by 11 6 , we multiply by the reciprocal of the second fraction, which is 6 11 . Therefore, the correct choice is option D: 3 1 × 6 11 .
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