4. [tex]$2 \frac{2}{3} \div \frac{1}{3}=[/tex]
A. [tex]$\frac{8}{9}$[/tex]
B. 4
C. [tex]$6 \frac{2}{3}$[/tex]
D. 8
Answer (1)
Convert the mixed number to an improper fraction: 2 3 2 = 3 8 .
Rewrite the division as multiplication by the reciprocal: 3 8 ÷ 3 1 = 3 8 × 3 .
Multiply the fractions: 3 8 × 3 = 3 24 .
Simplify the fraction: 3 24 = 8 . The answer is 8 .
Explanation
Understanding the problem We are asked to evaluate the expression 2 3 2 d i v 3 1 and choose the correct answer from the given options.
Converting to an improper fraction First, we need to convert the mixed number 2 3 2 to an improper fraction. To do this, we multiply the whole number part (2) by the denominator (3) and add the numerator (2). This gives us 2 × 3 + 2 = 6 + 2 = 8 . So, the improper fraction is 3 8 .
Rewriting the division Now we can rewrite the division as multiplication by the reciprocal of 3 1 . The reciprocal of 3 1 is 1 3 or simply 3. So, the expression becomes 3 8 × 3 .
Multiplying the fractions Multiplying the fractions, we have 3 8 × 3 = 3 8 × 3 = 3 24 .
Simplifying the fraction Finally, we simplify the resulting fraction: 3 24 = 8 .
Choosing the correct answer Comparing our final answer with the given options, we see that the correct answer is D. 8.
Examples
Understanding fraction division is crucial in everyday scenarios, such as dividing a pizza equally among friends. If you have 2 3 2 of a pizza and want to give each friend 3 1 of the whole pizza, this problem shows you can feed 8 friends. This skill extends to various situations, from cooking and baking to managing resources and finances, making it a valuable tool in practical problem-solving.
