Divide these two fractions: [tex]$\frac{4}{3} \div \frac{5}{8}=?$[/tex]
Answer (2)
To divide fractions, multiply the first fraction by the reciprocal of the second.
The reciprocal of 8 5 is 5 8 .
Multiply the numerators and denominators: 3 4 × 5 8 = 15 32 .
The final answer is 15 32 .
Explanation
Understanding the Problem We are asked to divide two fractions: 3 4 and 8 5 . To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
Reciprocal and Conversion to Multiplication The reciprocal of 8 5 is 5 8 . So, the division problem becomes a multiplication problem: 3 4 ÷ 8 5 = 3 4 × 5 8 .
Multiplying Numerators and Denominators Now, we multiply the numerators together and the denominators together: 3 4 × 5 8 = 3 × 5 4 × 8 3 × 5 4 × 8 = 15 32
Final Result The result of the division is 15 32 . This is an improper fraction, meaning the numerator is greater than the denominator. We can leave it as an improper fraction or convert it to a mixed number. Since the problem doesn't specify which form to use, we'll leave it as an improper fraction.
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. For example, if you have 3 4 of a pizza and want to divide it among 8 5 of your friends, you would perform this division to determine how much pizza each friend receives. Understanding fraction division helps in real-world scenarios involving proportions and ratios.
To divide the fractions 3 4 by 8 5 , multiply 3 4 by the reciprocal of 8 5 , which is 5 8 . The result is 15 32 , an improper fraction. This can also be expressed as a mixed number, but it is typically left as an improper fraction unless specified otherwise.
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