The Correct Answer and Explanation is:
The correct answer is 38.4.
To solve the problem “What is 96 Divided by 10/4?”, we must use the rule for dividing by a fraction. The process involves a key transformation of the division operation into a multiplication operation.
First, identify the components of the problem: we have a whole number, 96, which is the dividend, and a fraction, 10/4, which is the divisor. The rule for dividing by a fraction is to multiply the dividend by the reciprocal of the divisor. A reciprocal is found by inverting the fraction, meaning the numerator and the denominator switch places. The reciprocal of the fraction 10/4 is 4/10.
With this rule, we can rewrite the original expression, 96 ÷ (10/4), as a multiplication problem: 96 × (4/10).
To make the multiplication clearer, we can express the whole number 96 as a fraction by placing it over 1, which gives us 96/1. Now the problem is (96/1) × (4/10). To multiply two fractions, we multiply the numerators together and the denominators together.
For the numerators: 96 × 4 = 384.
For the denominators: 1 × 10 = 10.
This results in the new fraction 384/10. This fraction represents the division of 384 by 10. To divide a number by 10, you simply move its decimal point one place to the left. The number 384 has an implied decimal point at the end (384.0). Moving the decimal one position to the left gives us the final answer of 38.4.
An alternative method is to first simplify the fraction 10/4. Both 10 and 4 are divisible by 2, so 10/4 simplifies to 5/2. The problem then becomes 96 ÷ (5/2). Following the same rule, we multiply by the reciprocal of 5/2, which is 2/5. This gives us 96 × (2/5), which equals 192/5. Dividing 192 by 5 also yields 38.4, confirming the result.
