The Correct Answer and Explanation is:
The correct answer to the question “What is 56 Divided by 5/7?” is 78.4, which can also be expressed as the mixed number 78 2/5 or the improper fraction 392/5.
Here is a detailed explanation of how to arrive at this solution.
The problem presented is a division of a whole number by a fraction: 56 ÷ (5/7). The fundamental rule for dividing by a fraction is to multiply by its reciprocal. The reciprocal of a fraction is found by simply inverting it, or flipping the numerator (the top number) and the denominator (the bottom number).
First, we identify the fraction we are dividing by, which is 5/7. To find its reciprocal, we swap the numerator and the denominator. The reciprocal of 5/7 is 7/5.
Next, we rewrite the original division problem as a multiplication problem using this reciprocal. The expression 56 ÷ (5/7) becomes 56 × (7/5). This transformation is the key step in solving this type of mathematical problem.
To perform the multiplication, it is helpful to express the whole number 56 as a fraction. Any whole number can be written as a fraction by placing it over 1. Therefore, 56 can be written as 56/1. Our problem is now (56/1) × (7/5).
Now, we multiply the two fractions. We do this by multiplying the numerators together and then multiplying the denominators together.
For the numerators: 56 × 7 = 392.
For the denominators: 1 × 5 = 5.
This calculation results in the improper fraction 392/5. While this is a correct answer, it is often more useful to convert it into a decimal or a mixed number. To convert 392/5 to a decimal, we perform the division: 392 ÷ 5 = 78.4. To express it as a mixed number, we find how many whole times 5 goes into 392, which is 78, with a remainder of 2. This gives us the mixed number 78 2/5. All three forms of the answer are mathematically equivalent.
