Question

Change each of the following to improper fractions.

I. 9 3/8 =
II. 6 2/5 =
III. 3 7/8 =

Answer 1

To convert a mixed number to an improper fraction, multiply the whole number by the fraction's denominator and add the numerator. Examples: 9 3/8 becomes 75/8, 6 2/5 becomes 32/5, and 3 7/8 becomes 31/8. This demonstrates the relationship between multiplication and division in fractions.

Step-by-step explanation:

To change a mixed number to an improper fraction, you multiply the whole number by the denominator of the fraction part, then add the numerator of the fraction part. The result is the numerator of the improper fraction, with the denominator remaining the same as in the fraction part of the mixed number. Let's apply this method to the given mixed numbers:

1. 9 3/8 = (9 × 8) + 3 = 75/8
2. 6 2/5 = (6 × 5) + 2 = 32/5
3. 3 7/8 = (3 × 8) + 7 = 31/8

The process showcases the relationship between multiplication and division. In the case of fractions, dividing by a number is equivalent to multiplying by its reciprocal. When you convert a mixed number to an improper fraction, you're essentially multiplying (the whole number part by the fraction's denominator) and then adding (the fraction's numerator), which is the inverse operation of division.