Problem 132 - Introductory Algebra for College Students

Question

Explain how to convert an improper fraction to a mixed number and give an example.

Step-by-Step Solution

Answer

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the numerator of the fraction in the mixed number. For example, \(\frac{7}{4}\) becomes \(1 \frac{3}{4}\).

Step 1: Identify the Improper Fraction

An improper fraction has a numerator (the top number) that is greater than or equal to the denominator (the bottom number). For example, \(\frac{7}{4}\) is an improper fraction.

Step 2: Divide the Numerator by the Denominator

To convert the fraction to a mixed number, divide the numerator by the denominator. From the quotient you get the whole number, the remainder becomes the new numerator which is showcased over the initial denominator. So, \(7 ÷ 4 = 1\) remains \(3\).

Step 3: Write Down the Mixed Number

The quotient (the result of the division) becomes the whole number part and the remainder (what's left over after the division) becomes the numerator of a fraction over the original denominator. For \(\frac{7}{4}\), \(\frac{7}{4} = 1 \frac{3}{4}\)