Vocabulary

Mixed Number - a combination of a whole number and a fraction.

Proper Fraction - a fraction that is less than one, with the numerator less than the denominator.

Improper Fraction - a fraction that is greater than one, with the numerator greater than the denominator.

Concept

Convert improper fractions to mixed numbers or vice versa and simplify.

Rules

1. Convert a mixed number to an improper fraction:

• Multiply the whole number by the denominator.

• Add the answer from Step 1 to the numerator.

• Write the answer from Step 2 over the denominator.

2. Convert an improper fraction to mixed number:

• Divide the numerator by the denominator.

• Write down the whole number result.

• Use the remainder as the new numerator over the denominator. This is the fraction part of the mixed number.

3. In order to simplify a fraction, there must be:

• A number that will divide evenly into both the numerator and denominator so it can be reduced, or

• The numerator must be greater than the denominator, (an improper fraction), so it can be converted to a mixed number.

Example 1 Convert mixed number to improper fraction

Change the mixed number to an improper fraction.

$2\frac{3}{5}\mathrm{ = }$

Solution

$\frac{\mathrm{(2\; \times \; 5)\; +\; 3}}{5}$

Answer: $\frac{13}{5}$

Example 2 Convert improper fraction to a mixed number

Change the improper fraction to a mixed number. 

Solution

23 ÷ 4 = 5 with remainder of 3

Answer: $5\frac{3}{4}$

Example 3 Simplify improper fraction

Simplify.

$\frac{21}{49}\mathrm{ = }$

Solution

$\frac{\mathrm{21\; ÷\; 7}}{\mathrm{49\; ÷\; 7}}$= $\frac{3}{7}$

Answer: $\frac{3}{7}$

Pre-requisite Skills

Convert Between Mixed Numbers and Improper Fractions (4.14.11)

Write improper fraction as mixed number (5.7.1)

Write mixed number as improper fraction. (5.7.2)