Concept

● Like fractions are fractions with the same denominator. 
● Unlike fractions are fractions with different denominators. 
● A fraction is said to be in simplest form if its numerator and denominator have no common factors other than 1.
● Improper fractions should be written as mixed numbers
● Words that mean to add are: sum, plus, increase, total, altogether, combined, or
● Words that mean to subtract are: minus, less, difference, how much more

Rule

To add or subtract fractions:
1. Create equivalent fractions, so denominators are like if needed.
2. Add or subtract the numerators. The denominator stays the same.
3. Write the answer as a whole number, simplified fraction, or mixed number

Example

Sarah bought $\frac{7}{9}$ of a yard of fabric and her mother bought $\frac{5}{6}$ a yard of fabric. How many yards of fabric did they buy altogether?

Solution

Add $\frac{7}{9} + \frac{5}{6}$

Create equivalent fractions
The lowest common denominator of 9 and 6 is 18. 

$\frac{7}{9}\mathrm{ = }\frac{\mathrm{x}}{18}$	$\frac{7 \times 2}{9 \times 2}\mathrm{ = }\frac{14}{18}$
$\frac{5}{6}\mathrm{ = }\frac{\mathrm{x}}{18}$	$\frac{5 \times 3}{6 \times 3}\mathrm{ = }\frac{15}{18}$

Add the numerators, the denominator stays the same
$\frac{14}{18}+\frac{15}{18}\mathrm{ = }\frac{29}{18}$

Write the answer as a whole number, simplified fraction or mixed number.
$\frac{29}{18}\mathrm{ = }1\frac{11}{18}$

Answer: $1\frac{11}{18}$ yards

Pre-requisite Skills

Equivalent Fractions (5.10.5)

Simplifying fractions (5.10.6)

Convert improper fractions mixed numbers (6.4.5)

Add Fractions with Like Denominators (6.7.2)

Add Fractions with Unlike Denominators (6.7.3)