# Adding and subtracting fractions with unlike denominators

### Adding and subtracting fractions with unlike denominators

In this section, we will learn how to add and subtract fractions with unlike denominators. First, we will practice finding the lowest common denominator for a pair of fractions by determining the lowest common multiple of the denominators. The divisibility rules learned in previous section can be used to find the multiples of our denominators. Next, we will practice writing equivalent fractions. When writing equivalent fractions with common denominators, the numerator and denominator in each fraction are both multiplied by the same number. As shown in sections on adding/subtracting fractions with like denominators, we will write our answers in lowest terms by first finding the greatest common factor (GCF) of both the numerator and denominator in our equivalent fraction and then dividing both the numerator and denominator by this GCF.

#### Lessons

In this lesson, we will learn:

• Determine the Lowest Common Denominator of Two Fractions
• Evaluate Equivalent Fractions Using the Lowest Common Denominator
• Add and Subtract Fractions With Unlike Denominators
• Word Problems: Adding And Subtracting Fractions With Unlike Denominators
• Challenging: Add and Subtract Fractions With Unlike Denominators
• Introduction
a)
Simplify fractions: Method A - By using greatest common factors

b)
Simplify fractions: Method B - By using common factors

c)
What are equivalent fractions?

d)

e)
How to subtract frations?
• subtracting with improper fractions
• subtracting with mixed numbers

• 1.
Determine the Lowest Common Denominator of Two Fractions
Determine the lowest common denominator (LCD) for the pair of fractions using multiples.
a)
$\frac{2}{4},\frac{1}{8}$

b)
$\frac{8}{11},\frac{7}{33}$

c)
$\frac{4}{6},\frac{5}{9}$

• 2.
Evaluate Equivalent Fractions Using the Lowest Common Denominator
Determine the lowest common denominator (LCD) for the pair of fractions using multiples. Then, determine equivalent fractions for the pair of fractions using the LCD.
a)
$\frac{7}{12},\frac{2}{4}$

b)
$\frac{1}{2},\frac{1}{3}$

c)
$\frac{8}{10},\frac{8}{15}$

• 3.
Word Problems: Adding And Subtracting Fractions With Unlike Denominators
Calculate using the four square method. Write the answer in the lowest terms.
a)
$\frac{3}{6}+\frac{1}{4}$

b)
$\frac{4}{5}-\frac{1}{3}$

c)
$\frac{2}{3}+\frac{2}{10}$

d)
$\frac{8}{10}-\frac{32}{80}$

• 4.
Word Problems: Adding And Subtracting Fractions With Unlike Denominators
A cargo ship was $\frac{1}{8}$ full of food containers and $\frac{2}{4}$ full of furniture. How much space was left?

• 5.
Kate baked a tray of muffins for her two friends, Mary and Stephanie. Mary ate $\frac{1}{3}$ of the muffins and Stephanie ate $\frac{3}{6}$ of the muffins. What fraction of the muffins did the two friends eat in total?