Lesson 4.1: Adding and Subtracting Fractions

New Concept

To add or subtract fractions, they must have a common denominator. This lesson shows you how to find the lowest common denominator (LCD) for unlike fractions and rewrite them, enabling you to combine them accurately.

What’s next

Next, you'll work through interactive examples and practice cards to master finding the LCD and combining fractions. Let's get started!

Property

Fractions that have the same denominator are called like fractions.

To add (or subtract) two like fractions:

1. Add (or subtract) the numerators.
2. Keep the same denominator.

Examples

• To add $\frac{2}{9} + \frac{5}{9}$, we add the numerators: $2+5=7$. The denominator stays the same, so the sum is $\frac{7}{9}$.

Property

To write an equivalent fraction with a larger denominator:

1. Divide the old denominator into the desired denominator. This gives you the 'building factor'.
2. Use that factor to multiply the old numerator.

This process is shown as:

Examples

• To write $\frac{2}{5}$ with a denominator of 15, the building factor is $15 \div 5 = 3$. We multiply to get $\frac{2 \times 3}{5 \times 3} = \frac{6}{15}$.

Property

The lowest common denominator (LCD) for two fractions is the smallest number that both denominators divide into evenly. Finding the LCD is the same as finding the lowest common multiple (LCM) of their denominators.

To find the LCD, you can list multiples of the larger number until you find one that is also a multiple of the smaller number.

Examples

• For $\frac{1}{6}$ and $\frac{3}{8}$, we list multiples of 8: 8, 16, 24. Since 6 divides into 24, the LCD is 24.

Property

Fractions that have different denominators are called unlike fractions.

To add or subtract unlike fractions:

1. Find an LCD for the fractions.
2. Build each fraction to the LCD.
3. Combine the resulting like fractions.

Examples

• To add $\frac{1}{4} + \frac{5}{6}$, the LCD is 12. We build the fractions: $\frac{1 \times 3}{4 \times 3} + \frac{5 \times 2}{6 \times 2} = \frac{3}{12} + \frac{10}{12} = \frac{13}{12}$.

Property

An improper fraction is a fraction where the numerator is larger than the denominator, meaning it represents a number greater than one.

A mixed number combines a whole number and a fraction, such as $1\frac{1}{12}$, which means $1 + \frac{1}{12}$. To convert a mixed number to an improper fraction, add the whole number and the fraction part by finding a common denominator.

Examples

• To write $3\frac{1}{4}$ as an improper fraction, we calculate $3 + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{13}{4}$.