Lesson 57: Adding and Subtracting Fractions: Three Steps

New Concept

To solve fraction problems, follow three steps:

1. Put the problem in the correct shape.
2. Perform the operation.
3. Simplify the answer.

What’s next

Next, you'll see this three-step process applied to worked examples of adding and subtracting fractions. Then, you'll solve challenge problems on your own.

Property

Step 1: Shape the problem into the correct form, which means finding common denominators.
Step 2: Operate by performing the indicated action, like adding or subtracting.
Step 3: Simplify the answer by reducing it or converting it to a mixed number.

Examples

$\frac{5}{6} - \frac{1}{3} \rightarrow \text{Shape: } \frac{5}{6} - \frac{2}{6} \rightarrow \text{Operate: } \frac{3}{6} \rightarrow \text{Simplify: } \frac{1}{2}$

Property

To add fractions, you must first reshape them to have a common denominator. Once they are in the correct shape, operate by adding the numerators together while keeping the denominator the same. Lastly, simplify the resulting fraction or mixed number if possible.

Examples

$\frac{1}{2} + \frac{1}{6} \rightarrow \text{Shape: } \frac{3}{6} + \frac{1}{6} \rightarrow \text{Operate: } \frac{4}{6} \rightarrow \text{Simplify: } \frac{2}{3}$

$\frac{2}{3} + \frac{1}{4} \rightarrow \text{Shape: } \frac{8}{12} + \frac{3}{12} \rightarrow \text{Operate: } \frac{11}{12} \rightarrow \text{Simplify: Stays } \frac{11}{12}$

Property

To subtract fractions, first give the fractions a common denominator (Shape). Next, subtract the second numerator from the first while keeping the denominator the same (Operate). Lastly, reduce the resulting fraction to its simplest form if you can (Simplify).

Examples

$\frac{5}{6} - \frac{1}{2} \rightarrow \text{Shape: } \frac{5}{6} - \frac{3}{6} \rightarrow \text{Operate: } \frac{2}{6} \rightarrow \text{Simplify: } \frac{1}{3}$

$\frac{7}{10} - \frac{1}{2} \rightarrow \text{Shape: } \frac{7}{10} - \frac{5}{10} \rightarrow \text{Operate: } \frac{2}{10} \rightarrow \text{Simplify: } \frac{1}{5}$