Adding, Subtracting, Multiplying, and Dividing Fractions Study Guide: GED Math
Practice problems for these concepts can be found at:
Operations with Fractions—Overview
To do well when working with fractions, it is necessary to understand some basic concepts. Here are some math rules for fractions using variables:
Adding and Subtracting Fractions
How would you add 2 hours and $5? You can't. You can add and subtract only like objects: You can add $2 to $5 or 2 hours to 5 hours. It's the same with fractions. To add and subtract fractions, you need like fractions. Like fractions are fractions that have the same denominator. If the denominators are already the same, add or subtract the numerators and keep the denominator. Then, simplify if needed.
Subtract the numerators: (2 – 7) = –5.
Retain the denominator in your final answer: .
When subtracting fractions, the order of the fractions is important. Write the numerator that you are subtracting from first. Then subtract as you would any two numbers.
Fractions that have different denominators are called unlike fractions. Before you can add or subtract unlike fractions, you first need to change them into like fractions so that they have the same number in the denominator. This is called finding a common denominator.
There are two main ways to find a common denominator. One way is to multiply the denominators together. The other way is to multiply each denominator by 2, 3, 4, 5, and so on. Then compare the lists of multiples of each denominator. The numbers that are the same, or that are in common, are common denominators.
Follow these steps when adding or subtracting unlike fractions.
Step 1 Find a common denominator.
Step 2 Change each fraction so that it has the common denominator.
Step 3 Add or subtract the fractions as indicated.
Step 4 Reduce your answer to lowest terms.
- Find a common denominator for and .
Find a common denominator. The LCD of 4 and 24 is 24.
Convert the first fraction to have a denominator of 24: .
Perform the addition: .
Finally, simplify: .
List the multiples for each denominator.
Multiples of 4: 4, 8, 12, 16,…
Multiples of 6: 6, 12, 18, 24,…
The numbers 4 and 6 share the multiple 12. So, 12 is a common denominator for and . In fact, it is the LCD.
Find a common denominator for and .
Multiply the denominators together: 4 × 6 = 24. So, 24 is a common denominator for and . However, it can be reduced to 12, which is the LCD.
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