Common denominators, operations with fractions
Middle School Bridge • 6-8
Imagine you eat 1⁄4 of a cake in the morning and 2⁄4 in the afternoon. How much did you eat in total? When fractions share the same denominator, combining them is straightforward. But what happens when the denominators differ? This lesson teaches you a reliable method for adding and subtracting any two fractions.
When two fractions have the same denominator (called a common denominator), simply add or subtract the numerators and keep the denominator.
Compute 3⁄8 + 2⁄8.
Same denominator, so add numerators: 3 + 2⁄8 = 5⁄8.
When denominators differ, you must rewrite each fraction with a common denominator before combining. Use the Least Common Denominator (LCD) -- the smallest number that both denominators divide into evenly.
Compute 2⁄3 + 1⁄4.
Compute 5⁄6 − 1⁄4.
When one denominator is a multiple of the other, the LCD is simply the larger denominator. For instance, LCD of 3 and 9 is just 9. Only the fraction with the smaller denominator needs to be rewritten.
Never add the denominators together. 1⁄3 + 1⁄4 does NOT equal 2⁄7. The denominators tell you the size of each piece -- you cannot combine pieces of different sizes without first making them the same size.
1. 3⁄10 + 4⁄10
Same denominator: 3 + 4⁄10 = 7⁄10.
2. 1⁄3 + 1⁄6
LCD = 6. Rewrite 1⁄3 = 2⁄6. Then 2⁄6 + 1⁄6 = 3⁄6 = 1⁄2.
3. 3⁄4 − 2⁄5
LCD = 20. Rewrite: 15⁄20 − 8⁄20 = 7⁄20.
4. 5⁄8 + 1⁄6
LCD = 24. Rewrite: 15⁄24 + 4⁄24 = 19⁄24.
5. 7⁄9 − 1⁄3
LCD = 9. Rewrite 1⁄3 = 3⁄9. Then 7⁄9 − 3⁄9 = 4⁄9.
To add or subtract fractions, they must share a common denominator. If they already do, combine the numerators directly. If they do not, find the LCD, rewrite each fraction, then combine. Always simplify your final answer.