Finding a Common Denominator
Learn to find common denominators using the least common multiple (LCM) to add and subtract fractions with unlike denominators in Grade 6 math.
Key Concepts
Property To add or subtract fractions with different denominators, you must first rename them to have a common denominator. This is typically the least common multiple (LCM) of the original denominators.
Examples $$ \frac{1}{2} + \frac{1}{3} = \frac{1 \cdot 3}{2 \cdot 3} + \frac{1 \cdot 2}{3 \cdot 2} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} $$ $$ \frac{3}{4} \frac{2}{3} = \frac{3 \cdot 3}{4 \cdot 3} \frac{2 \cdot 4}{3 \cdot 4} = \frac{9}{12} \frac{8}{12} = \frac{1}{12} $$ $$ \frac{2}{3} + \frac{1}{4} = \frac{2 \cdot 4}{3 \cdot 4} + \frac{1 \cdot 3}{4 \cdot 3} = \frac{8}{12} + \frac{3}{12} = \frac{11}{12} $$.
Explanation Imagine trying to add half a pizza to a third of another pizza. The slices are different sizes, making it a mess! To fix this, you must recut both pizzas into slices of the same size, like sixths. Now you can simply count the new, identical slices to find your total. It’s the secret to making fraction math easy!
Common Questions
What is a common denominator and why do you need one?
A common denominator is a shared bottom number that allows you to add or subtract fractions with different denominators. Without it, the fractions represent different-sized pieces, making direct addition or subtraction impossible. Finding the least common multiple (LCM) of the denominators gives you the smallest common denominator to use.
How do you find the least common multiple to add fractions like 1/2 + 1/3?
To add 1/2 + 1/3, find the LCM of 2 and 3, which is 6. Then rename each fraction: multiply 1/2 by 3/3 to get 3/6, and multiply 1/3 by 2/2 to get 2/6. Now you can add them to get 5/6.
How do you subtract fractions with different denominators like 3/4 - 2/3?
Find the LCM of 4 and 3, which is 12, to use as the common denominator. Rename 3/4 as 9/12 and 2/3 as 8/12 by multiplying each fraction by the appropriate factor. Then subtract to get 1/12.
What Saxon Math Course 1 chapter covers finding a common denominator?
Finding a common denominator is covered in Chapter 6: Geometry and Number Operations in Saxon Math, Course 1. This Grade 6 skill focuses on renaming fractions using the least common multiple before adding or subtracting them.