Adding and Subtracting Fractions
Learn to add and subtract fractions with unlike denominators by finding the least common denominator and renaming fractions in Saxon Math Course 1.
Key Concepts
Property To add or subtract fractions that do not have common denominators, we rename one or more of them to form fractions that do have common denominators. Then we add or subtract.
Examples To solve $\frac{1}{2} \frac{1}{6}$, rename $\frac{1}{2}$ to $\frac{3}{6}$. Then, $\frac{3}{6} \frac{1}{6} = \frac{2}{6}$, which simplifies to $\frac{1}{3}$. To solve $\frac{1}{2} + \frac{3}{8}$, rename $\frac{1}{2}$ to $\frac{4}{8}$. Then, $\frac{4}{8} + \frac{3}{8} = \frac{7}{8}$. To solve $\frac{3}{4} \frac{3}{8}$, rename $\frac{3}{4}$ to $\frac{6}{8}$. Then, $\frac{6}{8} \frac{3}{8} = \frac{3}{8}$.
Explanation Adding or subtracting fractions is a three step dance! First, find the least common denominator for your fractions. Second, "rename" one or both fractions by multiplying by a clever form of 1 so their denominators match. Third, add or subtract the numerators and keep the new denominator. Finally, don't forget to simplify your answer if you can!
Common Questions
How do you add fractions with different denominators in 6th grade?
To add fractions with different denominators, first find the least common denominator shared by both fractions. Then rename one or both fractions by multiplying to make the denominators match, and finally add the numerators while keeping the new denominator. For example, to solve 1/2 + 3/8, rename 1/2 as 4/8, then add to get 7/8.
What does it mean to rename a fraction when subtracting?
Renaming a fraction means rewriting it as an equivalent fraction with a new denominator so it matches the other fraction. You multiply the numerator and denominator by the same number, which is like multiplying by a clever form of 1. For example, 1/2 becomes 3/6 so you can subtract 1/6 from it.
How do you find a common denominator for fractions?
A common denominator is the smallest number that both denominators divide into evenly, called the least common denominator. For fractions like 3/4 and 3/8, the least common denominator is 8, so you rename 3/4 as 6/8. This allows you to subtract or add the numerators correctly.
Do you need to simplify after adding or subtracting fractions?
Yes, after adding or subtracting fractions you should always check if your answer can be simplified. For example, 3/6 - 1/6 = 2/6, which simplifies to 1/3 by dividing both numerator and denominator by 2. Simplifying gives the answer in its most reduced form.