Adding and Subtracting Like Fractions
Adding and subtracting like fractions is a foundational fraction operation where the denominators are already the same, so you simply add or subtract the numerators while keeping the denominator unchanged. For example, 2/9 + 5/9 = 7/9 because the pieces are the same size, so you just count how many you have. This Grade 8 math skill from Yoshiwara Core Math Chapter 4 builds fluency with rational number operations that students need for algebra, equation solving, and working with proportions. Mastering like fraction operations is the entry point for the more complex skill of adding fractions with unlike denominators.
Key Concepts
Property Fractions that have the same denominator are called like fractions.
To add (or subtract) two like fractions: 1. Add (or subtract) the numerators. 2. Keep the same denominator.
Examples To add $\frac{2}{9} + \frac{5}{9}$, we add the numerators: $2+5=7$. The denominator stays the same, so the sum is $\frac{7}{9}$.
Common Questions
How do you add fractions with the same denominator?
To add fractions with the same denominator, add the numerators together and keep the denominator the same. For example, 3/8 + 2/8 = 5/8. You do not add the denominators.
How do you subtract fractions with the same denominator?
To subtract like fractions, subtract the smaller numerator from the larger one and keep the denominator. For example, 11/15 - 4/15 = 7/15. Remember to simplify the result if possible.
What are like fractions?
Like fractions are fractions that have the same denominator. For example, 1/5 and 3/5 are like fractions because both have a denominator of 5. This makes adding and subtracting them straightforward.
When do students learn to add and subtract like fractions?
Students typically learn to add and subtract like fractions in elementary school, but Grade 8 math courses like Yoshiwara Core Math revisit and solidify this skill as part of mastering all rational number operations in Chapter 4.
Do you add the denominators when adding fractions?
No, you never add or subtract denominators when adding or subtracting fractions. The denominator stays the same. Only the numerators change. For example, 2/7 + 3/7 = 5/7, not 5/14.
How do like fractions relate to unlike fractions?
Unlike fractions have different denominators, like 1/3 and 1/4. To add them, you must first convert them to like fractions by finding a common denominator. Mastering like fractions is the prerequisite for this more complex operation.