Adding and Subtracting Like Fractions
Adding and Subtracting Like Fractions covers how to combine fractions that share the same denominator by adding or subtracting only their numerators while keeping the denominator unchanged: a/c ± b/c = (a ± b)/c. This foundational operation appears in Yoshiwara Elementary Algebra Chapter 8: Algebraic Fractions and is essential for Grade 6 students before tackling fractions with different denominators. Simplifying the result to lowest terms completes the process.
Key Concepts
Property Fractions with the same denominator are called like fractions. To add or subtract like fractions, combine the numerators and keep the denominator the same. If $c \neq 0$, then $$\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c} \quad \text{and} \quad \frac{a}{c} \frac{b}{c} = \frac{a b}{c}$$ To add or subtract like fractions: 1. Add or subtract the numerators. 2. Keep the same denominator. 3. Reduce the sum or difference if necessary.
Examples To add $\frac{3x 2}{x+1} + \frac{x+6}{x+1}$, we combine numerators: $\frac{(3x 2)+(x+6)}{x+1} = \frac{4x+4}{x+1} = \frac{4(x+1)}{x+1} = 4$. To subtract $\frac{5a 1}{a 3} \frac{2a+8}{a 3}$, distribute the negative: $\frac{5a 1 (2a+8)}{a 3} = \frac{5a 1 2a 8}{a 3} = \frac{3a 9}{a 3} = \frac{3(a 3)}{a 3} = 3$. To subtract $\frac{y^2 3y}{y 5} \frac{2y+20}{y 5}$, we get $\frac{y^2 3y (2y+20)}{y 5} = \frac{y^2 5y 20}{y 5}$.
Explanation You can only add or subtract things of the same kind. The denominator tells you the 'kind' of fraction (e.g., fifths). So, you combine the numerators (how many) and keep the denominator (the kind) unchanged. Be careful to distribute the negative sign to all terms in the second numerator when subtracting.
Common Questions
How do you add or subtract fractions with the same denominator?
Keep the denominator the same and add or subtract the numerators: a/c + b/c = (a+b)/c. Then simplify the result if possible.
What are like fractions?
Like fractions share the same denominator. For example, 3/7 and 2/7 are like fractions because both have a denominator of 7.
Do you add the denominators when adding fractions?
No. When the denominators are the same, keep them as-is and only add the numerators. Adding denominators is a common mistake.
Where is adding and subtracting like fractions in Yoshiwara Elementary Algebra?
This topic is covered in Chapter 8: Algebraic Fractions of Yoshiwara Elementary Algebra.
What if the resulting fraction is not in simplest form?
Divide both numerator and denominator by their greatest common factor (GCF) to reduce the fraction to lowest terms.