Adding and Subtracting Unlike Fractions
Adding and subtracting unlike fractions is a Grade 7 math skill from Yoshiwara Intermediate Algebra requiring students to find a common denominator before combining fractions. Students rewrite each fraction using the LCD, then add or subtract the numerators while keeping the denominator.
Key Concepts
Property To add or subtract algebraic fractions: 1. Find the lowest common denominator (LCD) for the fractions. 2. Build each fraction to an equivalent one with the same denominator using the fundamental principle $\frac{a}{b} = \frac{a \cdot c}{b \cdot c}$. 3. Add or subtract the resulting like fractions: Add or subtract their numerators, and keep the same denominator. 4. Reduce the sum or difference if necessary.
Examples Subtract $\frac{x+1}{8} \frac{x 2}{12}$. The LCD is $24$. This becomes $\frac{3(x+1)}{24} \frac{2(x 2)}{24} = \frac{3x+3 (2x 4)}{24} = \frac{x+7}{24}$. Add $\frac{5}{x^2 9} + \frac{2}{x+3}$. The LCD is $(x 3)(x+3)$. The sum is $\frac{5}{(x 3)(x+3)} + \frac{2(x 3)}{(x 3)(x+3)} = \frac{5+2x 6}{(x 3)(x+3)} = \frac{2x 1}{x^2 9}$. Add $\frac{m}{m^2 2m} + \frac{3}{m^2 4}$. The denominators are $m(m 2)$ and $(m 2)(m+2)$. The LCD is $m(m 2)(m+2)$. The sum is $\frac{m(m+2)+3m}{m(m 2)(m+2)} = \frac{m^2+2m+3m}{m(m 2)(m+2)} = \frac{m(m+5)}{m(m 2)(m+2)} = \frac{m+5}{(m 2)(m+2)}$.
Explanation You can't add or subtract fractions with different denominators. First, find the LCD. Then, 'build up' each fraction by multiplying its top and bottom by the missing factors. Now they are like fractions, ready to be combined.
Common Questions
How do you add fractions with different denominators?
Find the LCD, rewrite each fraction with that denominator, then add the numerators. Keep the LCD as the denominator and simplify if possible.
How do you subtract 3/4 - 1/6?
LCD = 12. Rewrite: 9/12 - 2/12 = 7/12.
What is the LCD and how do you find it?
The LCD is the smallest common multiple of all denominators. For 1/4 and 1/6, the LCD = 12 (LCM of 4 and 6).
Do you always need to simplify after adding or subtracting fractions?
Yes, always check if the resulting fraction can be simplified by dividing numerator and denominator by their GCD.