To Add or Subtract Algebraic Fractions
This Grade 6 algebra skill from Yoshiwara Elementary Algebra teaches students to add and subtract algebraic fractions (rational expressions). Students find the LCD of the denominators, rewrite each fraction with the common denominator, then add or subtract the numerators and simplify the result.
Key Concepts
Property 1. Find the lowest common denominator (LCD). 2. Build each fraction to an equivalent one with the LCD. 3. Add or subtract the numerators, and keep the same denominator. 4. Reduce if necessary.
Examples Problem: Calculate $\frac{4}{x 3} + \frac{2}{x+1}$.
Step 1: Find the LCD. The denominators are prime, so the LCD is $(x 3)(x+1)$.
Common Questions
How do you add algebraic fractions?
Find the LCD of the denominators, rewrite each fraction with the LCD, add the numerators, and simplify the result.
How do you subtract algebraic fractions?
Same process as addition: find the LCD, convert each fraction, then subtract the numerators. Be careful with distributing the negative sign.
What is an example of adding algebraic fractions?
1/x + 2/x^2: LCD is x^2. Rewrite: x/x^2 + 2/x^2 = (x+2)/x^2.
What is a common mistake when subtracting algebraic fractions?
Forgetting to distribute the subtraction sign to all terms in the second numerator. For example, (3x)/(x+1) - (x-2)/(x+1) = (3x - x + 2)/(x+1) = (2x+2)/(x+1).
Where is adding and subtracting algebraic fractions taught?
Adding and subtracting algebraic fractions is covered in the Yoshiwara Elementary Algebra textbook for Grade 6.