Adding and Subtracting Fractions

Questions

1. Find the lowest common denominator , then add the fractions

2. Find the lowest common denominator, then add the fractions

3. Combine

4. Combine

5. Combine

6. Combine

7. Combine

8. Combine

Solutions

1. Technique: prime factor the numerators to determine the LCD (lowest common denominator).

multiply by appropriate numbers to get common denominator
simplify
now that the denominators are the same , you can add numerators
simplify

2.

3. The denominators are already the same.

4. The denominators are already the same.

5.

Note: we usually would write 18 = 2 × 9 but since we are going to cancel everything in the numerator , it helps to write
as 18 = 1 × 2 × 9 so we can see that there will still be a 1 left in the numerator.

6. First, convert the mixed numbers to improper fractions since we know how to add improper fractions.

Now get a lowest common denominator .

Now we can add .

7.

8. First, convert the mixed numbers to improper fractions since we know how to add improper fractions.

Now get a lowest common denominator.

Now we can add.