1. Rational Numbers & Equations
Lesson 3
Rational Numbers & Equations
Adding and Subtracting Fractions

2. Warm-Up Convert to an improper fraction. Convert to a mixed number.
Write in simplest form.
Write a fraction that is equivalent to .

3. Adding and Subtracting Fractions
Target:
Add or subtract fractions with like and unlike denominators.

4. Vocabulary
Least Common Multiple: The smallest multiple that is common to two or more numbers.
Least Common Denominator: The least common multiple of two denominators.

5. Example 1
Find the least common multiple of:
8 and 12
4 and 5
List a few multiples and find the smallest number in both lists.
List multiples of 5. 5, 10, 15, 20, 25, …
8: 8, 16, 24, 32, 40, …
12: 12, 24, 36, 48, …
Find the first multiple that 4 goes into evenly.
The LCM is 24.
5 - no, 10 - no, 15 - no, yes
The LCM is 20.

6. Adding and Subtracting Fractions
If denominators are not equal, rewrite the fractions as equivalent fractions with common denominators using the least common denominator.
Add or subtract the numerators.
Write the sum or difference over the common denominator.
Write the fraction in simplest form.

7. Example 2 Find the value of .
The fractions already have common denominators.
Add numerators.
Write in simplest form.

8. Example 3 On Monday, the Portland International Airport reported
inch of rain. On Tuesday it rained inch. What was
the total rainfall for these two days?
The LCM is 16. Write
with a denominator of 16.
Add the fractions.
Write as a mixed fraction.
It rained inches in Portland on Monday and Tuesday.

9. Example 4 Find the value of . The LCM of 3 and 4 is 12.
Rewrite fractions.
Subtract.

11. Exit Problems
Write each answer in simplest form.

12. Communication Prompt
What do you find to be the most difficult part about adding or subtracting fractions?