1. 5.3 Adding and Subtracting Mixed Numbers
I can add and subtract mixed numbers with unlike denominators

2. Additional Example 1A: Adding and Subtracting Mixed Numbers
Find the sum. Write the answer in simplest form. 1 8 __ 5 6 __
3 + 2 = 5
Estimate the sum. 1 8 __ 6 48 __
Multiply the denominators · 6 = 48 3 3 5 6 __ 40 48 __
Write equivalent fractions with a denominator of 48. +1
+ 1
______ ______
Add the fractions and then whole numbers, and simplify. 46 48 __ 23 24 __
= 4
4 is close to the estimate of 5. The answer is reasonable. 46 48 __

3. Check It Out: Example 1C
Find the difference. Write the answer in simplest form. 3 4 __ 1 8 __
– 2
8 – 2 = 6
Estimate the difference.
Think: 8 is a multiple of 4, so 8 is the LCD. 3 4 __ 6 8 __ 7 7
Write equivalent fractions with a denominator of 8. 1 8 __ 1 8 __ –2
– 2
______ ______ 5 8 __
Subtract the fractions and then the whole numbers. 5 5 8 __
5 is close to the estimate 6. The answer is reasonable.

4. Additional Example 2: Measurement Application
The length of Jen’s kitten’s body is inches. Its tail is 5
inches long. What is the total length of its body and tail? 1 4 __ 1 8 __ 1 4 __ 8
Add
Find a common denominator. Write equivalent fractions with the LCD, 8, as the denominator. 1 4 __ 2 8 __ 10 10 1 8 __ 1 8 __ +5
+ 5
______ ______
Add the fractions and then the whole numbers. 3 8 __ 15 3 8 __
The total length of the kitten’s body and tail is inches.
You can use mental math to find an LCD. Think: 8 is a multiple of 4 and 8.
Helpful Hint

5. Check It Out: Example 2
The length of Regina’s mouse’s body is inches. Its tail is 2
inches long. What is the total length of its body and tail? 2 3 __ 1 6 __ 2 3 __ 1 6
Add
Find a common denominator. Write equivalent fractions with the LCD, 6, as the denominator. 2 3 __ 4 6 __ 2 2 1 6 __ 1 6 __ +2
+ 2
______ ______ 5 6 __
Add the fractions and then the whole numbers. 4 5 6 __
The total length of the mouse’s body and tail is inches.

6. Lesson Quiz
Find each sum or difference. Write the answer in simplest form.
5. Miles worked hours on Friday and hours on
Saturday. How many total hours did he work? 3 1 4 __ 16 13 24 __ 8 7 40 __ 6 7 30 __ 3 __ __ 2 4 3 5 12 __
14 hours