1. 5-3 Adding and Subtracting Mixed Numbers Warm Up Problem of the Day
Course 1
Warm Up
Problem of the Day
Lesson Presentation

2. Add or subtract. Write each answer in simplest form.
Warm Up
Add or subtract. Write each answer in simplest form. – – 7 12 __ 1 2 __ 1 12 __ 3 11 __ 2 3 __ 31 33 __ 1 6 __ 3 4 __ 11 12 __ 11 12 __ 1 3 __ 7 12 __

3. Problem of the Day The sum of every row, column and diagonal is
the same. Complete the
magic square. 1 __ 3 1 3 __ 11 12
___ 4 1 6 __ 5 6 __ 12 1 __ 2 3 __ 1 4 __

4. Learn to add and subtract mixed numbers with unlike denominators.

5. Additional Example 1A: Adding and Subtracting Mixed Numbers
Find the sum. Write the answer in simplest form. 1 8 __ 5 6 __ 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
______ ______ 46 48 __ 23 24 __
Add the fractions and then whole numbers, and simplify.
= 4

6. Additional Example 1B: Adding and Subtracting Mixed Numbers
Find the difference. Write the answer in simplest form. 2 3 __ 1 4 __
5 – 1 2 3 __ 8 12 __
The LCD of 3 and 12 is 12. 5 5 1 4 __ 3 12 __
Write equivalent fractions with a denominator of 12. –1
– 1
______ ______ 5 12 __
Subtract the fractions and then the whole numbers. 4

7. Additional Example 1C: Adding and Subtracting Mixed Numbers
Find the sum. Write the answer in simplest form. 1 2 __ 4 5 __ 1 2 __ 5 10 __ 2 2
The LCD of 2 and 10 is 10. 4 5 __ 8 10 __
Write equivalent fractions with a denominator of 10. +4
+ 4
______ ______ 13 10 __ 3 10 __
Add the fractions and then the whole numbers, and simplify.
= 7 13 10 __ 3 10 __
6 = 6 + 1

8. Additional Example 1D: Adding and Subtracting Mixed Numbers
Find the difference. Write the answer in simplest form. 2 3 __ 2 9 __
6 – 3 2 3 __ 6 9 __
Think: 9 is a multiple of 3, so 9 is the LCD. 6 6 2 9 __ 2 9 __
Write equivalent fractions with a denominator of 9. –3
– 3
______ ______ 4 9 __ 3
Subtract the fractions and then the whole numbers.

9. Check It Out: Example 1A
Find the sum. Write the answer in simplest form. 1 4 __ 1 6 __ 1 4 __ 6 24 __
Multiply the denominators · 6 = 24 2 2 1 6 __ 4 24 __
Write equivalent fractions with a denominator of 24. +3
+ 3
______ ______ 10 24 __ 5 12 __
Add the fractions and then whole numbers, and simplify.
= 5

10. Check It Out: Example 1B
Find the difference. Write the answer in simplest form. 1 2 __ 3 7 __
– 1 1 2 __ 7 14 __ 4 4
The LCD of 2 and 7 is 14. 3 7 __ 6 14 __
Write equivalent fractions with a denominator of 14. –1
– 1
______ ______ 1 14 __
Subtract the fractions and then the whole numbers. 3

11. Check It Out: Example 1C
Find the sum. Write the answer in simplest form. 7 8 __ 2 3 __ 7 8 __ 21 24 __ 2 2
The LCD of the denominators is 24. 2 3 __ 16 24 __
Write equivalent fractions with a denominator of 24. +4
+ 4
______ ______ 37 24 __ 13 24 __
Add the fractions and then the whole numbers, and simplify.
= 7
6 = 6 + 1 37 24 __ 13

12. Check It Out: Example 1D
Find the difference. Write the answer in simplest form. 3 4 __ 1 8 __
– 2
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

13. 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 __ 1 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.
Helpful Hint
You can use mental math to find an LCD. Think: 8 is a multiple of 4 and 8.

14. 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.

15. Lesson Quiz
Find each sum or difference. Write the answer in simplest form. –
– 4
5. Miles worked hours on Friday and hours on
Saturday. How many total hours did he work? 3 1 4 __ 16 13 24 __ __ 11 __ 2 __ 1 __ 3 12 3 6 8 __ 7 __ 3 8 7 40 __ __ 2 1 6 7 30 __ __ 8 10 5 6 3 __ __ 2 4 3 5 12 __
14 hours