(7) Lesson 4.4 - Add and Subtract Unlike Fractions

1. Course 2, Lesson 4-4
Add or subtract. Write in simplest form.
1. 2.
3. 4.
5. For their foreign language requirements, of students take
French and of students take Spanish. The remaining students
take sign language. What fraction of students take sign
language?
6. Eric had of a bottle of shampoo left. He used of the
bottle on his dog. How much shampoo did Eric have left?
+
3 2
10 10

9 6
21 21

7 3
13 13
 
   
 
+
3 6
8 8
2
5
1
5
7
10
2
10

2. Course 2, Lesson 4-4
Answers
1. 2.
3. 4.
5.
6. of a bottle
1
2
1
7
4
13
1
1
8

2
5
1
2

3. WHAT happens when you add,
subtract, multiply, and divide
fractions?
The Number System
Course 2, Lesson 4-4

4. Course 2, Lesson 4-4 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of
Chief State School Officers. All rights reserved.
The Number System
• 7.NS.1 Apply and extend previous understandings of addition and
subtraction to add and subtract rational numbers; represent addition
and subtraction on a horizontal or vertical number line diagram.
• 7.NS.1d Apply properties of operations as strategies to add and
subtract rational numbers.
• 7.NS.3 Solve real-world and mathematical problems involving the four
operations with rational numbers.

5. Course 2, Lesson 4-4 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of
Chief State School Officers. All rights reserved.
The Number System
• 7.EE.3 Solve multi-step real-life and mathematical problems posed with
positive and negative rational numbers in any form (whole numbers,
fractions, and decimals), using tools strategically. Apply properties of
operations to calculate with numbers in any form; convert between forms
as appropriate; and assess the reasonableness of answers using mental
computation and estimation strategies.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.

6. • To add unlike fractions
• To subtract unlike fractions
Course 2, Lesson 4-4
The Number System

7. Course 2, Lesson 4-4
The Number System
• unlike fractions
1 1and
42
3 5and
4 9

8. Course 2, Lesson 4-4
The Number System
To add or subtract fractions with different denominators,
• Rename the fractions using the least common denominator (LCD).
• Add or subtract as with like fractions.
• If necessary, simplify the sum or difference.

9. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
1. Find + .
Rename using the LCD, 4.
Divide the number line into
fourths since the LCD is 4.
=
1
2
Using either method, + = .
Use a number line.
1
4
Use the LCD.
The least common denominator of and is 4.
=
= Add the fractions.
Simplify.

10. Answer
Need Another Example?
Find + . Write in simplest form.

11. 1
Need Another Example?
2
3
Step-by-Step Example
2.
Associative Property of Addition
Commutative Property of Addition=
Simplify.
=
= + 1 or 1
Find – + + .

12. Answer
Need Another Example?
Find – + + . Write in simplest form.

13. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
3. Find – – .
Rename using the LCD, 6.
Divide the number line into
sixths since the LCD is 6.
=
Simplify.
=
7
Use a number line.
2
3
1
2
– –
Use the LCD.
– –
= Rewrite – as .
or Subtract the numerators. Simplify.
Check by adding
Using either method, – – = – or –1 .

14. Answer
Need Another Example?
Find – – . Write in simplest form.

15. Need Another Example?
Step-by-Step Example
4. Use the table to find the
fraction of the total population
that has type A or type B blood.
1
2
3
4
5
Add the fractions.
Rename using the LCD, 50.=
Simplify.
=
To find the fraction of the total
population, add and .
+
+
= or
So, of the population has type A or type B blood.

16. Answer
Need Another Example?
In one town, of the adopted dogs are German shepherds,
are golden retrievers, are Jack Russell terriers,
are poodles, and are mixed breeds. Find the fraction of adopted
dogs that are either golden retrievers or mixed breeds.

17. How did what you learned
today help you answer the
WHAT happens when you add,
subtract, multiply, and divide fractions?
Course 2, Lesson 4-4
The Number System

18. How did what you learned
today help you answer the
WHAT happens when you add,
subtract, multiply, and divide fractions?
Course 2, Lesson 4-4
The Number System
Sample answer:
When you add or subtract unlike fractions:
• Rename the fractions using the least common
denominator.
• Add or subtract as with like fractions.
• If necessary, simplify the sum or difference.

19. Find .
Course 2, Lesson 4-4
Ratios and Proportional RelationshipsThe Number System
3 2- +
58