1. Tennessee Adult Education Mathematics Level 3 Curriculum 2011
Lesson 5
Fractions

2. Vocabulary Numerator: The top number of a fraction
Denominator: The bottom number of a fraction
Reduce/ simplify: these words both mean to break a fraction down to its simplest form.
Example:
How many parts are shaded (Numerator)
What fraction of the circle is shaded?
How many parts total (Denominator)
Read this fraction as three fourths

3. GCF = Magic Number
In order to reduce fractions, it is imperative to find the GCF(Greatest Common Factor)
The GCF is the greatest number that will divide into both the numerator and the denominator evenly. (It can not be 1)
Finding the GCF (magic number):
List all of the number’s factors.
8: 1, 2, 4, 8
What is the highest factor 8 and 16 have in common?
16: 1, 2, 4, 8, 16 8
= GCF or Magic Number

4. GCF=Magic Number
4 parts of 8 is the same as 1 part of 2: =

5. Reducing Fractions
In order to reduce fractions find a number that will fit into both the numerator and the denominator evenly. (It cannot be one) This number is called the “Magic Number.”
Then, divide both the numerator and the denominator by this “Magic Number.” (GCF)
Circle the number so it is not confused with the rest of the problem. 4
1. How many times will 4 divide into 4?
Example: = 1
What is a number that will divide into 4 and eight evenly?
2. How many times will 4 divide into 8? 2 4
Magic Number

6. Guided Practice
Reduce the following fractions = = = =

7. Guided Practice Reduce the following fractions 4 3 4 3 = = 2 4 2 4 = =
What will divide into 4 and 12 evenly? 4
What will divide into 6 and 9 evenly?
1. How many times does 3 divide into 6?
1. How many times does 4 divide into 4? 3 4 2 1 3
2. How many times does 3 divide into 9? = =
2. How many times does 4 divide into 12? 3 3
What will divide into 4 and 6 evenly? 2
What will divide into 4 and 16 evenly? 4 2
1. How many times does 2 divide into 4? 4
1. How many times does 4 divide into 4? 2 = 1 =
2. How many times does 4 divide into 16?
2. How many times does 2 divide into 6? 3 4

8. Adding and Subtracting Fractions with like denominators
When adding and subtracting fractions with like denominators (the bottom numbers are the same) Just add or subtract the numerator. (the top number) The denominator (the bottom number) stays the same. After the problem is solved, check the answer and make sure the answer does not need to be reduced.
Example 1:
Example 2: 2 5 - = = + = =

9. Guided Practice 1. 2. + = + = 3. 4. - = - =

10. Guided Practice
Remember: Only add or subtract the top number (numerator)
2 + 1 = 3
3 + 1 = 4
Now Reduce 2 1. 2. + = + = =
Bottom number stays the same (4)
Bottom number stays the same (6)
2 - 1 = 1
7 - 3 = 4
Now Reduce 4 3. 4. - = - = =
Bottom number stays the same (3)
Bottom number stays the same (8)

11. Multiplying Fractions
When multiplying fractions, just multiply across the top and across the bottom. Don’t forget to reduce the answer.
1. How many times will 6 divide into 6?
Example: 6
3 x 2 = 6 1 x = =
2. How many times will 6 divide into 18?
6 x 3 = 18
What number will divide into 6 and 18? 3 6
Magic Number

12. Guided Practice Multiply then reduce when necessary. 1. x = 2. x = 3.1. x = 2. x = 3. x =

13. Guided Practice Multiply then reduce when necessary.
There is not a number that will divide into both the numerator and the denominator, so there is no need to simplify.
1 x 3 = 3 1. x =
2 x 4 = 8
1 x 1 = 1 2. x =
5 x 3 = 15
What number will divide into 3 and 12? 3 3
Magic Number
1 x 3 = 3
How many times will 3 divide into 3? 3. x = =
3 x 4 = 12 1
How many times will 3 divide into 12? 4

14. Dividing Fractions
When dividing fractions, find the reciprocal of the second fraction. Reciprocal means to flip it. After finding the reciprocal of the second fraction, multiply the two fractions together.
Reciprocal
What is a number that will divide into 4 and 6?
Example: 2 2
Magic Number
1 x 4 = 4 ÷
Changes to: x = = =
2 x 3 = 6
How many times will 2 divide into 4? 2 3
How many times will 2 divide into 6?

15. Guided Practice
Remember to find the reciprocal of the second fraction then multiply. 1. ÷ = 2. ÷ = 3. ÷ =

16. Guided Practice
Remember to find the reciprocal of the second fraction then multiply.
There is not a number that will divide into both the numerator and the denominator, so there is no need to simplify.
1 x 2 = 2 1. ÷ =
Changes to x =
3 x 1 = 3
1 x 3 = 3 2. ÷ =
Changes to x =
2 x 5 = 10
How many times will 2 divide into 10? 5
How many times will 2 divide into 24? 2 12
5 x 2 = 10 3. ÷ =
Changes to x = =
8 x 3 = 24
What is a number that will divide into 10 and 24? 2
Magic Number