Exploring Fractions

1. Exploring Fractions created by Michele Hinkle

2. The number that tells how many equal parts are described is the numerator. The number that tells the number of equal parts in the whole is called thedenominator. A fraction is a way of representing part of a whole or part of a group. What fraction of the candy is orange? 3 9

3. The pizza has been cut into three equal parts. We call these thirds. A third is written as 1 3 .

4. The whole pizza cut into three equal parts gives us thirds. Think about just one slice. We can write this using a fraction 1 3.

5. Think about two slices. Two slices is two thirds. We can write two thirds as 2 3 . The top number of the fraction tells us how many slices we have. We call it thenumerator. The bottom number tells us how many parts in the whole pizza. We call it the denominator.

6. If all the pieces of a whole are present, we call that 1 whole. Since 6 slices of the cake are present, we can say that 6 6 = 1 whole

7. Here are all the fractions you can make from a cake cut into six slices.

8. Representing Fractions 3 6

9. Equivalent Fractions

10. 1 2 • 124 • 4 and 8 are equivalent fractions. 0 0 0 1 1 1 1 4 2 4 3 4 1 8 2 8 3 8 4 8 5 8 6 8 7 8 Equivalent Fractions name the same amount.

11. 2 5 = 2 5 4 10 = = 2 5 6 15 = = To find equivalent fractions, you can multiply the numerator and denominator of a fraction by the same nonzero number. 2 x 2 5 x 2 2 x 3 5 x 3

12. 1 2 3 7 Compare and 1.Multiply 3 6 3 7 Since 1 2 3 3 3 6 is not the same as = x , these fractions are not equivalent 2. Compare 3 6 3 7 and

13. Simplifying Fractions • A fraction is in simplest • form when its numerator • and denominator have • no common factors other • than 1.

14. 6 18 3 3 2 6 6 18 ÷ = = ÷ Divide the numerator and the denominator by a common factor. 1 1 and 3 have no other common factor greater than 1. 2 Keep dividing by common factors until the only common factor is 1. 2 6 2 6 ÷ 2 2 1 3 = = ÷ 3 is a common factor of 6 and 18. 2 is a common factor of 2 and 6.