1. or “Half of one, Six twelfths of the other”
Equivalent Fractions or
“Half of one,
Six twelfths of the other”

2. What is a fraction?
A fraction is part of a whole that is made up of equal parts.

3. Multiply by 1
5 x 1 =
235 x 1 =
2/3 x 1 =
a x 1 = 5
235
2/3 a

4. What is 1?

5. Was there something else?
Yes, it could also be part of a whole group of items.
Here is a group of cookies.
We could say 1/5 of these cookies are chocolate chip. We could also say that 4/5 are Oreos. 1 5 4 5 3 4
Oops, let’s make that 3/4 are Oreos.

6. Say, what?
Okay, try this. Let’s take a rectangle and divide it into 8 parts.
Now, if we color 2 parts, we say that 2/8 of the rectangle are shaded. 2 8

7. I’m with you. What’s next?
Now, let’s take that same rectangle and divide it into 16 parts.
If we color 4 parts, we say that 4/1 of the rectangle are shaded. 4 16

8. So that means? So that means 2/8 is equivalent to 4/1 .16
And we write it this way: = 2 8 4 16

9. Give us another example.
Okay, how about: 3 9 1 3 3 9 1 3 =

10. Vocabulary
Equivalent fractions are fractions that represent the same amount. 2 4 = 8 4

11. Creating Equivalent Fractions
Multiply the numerator and denominator by the same number.
Divide the numerator and denominator by the same number (it has to be a common factor to work with division)
We can choose any number to multiply by. Let’s multiply by 2. 3
x 2 6
So, 3/5 is equivalent to 6/10. = 5
x 2 10

12. How do you find equivalent fractions?
You can multiply (or divide), but you must multiply (or divide) both the numerator AND denominator by the same number. 1 4 3 12 x3 = x3 2 5 4 10 x2 = x2

13. What about dividing?
Here’s how. 4 20 1 5
÷ 4 =
÷ 4 4 14 2 7
÷ 2 = ÷2

14. What if you’re not sure?
Here is how you can check to see if two fractions are equivalent.
You can “cross-multiply.”
5 x 2 = 10 1 5 2 10 =
1 x 10 = 10
Since both products are the same, these two fractions are equivalent.

15. How do you know if they’re not equivalent?
Here is an example. You still “cross-multiply.”
3 x 4 = 12 2 3 4 5 =
2 x 5 = 10
Since both products are NOT the same, these two fractions are NOT equivalent.

16. Vocabulary: Simplest Form
Fractions are in simplest form when the numerator and denominator do not have any common factors besides 1.
Examples of fractions that are in simplest form: 4 2 3 5 11 8

17. Vocabulary: Simplify
Simplify means to reduce a fraction to it’s simplest form.

18. Writing Fractions in Simplest Form.
Find the greatest common factor (GCF) of the numerator and denominator.
Divide both numbers by the GCF.

19. Example: 20 5
÷ 4 =
Simplest Form 28
÷ 4 7 20 28
20: 1, 2, 4, 5, 10, 20
We will divide by 4.
28: 1, 2, 4, 7, 14, 28
1 x 20
2 x 10
4 x 5
1 x 28
2 x 14
4 x 7
Common Factors: 1, 2, 4
GCF: 4