1. Fractions
Any fraction can be written in many ways and still have the same value…
…are all the same…
0.5

2. Equivalent Fractions
Fractions are equivalent (equal) if they have the same value
We could change them to decimals to see if they are equal or leave them as fractions

3. How would we use this?
1. We might want the fraction to look “simpler” like ½ instead of 44/88
2. We might want to compare fractions to see which is bigger or smaller (it’s easy if they have the same denominator)
3. We might want to add or subtract fractions

4. We know that we can multiply or divide by 1 and the number stays the same
Since…
= 1
We can multiply or divide any fraction by these and the fraction keeps its value

5.  = ÷ =

6. What if we have 2 fractions like…
Why might we want them to have the same denominator?
to compare
to add or subtract

7. We need to find a common denominator
 5
 8
 8
 5

8. There are many common denominators, but only one is the smallest
 6
 8
 8
 6
Is there a smaller denominator we could use?
Yes, 24!

9. What we are doing is looking at the multiples of numbers…
The multiples of 6 are:
6, 12, 18, 24, 30, 36, 42, 48 and so on
The multiples of 8 are:
8, 16, 24, 32, 40, 48 and so on
Both 24 and 48 are common, but 24 is the least

10. Remember! You CAN’T have a Greatest Common Multiple! Why not?

11. Let’s compare some fractions
Which is larger,
What is the LCD?
Yes, 24

12. Compare these: The multiples of 16 are: 16, 32, 48, 64, 80 …

13. Another way of using equivalent fractions is to put fractions in simplest form or lowest terms
Would this fraction be easier to “understand” if the numbers were smaller?

14. We know we can divide both the numerator and denominator by the same number and get an equivalent fraction…

15. ÷ 2 ÷ 6 ÷ 2 ÷ 6 = = What number goes into both 36 and 96?
Sure, there are many, but let’s try 6 = =
÷ 2
÷ 6
Now 2…
What number goes into both 36 and 96?

16. ÷ 12
We could have done this in one step if we had used the GCF of 36 and 96… =
÷ 12 12
The GCF of 36 and 96 is…

17. Practice…

18. = Why would we want to do that?
We can also multiply the numerator and denominator by the same number…
 2 =
 2
Why would we want to do that?

19.  2
 3 = =
 2
 3
Can you think of a reason besides comparing that we might want the same denominators?
More on this next lesson

20. To summarize... We use common factors or GCF to...
simplify a fraction (lowest terms)
We use common multiples or LCM to...
find common denominators