Equivalent Fractions, Simplifying Fractions, and Least Common
Denominator (LCD)
Draw/model the following fractions:
1
2
4
8
What do you notice about your pictures?
*1/2 and 4/8 are equivalent fractions. Both fractions, in their
reduced, simplified form are the same fraction, 1/2.
1
How do we write 1 as a fraction?
1
1
2
2
3
3
4
4
and so on...
*We can take any fraction and multiply it by one, without actually
changing the fraction's model or picture ("how much" it is worth).
Doing that we can make many equivalent fractions.
Try making equivalent fractions to 3
4
--> Multiply 3/4 by 2/2 to get 6/8
--> Multiply 3/4 by 3/3 to get 9/12
...and so on...
So, 3/4 = 6/8 = 9/12, and we could continue the above process on and
on.
2
We use equivalent fractions to find a least common denominator
(LCD) that we'll use next week when we add fractions.
Create equivalent fractions using the given denominator.
1/4 with a denominator of 32
8/32
7/8 with a denominator of 24
21/24
8/9 with a denominator of 63
56/63
3
Sometimes, our fractions are not completely reduced or simplified
and we need to "reduce" or "simplify" our fractions.
We can do this by doing the opposite of multiplying by one like we
did before, but divide our fractions by 1. The 1 we'll choose will be
a fraction that has a common factor of our numerator and
denominator.
For example, reduce 8/32.
Well, we know both 8 AND 32
are divisible by 8, so lets divide our
numerator AND denominator by 8!
8 ÷ 8= 1
32 ÷ 8 = 4
So 8/32 = 1/4!
4
Your turn!
Simplify the following fractions.
a) 2/4
b) 9/63
1/2
c) 18/24
1/7
d) 45/5
3/4
e) 27/81
9
1/3
5