Comparing Fractions: MUST COMPARE AGAINST THE SAME WHOLE
You cannot compare fractions unless you are comparing 2 same size wholes.
We assume that all fraction, unless told otherwise, are made from the same whole.
o Think of money: we have quarters, dimes, nickels, and pennies. Their amount is based off how many equal
a dollar.
o Percent’s: out of a hundred.
o Any fraction can be turned into a percent by creating an equivalent fraction with a 100 as the
denominator. (See the bottom of the 3rd page for the basic fraction to percent equivalents).
Conjectures/Strategies for comparing:
 Use benchmarks: half or whole
o When you are 1 piece away from a whole the smaller the piece the closer you are
 2/3 and 4/5
 1/3 is a decent size piece (33.33%)
 1/5 is small, only 20 cents or 20%
o 4/5 is the bigger fraction because it is closer to a whole than 2/3


4/10 and 5/6
 Half of 10 is 5. Since 4 is less than 5, 4/10 is less than half
 Half of 6 is 3. Since 5 if more than 3, 5/6 is more than half
 5/6 is bigger than 4/10
If numerators or denominators are the same think about what that means for the size of the pieces.
o 2/6 and 2/4
 Both fractions have 2 pieces but the size of the pieces are different.
 Sixths are cut smaller than fourths (the less pieces you cut a whole into the bigger the pieces)

3/8 and 5/8
 Both fractions have their wholes cut into eight pieces so the pieces are equal.
 The more pieces the more you have since the pieces are equal in size.
Simplifying Fractions:
Your numerator should be a prime number if it is simplified, unless the denominator is prime.




Divide the top and bottom by the same number (the BE FAIR rule of math: what you do to one you do to the
other)
Always try to divide by 2. If 2 doesn’t work try 3 or 5.
If the numerator is a prime number the only thing you can divide into the top and bottom is the numerator
(see the second example)
Keep dividing until you can no longer divide the top and bottom by the same number.
Example 1: Simplify 6/8
 Both 6 and 8 can be divided by 2
6
--8
divided by 2
=
divided by 2
3
--4
Example 2: Simplify 3/6
 3 can not be divided by 2
 But 3 can be divided by itself anf 6 can be divided by 3 as well
3
--6
divided by 3
=
divided by 3
1
--2
Example 3: Simplify 8/12
 8 and 12 can both be divided by 2
 Keep dividing by 2 can you can no longer divide top and bottom by 2 (or another number)
8
--12
divided by 2
=
divided by 2

8
--12
divided by 2
=
divided by 2
2
--3
I could have thought of the biggest number that can go into 8 and 12 and that would be 4.
divided by 4
=
divided by 4

4
--6
2
--3
I know 2/3 is the simplest form because 2 cannot be divided by anything other than 2 and 3 cannot be divided by 2.
Example 4: Simplify 5/10
 5 can only be divided by itself.
 10 can be divided by 5
5
--10
divided by 5
=
divided by 5
1
--2
Example 5: Simplify 4/5 (Even though 4 is not prime, 5 is. This fraction is already simplified since nothing goes into 4 and 5).
Equivalent Fractions:

It is the opposite of simplifying. You must multiply the top and bottom by the same number.
For example:
3
X2
--=
4
X2
6
--8
X2
=
X2
12
--16
So since I multiplied the top and the bottom by the same number I can say:
o ¾ is equal to 6/8
o 6/8 is equal to 12/16
o I can also say ¾ is equal to 12/16
Example 2:
5
--6
Example 3:
X2
=
X2
10
--12
5
--6
X3
=
X3
Example4:
15
--18
5
--6
X5
=
X5
25
--30
In all the examples above the fraction on the left is equivalent to the fraction on the right since I used the same factor to
multiply the top and the bottom.
 I have kept the value the same.
 I have just made the pieces look different.
Fraction of a Number:
 Sometime you already know a numerator or denominator so you have to figure out exactly what number to multiply
by, as in a fraction of a certain number
o I want ¾ of 20.
3
?
--=
--4
20 Think: What times 4 gets you 20? 4 times 5
SO,
3
X5
15
--=
--4
X5
20
o
I want 4/5 of 25
4
--5
SO,
4
--5
=
X5
=
X5
?
--25 Think: What times 5 gets you 25? 5 times 5
20
--25
*****If you need to do percent of a number, you can always turn a percent into a fraction (100 would be the denominator or if
you have memorized the benchmark percent’s.
1/12 = 8/3% 1/10 = 10%
1/8 = 12.5%
1/6 = 16.67% 1/5 = 20%
¼ = 25%
1/3 = 33.3%
½ = 50%