Unit 5 Math Fractions “Cheat Sheet”
1.
A fraction is a piece of the whole. It has 2 parts, the denominator, which is the digit under the fraction
bar, and the numerator, which is the digit on the top of the fraction bar.
2
Numerator
3
Denominator
2.
To find a fractional part of a whole set of items, you can divide and multiply.
Ex: What is ¼ of 12?
Step 1: Divide the whole set (in this case 12) by the denominator (4).
12 divided by 4 = 3
Step 2: Multiply the answer from the division problem (3), by the digit in the
numerator (1).
3 X 1= 3
Step 3: Now you have your answer, ¼ of 12 = 3
3.
A mixed number fraction is an amount that is represented with a whole number and a fraction, for
example 3 ¼. You read it, three and one-fourth. An improper fraction is a fraction where the numerator
is greater than the denominator, for example 13/4.
You can change from a mixed number to an improper fraction.
Ex: Change 6 ½ into an improper fraction.
Step 1: Multiply the denominator in the fraction (2) times the whole number (6).
2 X 6 = 12
Step 2: Take the answer from the multiplication problem (12), and add it to the
numerator in the fraction (1).
12 + 1 = 13.
Step 3: The answer from the addition problem(13) is now the new numerator and use the
same denominator(2) from the original fraction. Now your answer is 13/2.
*** 6 ½ is the same thing as 13/2. They are equal, or equivalent fractions.
You can change from an improper fraction to a whole or mixed number by dividing.
Ex: Change 13/2 to a whole number or mixed fraction.
Step 1: Just divide 13 by 2.
6
2 ) 13
-12
1
Whole number
Denominator
Numerator
Answer:
6½
4.
When comparing and ordering fractions, you must first look at the denominators.
* If the denominators are the SAME, then you compare the numerators and put them in order
based on the numerators.
*If the numerators are the SAME, the pieces will be the same for each fraction, so compare the
denominators. Remember…the smaller the denominator is, the larger the piece will be.
*If you are comparing just two fractions, then you can cross multiply to figure out which fraction is
bigger.
Ex: Which is greater? 2/3 or 4/5
Step 1: Multiply the denominator of the first fraction times the numerator in the second
fraction.
Step 2: Now multiply the denominator of the second fraction times the numerator in the
first fraction.
5 X 2= 10
4 X 3 = 12
2
4
3
5
Step 3: The answer of 10 helps describe 2/3 and the answer of 12 describes 4/5. Which
Number is greater? 10 or 12? Right – 12! So 4/5 is greater than 2/3.
5.
Adding fractions.
* In order to add fractions, you need to have common denominators. If you already have
common denominators, then just use that denominator in your answer and just add the digits on the top
of the fraction bar.
Ex: 4/7 + 2/7 = 6/7
*If you do not have common denominators, then you need to make the have common
denominators. That means you will find have to change one of the fractions into an equivalent fraction.
Ex: 2/4 + ½ = ?
Step 1: Decide which fraction you don’t want to change and which one you want to
change. For this example, I am going to keep 2/4 and I will change ½.
Step 2: I need to change ½ into an equivalent fraction. I need to change it into a fraction
that has a denominator of 4.
1
?
2
4
Step 3: Think about the denominators, 2 and 4. Think: What can I do to 2 to get 4? I can
multiply 2 X 2 to get 4. Correct! BUT…whatever you do to the bottom, you need
to do to the top. So you also then have to multiply 1 X2 and you will get 2.
So, ½ is equal to 2/4. Now you can add 2/4 + 2/4 and get 4/4, or 1 whole.
6.
To simply find an equivalent fraction, multiply both the numerator and the denominator of the fraction
by the same number.
6
X2
=
12
8
X2
=
16
If it’s a fraction with larger digits, then you can also use division instead to find an equivalent fraction.
16
/2
=
8
18
/2
=
9
7. Changing a fraction to a decimal.
*One way to change a fraction to a decimal is to find an equivalent fraction with a denominator of
10, 100, or 1000.
Ex: ¾ is what decimal?
Step 1: Look at the denominator. It is a 4. THINK: Which number, 10, 100, or 1000 can
be divisible by 4 or 4 X ? will give me one of those numbers? 4 X 25 = 100! So multiply the top
and bottom digits by 25 to get an equivalent fraction.
3
X 25
75
4
X 25
100
Step 2: Use the equivalent fraction to figure out what the decimal value of ¾ is. Use what
you know about place value to help you. 75/100 is read as seventy-five hundredths and written as
0.75. So ¾ = 0.75
*If you can’t change the fraction into an equivalent fraction with a denominator of 10,
100, or 1000, then you can divide. Divide the numerator by the denominator to see what decimal answer
you get.
(Next page)
Ex: 1/8 is what decimal?
Step 1: Divide the denominator by the numerator. You may use whichever
method of division you prefer, traditional or partial-quotients. If the problem asks you to find your answer
to a certain place value, then make sure you take that into account when you solve.
Traditional,
to the nearest
tenth:
0.1
8 1 .0
-0
1 0
- 8
2
Traditional,
to the nearest
hundredth:
0 . 12
8 1 .0 0
-0
1 0
- 8
20
-16
2
P-Q,
to the nearest
tenth:
8
1 .0
- 8
2
P-Q,
to the nearest
hundredth:
1
8
1 .0 0
- 80
20
- 16
2
10
2
*If you need to change a mixed number fraction into a decimal, use the whole number in your
answer and then find out what decimal the fraction piece is.
Ex: 3 1/8 is what decimal? Use the 3 in your answer – it will go on the left-side of the
decimal point and then figure out what 1/8 is as a decimal. Since we already know that 1/8 = 0.1 the
answer to What is 3 1/8 as a decimal? Is 3.1
8.
Percents
*To convert a decimal to a percent, just multiply the decimal by 100. Or move the decimal 2
places to the right. Remember to use a % sign in your answer!
* To convert a fraction to a percent…
1. First see if you can change it into an equivalent fraction over 100.
Ex: 89/100 = 89%
2. If you can’t change it to an equivalent fraction over 100, then divide and turn it into a
decimal (go at least 2 places after the decimal point) and multiply by 100, or move the decimal two places
to the right.
Ex: 3/8 = ? %
0 .37
8) 3.00
-24
60
-56
4
0.37 x 100 = 37%