Converting Fractions to Decimals
Two methods:
1. Building a fraction to a base ten number
2. Dividing numerator by denominator
Building up the fraction to a base ten number:
1 5 5
x 5 .5
2 10
5 4 20
.20
25 4 100
7
7 25 175
* 1.75
4 4 25 100
8/3 : Repeating Decimal
2.666
3 8 3 8.000
= 2.6
6 Put a bar over the first
number(s) that repeats
20 And drop the rest.
18
02
Mixed Fraction to a Mixed Decimal
Whole numbers to the left of the fraction 7
And to the left of the decimal numbers
3
15
Convert fractional part to decimal
3.46
Divide.
.4 6
15 7.00
60
100
090
0100
Percent
Section Understanding
Percent
Percent, %, means per hundred.
The percent number is that number compared to
a total of 100.
100
90
Example: For 80
every $100 70
60
invested,
50
you received $6 in 40 100
return; the interest 30 Return
20
rate is 6 % 10
0
1st 2nd 3rd 4th
Qtr Qtr Qtr Qtr
100 100 100 100 100
Return 6 50 75 125
What is the percentage for the following:
386/100 386%
1/100 1%
.07/100 .07%
Write as a decimal
38% .38
6% .06
47% .47
375% 3.75
What are the rules to
change % to a decimal?
Ex: 82%
Drop the % symbol
82
Perform the operation the symbol
represents - Divide by 100
- move decimal 2 places
.82
What is the clue word? Per
- per hundred or divide by 100
Writing a Decimal as a
Percent
Move the decimal 0.47 (100%)
point two places 47
to the right -
multiply by 100
Add the % symbol
at the end 47%
of the number
Which way to move
decimal?
Remember the alphabet
D before P
L before R
.52 .005 .5%
52% D P
D P L R
L R
Remember - 47% is 47 out of every 100.
You may not have 47 items.
A ratio is a comparison.
For every 100 total items, there is 47.
If there were 10 total items,
you would have 4.7 items
Changing Between Percents,
Decimals, and Fractions
Percent to 75%
fraction 75
Drop the symbol 75/100
Write the percent
number over 100 3/4
reduce
Example: 225% Rewrite symbol as 1/100
225 x __1_ = 225
1 100
100
2 25/100 = 2 1/4 Simplify (reduce fraction)
Example 3
9 %
8
75
% Change to improper fraction
8
75 1
Change symbol to fraction
8 100
3
3
1 Reduce
8 4 32
Memorize the following
equivalents
25% ¼
50% ½
75% ¾
33 1/3% 1/3
66 2/3% 2/3
10% 1/10
Fraction to Percent
Can you easily change the denominator to equal 100?
1 ? 1 25 25
25%
4 ? 4 25 100
34 ? 34 4 136
136%
25 ? 25 4 100
If denominator cannot be changed easily
to 100, find decimal number first.
.166
1
6 1.000 .16 16.67%
6 Rounded to the nearest
06
Hundredth of a percent
040
036
0040
Alternative method for fraction to
percent:
7 n
Write a proportion
8 100
Cross multiply 7*100 = 8 n
700 8n
700 = 8n
8 8
N = 87.5%
Changing a fraction to a percent containing a fraction:
Stop the division after two steps
0.91
11 8 .91 2 100 91 2 %
12 11.00 .91
12 12 3 100 3
108
0020
0012
0008
Solving Percent Problems
Using an equation
Translating a Percent Problem into
an Equation
What is 5% of 19.00?
N = .05 x 19.00
N = .95
Find 0.6% of 400 35% of what is 60?
.35 x N = 60
N = .006 x 400
N = 60 / .35
N = 3.6 N = 1714.2
Words to symbols
“What” becomes n
“Is” becomes =
Percent numbers become decimals
“of” means multiplication
Example
90 is what percent of 20?
90 = p x 20 =4.5 * 100%
90 20 n = 450%
20 20
4.5 = n
Solving % Problems by
Proportion
Identify the Parts of the Percent
Proportion
The base, b, is always multiplied by the rate.
In, 16% of 370, 370 is the base.
The amount, a, is always by itself on one side of
the equation.
In “What percent of 18 is 4.5?”, 4.5 is the amount.
PIE A, amount
Base = b P= percent
A = b (p) A A
p b
b p
Change decimal to percent
Set up Proportion
A p
Cross multiply and then divide
b 100 By the variable’s number
Ex: Find 260 % of 40
a 260 Reduce fraction and cross multiply
40 100
A(10)=40( 26)
A = 4 * 26 A = 104
What percent of 4000 is 160?
A p
b 100
160 p
400 p = 16* 100
4000 100
400 p 16 * 100
400 400
16
P
4
P4 %
END