Convert - Fraction → Percent
#ARTH-7-23
Category
Description
How to convert a fraction to a percent.
Course(s)
Mini-Lesson
085
x
Arithmetic
091
6.4
Definition(s)
093
x
Sub-category
095
x
097
x
Fractions
100
x
ADN
E18
ch5
PHT
ch1
Fraction
A fraction is a comparison of a part of something to its whole.
The numerator is the number of equal parts being considered.
The denominator is the number of equal parts in the whole.
Percent
Percent means “per one hundred”. Percent is a ratio out of 100 and is
represented by the % symbol.
Proportions
A proportion states that two ratios or rates are equal.
If
Rule
Example
𝑎
𝑏
&
𝑐
𝑑
are two equal ratios, then
𝑎
𝑏
=
𝑐
𝑑
is a proportion.
Fraction to percent conversion:
𝑛
Set up a proportion equal to 100
OR
Divide (𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟 ÷ 𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟) to find the decimal, and then
change to a percent by shifting the decimal two places to the right.
Write the fraction as a decimal:
𝟑
𝟖
a. Method One: Set up a proportion
3
𝑝
= 100
8
3 ∙ 100 = 8 ∙ 𝑝
300 = 8 ∙ 𝑝
8
8
37.5 = 𝑝
set up a proportion
cross-multiply
divide
Answer: 37.5%
ARTH-7-23 | Page 1
b. Method Two: Divide to find decimal, then shift decimal to find
percent
0.3 7 5
8 3.0 0 0
-2 4
6 0
-5 6
4 0
-4 0
0
Answer: 0.375 = 37.5%
Practice
Remember!
A proportion will give you a percent immediately; however division gives
you a decimal that must then be changed to a percent!
Problems
Write each of the following fractions as a percent.
1.
2.
3.
See also
Practice
3
4
9
16
4
11
ARTH-2-11: divide - whole numbers - single digit divisors
ARTH-2-12: divide - whole numbers - multiple digit divisors
ARTH-7-22: convert - fraction → decimal
ARTH-8-13: convert - decimal → percent
ARTH-9-6: proportion - definitions
ARTH-9-8: solve - proportion for unknown
ARTH-10-1: percent - definition
ARTH-10-3: convert - percent to fraction
Answers
75%
56.25%
ARTH-7-23 | Page 2
36.36% ≈ 36.4%