About Percent Proportions
What is Percent?
Percent in mathematics is a numerical value or a ratio representing a part of a whole. It is denoted by a number followed by the ‘%’ symbol.
For example, 1 out of 100 is 1%, 2 out of 50 is 4%, 1 out of 1000 is 0.1% and so on.
Percentage is used to compare two or more quantities on a common base of 100.
What is Percent Proportion?
The percentage of a part to whole can be expressed as:
percent = \(\frac{\text{part}}{\text{whole}}\times 100\)
This equation can be rewritten as:
\(\frac{\text{percent}}{100}\) = \(\frac{\text{part}}{\text{whole}}\) or \(\frac{\text{part}}{\text{whole}}=\frac{\text{percent}}{100}\)
The equation implies the equivalence of two ratios, which are, percent to 100 and part to whole.
So the two fractions or ratios are in proportion. Therefore, this equation is known as percent proportion.
Solved Examples
Example 1: What number is 25% of 400?
Answer:
Here, we can use the percent proportion formula:
\(\frac{\text{part}}{\text{whole}}=\frac{\text{percent}}{100}\)
Substitute 400 for whole and 25 for percent in the formula:
\(\frac{\text{part}}{400}=\frac{25}{100}\)
part\( =\frac{25}{100}\times 400\) Multiply both sides by 400
part = 100 Simplify
Hence, 100 is 25% of 400.
Example 2: Find 30 is 20% of what number?
Answer:
The percent proportion formula states that
\(\frac{\text{part}}{\text{whole}}=\frac{\text{percent}}{100}\)
Substitute 30 for part and 20 for percent
\(\frac{30}{\text{whole}}=\frac{20}{100}\)
\(\frac{1}{\text{whole}} =\frac{20}{100\times 30}\) Divide both sides by 30
\(\frac{1}{\text{whole}} =\frac{1}{150}\) Simplify
whole = 150 Reciprocal
Hence, 30 is 20% of 150.
Example 3: Andrew scored 12 out of 30 in a math test. If the pass percentage is 35%, find out whether Andrew passed the test or not?
Answer:
Here, we will use the percent proportion equation for finding out percentage marks scored by Andrew. Then we will compare it with 35% to find out whether he passed the test or not.
The percent proportion formula states that
\(\frac{\text{part}}{\text{whole}}=\frac{\text{percent}}{100}\)
Substitute 12 for part and 30 for whole
\(\frac{12}{30}=\frac{\text{percent}}{100}\)
\(\frac{12}{30}\times 100\) = percent Multiply both sides by 100
40 = percent Simplify
So Andrew scored 40% in the test. Now, 40 > 35 implies that Andrew scored more than the passing percentage.
Therefore, Andrew passed the test.
Example 4: What number is 22% of 200?
Answer:
Here, we can use the percent proportion formula:
\(\frac{\text{part}}{\text{whole}}=\frac{\text{percent}}{100}\)
Substitute 200 for whole and 22 for percent in the formula:
\(\frac{\text{part}}{200}=\frac{22}{100}\)
part = \(\frac{22}{100}\times 200\) Multiply both sides by 200
part = 44 Simplify
Hence, 44 is 22% of 200.
Percent proportion is a way of expressing percent as a proportion equation.
Proportion states the equivalence of two ratios or fractions, whereas the percentage expresses a ratio or a fraction whose denominator is always 100.
The symbol for percentage is ‘%’.
Percentages are highly useful when it comes to understanding various aspects of real life situations. Percentages are used for expressing discounts on products and services, bank interest rates, rates of inflation and many statistical data.