What is meant by ‘Percent’?
A ‘percent’ is the value of a part-to-whole ratio where the whole is equal to 100. The percent can be expressed as a fraction with a denominator of 100. The symbol ‘%’ is used to denote values as percents. For example,
How do we write Percents as a Fraction?
While expressing percents as a fraction, we first omit the percent symbol. The percent value is the numerator, and the denominator is 100.
Let’s consider an example:
45% in fraction form will be: \(\frac{45}{100}\).
[Note: Fractions obtained from percents may be further simplified if required.]
How to write percent in Decimal Form?
While expressing percents as a decimal, we first omit the percent symbol. The decimal point is moved two places left to account for the division by 100. It can be represented as,
Note: Percents can also be represented in the model format as well.
Solved Examples
Example 1: Represent \(\frac{6}{20}\) as a percent.
Solution:
Here, the denominator is 20 and \(20 \times 5 = 100\)
So, multiply the numerator and the denominator by the same number, that is, 5.
Write the numerator with the percent symbol to express the percent value.
\(\frac{6}{20} = \frac{6 \times 5}{20 \times 5} = \frac{30}{100} = 30%\)
Hence, \(\frac{6}{20}\) as a percent is 30%.
Example 2: Express 65% as a decimal, and draw a model diagram to represent 65%.
Solution:
Represent 65% as a decimal by removing the percent symbol, and placing a decimal point.
The decimal point moves ‘two decimal places’ to the left.
65% = 0.65
The following model expresses 0.65 or 65%.
Example 3: Adam is hosting a garage sale. He sold 32 items out of 50 items that were on sale. Can you find the percent of items that he sold?
Solution:
Total number of items = 50
Number of sold items = 32
In order to find the percent of items sold, we express the fraction as, \(\frac{32}{50}\).
Now, the denominator is 50 and when multiplied by 2 we get 100.
So, multiply both the numerator and the denominator by 2. T
Write the numerator with the percent symbol to express the percent value.
\(\frac{32}{50}= \frac{32 \times 2}{50 \times 2} = \frac{64}{100} = 64%\)
Hence, Adam sold 64% of the items in the garage sale.
50% of any number means half of the given number.
By learning about percentage, we can clearly understand real-life situations such as discounts in shops, bank interest rates, rate of change and many other instances and quickly solve math problems based on these concepts.
The most basic use of percentages is to compare quantities and values in percent form.
Ratios are mostly used to compare quantities, and the quantities are of the same kind.