Now as we know all about fractions, let’s understand the percentage.
The percentage is another way to express fractions. The only difference is, in the case of percentage the denominator is always ‘100’.
Fraction like \(^{20}/_{100} , ^{50}/_{100}\)represents a percentage. Instead of writing percentage as a fraction, we use “%” notation which simply means ‘out of 100’. 25% is \(^{25}/_{100}\) , 10% = \(^{10}/_{100}\) , 100% = \(^{100}/_{100}\).
Let's see the pictorial representation of 25% or fraction 1/4 - they both represent the same part of a total
The percentage can also be expressed as a decimal value, for example, 15% is \(\frac{15}{100}\) (to the base of 100) which is 0.15 in decimals. Let us express few percentages in fraction, ratio and decimal.
\(50\% = \frac{50}{100} = \frac{1}{2} = 1 : 2 = 0.5\)
\(20\% = \frac{20}{100} = \frac{1}{5} = 1: 5 = 0.2\)
\(0.5\% = \frac{0.5}{100} =\frac{5}{1000} = \frac{1}{200} = 0.005\)
Example 1: What is 20% of 5?
Express percentage as fraction: 20% = \(\frac{1}{5}\)
20% of 5 = \(\frac{1}{5}\) of 5 = 1
Example 2: What is 75% of 20?
75% \(= \frac{75}{100} = \frac{3}{4} \)
Find \(\frac{3}{4}\) of 20
\(\frac{3}{4} \times 20 = 15\)
Therefore, 75% of 20 = 15
Example 3: 50% of 20 apples are rotten. How many are good to eat?
50% of 20 = \(\frac{1}{2}\)of 20 = 10
10 apples are rotten, therefore 10 are good to eat.
Example 4: Bill spent 60% of his saving on buying a new toy car. He spent $120 to buy this new toy. How much savings did he have before buying this toy car?
Bill spends $60 on a toy car when his total saving was $100
Therefore if he spends $120, his saving was \(\frac{120 \times 100}{60} = 200\)
His total saving was $200 before buying the toy car.
Example 5: Bill scored 35 out of 50 in Maths. Express his marks in percentage.
Bill scored \(\frac{35}{50} \times100 = 70 \)%
To solve any percentage problem, express percent as a fraction and then handle the operation.
Many values of percentage range from 0 to 100. There is however no restriction and it is possible and mathematically correct for some percentages to be outside this range. For example, percentage values like 120%, -20% and others are common. For example, the price of an item is $100 and there is a 10% rise in its price (a $10 increase) the new price will be $110. It is important to note that the new price is 110% of the first price.
Example 6: The original price of a shirt was $50. It was decreased to $30. What is the percent decrease in the price of this shirt?
The actual decrease is $50 - $30 = $20
When an actual price is $50, the shirt price is reduced by $20
Therefore, when the price is $100, the shirt price is reduced by \(\frac{20}{50} \times 100 = 40%\)%
The percent decrease of the price of this shirt is 40%
Example 7: In a furniture store, a chair that sells for $150 is marked "10% off." What is the discount? What is the sale price of the chair?
The chair is selling at a 10% discount. So, 10% of $150 is $15. The discount on the chair is $15.
The sales price of the chair is $150 - $15 = $135
