Percent and Percentage
ICSE Class 8 · Mathematics · Chapter 7
What this chapter covers
- The meaning of percent
- Converting between fractions, decimals, ratios and percentages
- Percentage of a quantity, and one quantity as a percentage of another
- Finding the whole when a percentage is known
- Percentage increase and percentage decrease
- Finding the new value and the original value
- Successive percentage changes
- Applications of percentage
Key definitions
Percent means "out of every hundred" or "for each hundred".
A percentage is a fraction whose denominator is 100, written with the % sign instead of the denominator.
Percentage increase is the increase in a quantity expressed as a percentage of its original value.
Percentage decrease is the decrease in a quantity expressed as a percentage of its original value.
A multiplying factor is the single number by which the original value is multiplied to get the new value after a percentage change.
Key points
- Percent means "out of every hundred"; x% = (x)/(100).
- To change a fraction or decimal into a percentage, multiply by 100; to change a percentage into a fraction, divide by 100 and simplify.
- x% of Q is (x)/(100) × Q.
- To express A as a percentage of B, work out (A)/(B) × 100%, with both quantities in the same unit.
- If x% of a number is P, the number is (P × 100)/(x).
- Percentage increase or decrease is the change divided by the original value, multiplied by 100%.
- An increase of r% has the multiplying factor (100 + r)/(100); a decrease of r% has the factor (100 - r)/(100).
- To find an original value, divide the new value by the multiplying factor; never add or subtract the percentage of the new value.
- Successive percentage changes are combined by multiplying their factors, not by adding the percentages.
- In mixture problems, build the answer around the quantity that does not change.
Questions answered
Write (3)/(25) as a percentage.
(3)/(25) × 100% = 12%.
Write 0.6% as a decimal and as a fraction in lowest terms.
0.6% = (0.6)/(100) = 0.006 = (6)/(1000) = (3)/(500).
Find 16% of 2.5 kg, giving your answer in grams.
0.16 × 2500 g = 400 g.
What percentage of 2 hours is 18 minutes?
2 hours = 120 minutes, so (18)/(120) × 100% = 15%.
30% of a number is 54. Find the number.
(54 × 100)/(30) = 180.
In a class of 45 students, 60% are girls. How many boys are there?
Boys are 40% of 45, which is 0.4 × 45 = 18 boys.
The price of a notebook rose from ₹40 to ₹46. Find the percentage increase.
Increase = ₹6, so (6)/(40) × 100% = 15%.
A number decreased by 15% becomes 391. Find the number.
The new value is 85% of the number, so the number is (391)/(0.85) = 460.