Percentages

A percentage is a fraction out of 100. The symbol % literally means "÷ 100". So 25% means 25 out of every 100, which is the same as 25/100 = 0.25 = 1/4. Percentages, fractions and decimals are three ways to write the same kind of number — pick whichever is easiest for the question in front of you.

You meet percentages every day in Kenya: a 16% VAT line on a Naivas receipt, a 10% M-Pesa transaction fee, a school report card showing 72%, a Black Friday sale of "30% off", a bank deposit promising 7% interest per year. Knowing how to flip between %, fractions and decimals is the most useful single skill in this strand.

Convert percentage → decimal: divide by 100 (move the decimal point two places left). 75% = 0.75. 8% = 0.08. 125% = 1.25.

Convert decimal → percentage: multiply by 100 (move the decimal point two places right). 0.4 = 40%. 0.07 = 7%. 1.6 = 160%.

Convert fraction → percentage: divide and multiply by 100 (or get an equivalent fraction with denominator 100). 3/4 = (3 ÷ 4) × 100 = 75%. Or: 3/4 = 75/100 = 75%.

Convert percentage → fraction: write the % over 100 and simplify. 60% = 60/100 = 3/5.

Find a percentage of a number: convert the % to a decimal, then multiply. 30% of 200 = 0.30 × 200 = 60.

Express one number as a percentage of another: divide and multiply by 100. 15 out of 60 as a percentage = (15 ÷ 60) × 100 = 25%.

Percentage increase or decrease: find the change, divide by the original amount, multiply by 100. A phone's price rises from 8,000 to 10,000. Change = 10,000 − 8,000 = 2,000. % increase = (2,000 ÷ 8,000) × 100 = 25%.

Reverse percentage problems: if you know the answer AFTER a percentage was applied, divide by the percentage AS A DECIMAL to find the original. After a 20% discount a uniform costs KES 1,200. Original price = 1,200 ÷ 0.80 = KES 1,500.

Common mistakes to avoid:

• Forgetting that % means "÷ 100". When in doubt, write the % as a fraction over 100 and simplify from there.
• For percentage change, dividing by the new amount instead of the original. Always divide by what you STARTED with.
• Adding percentages of different totals as if they were the same kind of thing. 10% of 500 plus 10% of 700 is not 20% of anything obvious.
• Confusing "20% more" with "20% of". KES 100 increased by 20% is 120; 20% of 100 is just 20.

CBC Grade 5 introduces percentages as "out of 100"; Grade 6 covers conversions between %, fractions and decimals and finding percentage of an amount; Grade 7 brings percentage increase, decrease, profit, loss, simple interest and commission — the foundation for the financial literacy strand and a regular KPSEA question type.