Decimals, fractions and percentages
Maths · Key Stage 2 · The School
Three costumes, one number
A half can be written 1/2, 0.5 or 50%. Same amount, three costumes for three jobs: fractions for exact shares, decimals for calculating, percentages for comparing. Learn the common set by heart: 1/2=0.5=50%, 1/4=0.25=25%, 3/4=0.75=75%, 1/10=0.1=10%, 1/5=0.2=20%, 1/3≈0.333≈33.3%.
Percent means "per hundred"
Per cent literally means per hundred, so 37% means 37 out of every 100. To find 10% divide by 10; to find 1% divide by 100. Everything else is built from those two: 30% is three lots of 10%; 15% is 10% + half of it; 7% is seven lots of 1%. Mental percentages are just repeated halving and adding.
Comparing a mixed list
Order 0.6, 55%, 3/5. Convert everything to one costume — decimals are easiest: 0.6, 0.55, 0.6. So 55% is smallest and the other two are EQUAL. Notice how the answer would be invisible without converting; whenever you must compare, convert first and compare second.
A percentage of an amount, worked through
Find 35% of 80 with no calculator. Build it from the two you can always get: 10% by dividing by 10, and 1% by dividing by 100. 10% of 80 is 8, so 30% is three of those, 24. 5% is half of 10%, so 4. Add them: 35% of 80 = 24 + 4 = 28. Now check it is sensible — 35% is a bit over a third, a third of 80 is about 27, and 28 sits right there. The same route handles the awkward ones: 17.5% is 10% + 5% + 2.5%, each one half of the one before. And it runs backwards too: if 20% of a number is 14, then 10% is 7, so the whole thing is 70.