L4 · Percent of a number (1% to 100%)

Learning goal

“I can find any percent from 1% to 100% of a number by building it from friendly chunks - 10%, 5%, 1% and the benchmark percents 25%, 50%, 75% - on a hundred grid.”

Percent — "per hundred": 35% means 35 out of every 100, the fraction 35/100.

Whole — the full amount a percent is taken of: in "30% of 90", the whole is 90.

Part — the amount the percent picks out: in "30% of 90 = 27", the part is 27.

Chunking — building a percent from pieces you can find instantly: 35% = 25% + 10%.

Worked example

Find 10%, 5% and 1% of 240. Step 1: Percent means "out of 100", and 100% of 240 is 240 itself. Step 2: 10% is one tenth of the whole: 240 / 10 = 24. On the hundred grid, that is one full row of the ten rows. Step 3: 5% is half of 10%: 24 / 2 = 12. And 1% is one hundredth: 240 / 100 = 2.4. Step 4: The benchmarks ride along free: 50% = half = 120; 25% = half of a half = 60; 75% = 50% + 25% = 180. Say it plainly: if you can find 10%, 5%, 1%, 25%, 50% and 75% of anything, you can build EVERY percent from 1 to 100 - the rest is addition.

Check yourself — explain it

5% of a number is found by halving 10% because...

Paired problem — example still visible

Find 25% of 48. -> Half is 24, half again -> 12

Faded completion — last step is yours

"1% of 350: divide by 100 -> ___; so 3% of 350 = 3 x ___ = ___" -> 3.5; 3.5; 10.5

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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