Percentages of quantities
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 7 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Sale! Thirty-five percent off
- Percent means per hundred
- The multiplier method
Read the transcript of the teaching part
Last time
Before we start: last time, in Percentage change, reverse percentages and profit, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Sale! Thirty-five percent off
Every shop window shows percentages. Thirty-five percent off, twenty percent tax, eight percent interest. A percentage is a fraction out of one hundred. Today you find a percentage of any amount, write one number as a percentage of another, and increase or decrease with a single multiplier.
Percent means per hundred
Thirty-five percent means thirty-five out of a hundred, which is thirty-five hundredths, or zero point three five. Method one is the building blocks. Find ten percent by dividing by ten, and one percent by dividing by a hundred. For thirty-five percent of two hundred and forty: ten percent is twenty-four, so thirty percent is seventy-two, and five percent is twelve. Add: seventy-two plus twelve is eighty-four.
The multiplier method
Method two is faster on a calculator. Change the percentage to a decimal and multiply. Thirty-five percent is zero point three five. Zero point three five times two hundred and forty is eighty-four. Both methods agree, and the multiplier one is the one that works for decimals and awkward percentages.
Chapter 3: Fractions, decimals and percentages
- Fractions and mixed numbers 6 min
- Decimals, conversions and recurring decimals 6 min
- Percentages of quantities 6 min
- Percentage change, reverse percentages and profit 6 min
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