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Section 12.3 · Number

Direct proportion

Recognise direct proportion and solve problems with it, using the unitary method.

6 teaching slides 43 practice questions Worked answers for every question

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2 · Key words

direct proportionWhen one doubles, so does the other.
unitary methodFind the value of one, then scale up.
rateHow much of one quantity goes with one of another.
scale upMultiply once you know the value of one.
inverse proportionWhen one doubles, the other halves.

3 · Summary of the sectionrevise from this

  • Two quantities are in direct proportion when doubling one doubles the other.
  • Then dividing one by the other always gives the same number — the rate.
  • The unitary method: find the value of one, then multiply.
  • It is two steps: divide to get one, multiply to get many.
  • The graph of two directly proportional quantities is a straight line through the origin.
  • A taxi fare is not directly proportional to distance — the fixed charge lifts the graph off the origin.
  • In inverse proportion, doubling one halves the other: twice as many workers, half the time.
  • Ask “does zero of one give zero of the other?” — it is the quickest test for direct proportion.
PDFPrintable worksheet All 43 questions, space to work PDFWorked answers Full solutions, not just the answer

Video lessons1 videos

Math Antics - What Percent Is It?

American stretchmathantics

Proportional reasoning in its percentage form — the same idea in different clothes.

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4 · Practice43 questions, easiest first

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12.2 Sharing in a ratio
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End-of-unit {UNUM} test