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Section 7.5 · Number

Making fraction calculations easier

Use the structure of a calculation — cancelling, reordering and dividing before multiplying — to work with fractions efficiently.

6 teaching slides 39 practice questions Worked answers for every question

1 · Teaching slidesuse ← → keys

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2 · Key words

cancelDivide a numerator and a denominator by a common factor before multiplying.
reciprocalThe fraction upside down; a pair multiply to 1.
commutativeAddition and multiplication may be done in any order.
efficientChoosing the order of steps that keeps the numbers small.

3 · Summary of the sectionrevise from this

  • Look at a calculation before you start it — the order is your choice.
  • Cancel first when multiplying, so the numbers stay small and the answer is already simplified.
  • For a fraction of a quantity, divide first, then multiply: 3/4 of 48 is 48 ÷ 4 × 3, not 48 × 3 ÷ 4.
  • In an addition, reorder to pair fractions that make a whole: 1/4 + 1/2 + 3/4 becomes 1 + 1/2.
  • Spot reciprocals: 5/8 × 8/5 = 1, no working needed.
  • Addition and multiplication may be reordered freely; subtraction and division may not.
  • Estimating first tells you roughly what to expect, so a slip stands out.
  • The efficient route is not a different method — it is the same method, done in a kinder order.
PDFPrintable worksheet All 39 questions, space to work PDFWorked answers Full solutions, not just the answer

Video lessons1 videos

Math Antics - Simplifying Fractions

American stretchmathantics

Worth a second viewing here: cancelling early is the same idea as simplifying, done at the start.

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4 · Practice39 questions, easiest first

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7.4 Dividing fractions
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End-of-unit {UNUM} test