8. Working with Fractions

8 topics1 h

Chapter 8 of NCERT Mathematics for Class 7: Working with Fractions. Three sections — Multiplying fractions, Dividing fractions and Fractions inside a problem. Eight videos, 1 h in all.

Worked answers to the 24 exercise questions in this chapter →

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Part 1

Multiplying fractions

9 minA whole number times a fraction, read as repeated distanceMultiplication is never redefined here. One situation is held still — distance is speed times time — and the arithmetic has to keep up.9 min · 12 partsहिंदी9 minA fraction of a fraction, and why the numerators and denominators multiplyThat the numerators multiply and the denominators multiply is not a convention anyone chose. It is what a square forces on you.9 min · 12 partsहिंदी10 minCancelling common factors before multiplying, not afterCancelling before you multiply is not a new permission. It is the rule you have had for years, used a step earlier.10 min · 12 partsहिंदी9 minWhy multiplying can make a number smaller“Does multiplying make a number bigger?” is not a question with an answer. It is a question missing a condition.9 min · 12 partsहिंदी

Part 2

Dividing fractions

9 minRestating a division as a missing-factor multiplicationDividing by a fraction needs no new rule, because division was never an operation in its own right.9 min · 12 partsहिंदी10 minReciprocals, and Brahmagupta's rule for dividing fractions“Turn the second one upside down and multiply” is a conclusion, not a rule. Brahmagupta wrote down why.10 min · 12 partsहिंदी10 minWhy dividing can make a number bigger6 ÷ ¼ = 24. Dividing made the number four times bigger, and that is not a trick — it is what the question was asking all along.10 min · 12 partsहिंदी

Part 3

Fractions inside a problem

10 minFractional relations between two quantitiesNobody measures the miser's gift against a whole coin. It is only ever worth something compared with what he could have given.10 min · 12 partsहिंदी

What you will be able to do

  • Explain why a fractional speed does not change how a distance is computed
  • Represent a fraction as a shaded part of a unit square
  • Write a product of two fractions as one fraction whose numerator and denominator are each an unmultiplied product
  • Predict, before computing, whether a product will land above or below each of its factors, from where those factors sit relative to 1
  • Rewrite any division as a multiplication with one factor missing
  • State what makes one number the reciprocal of another, in terms of their product
  • Predict whether a quotient will land above or below its dividend, from where the divisor sits relative to 1
  • Turn a word problem into a division or a multiplication before computing anything

What this chapter assumes you already know

  • A fraction as a number of equal parts of a whole, and where it sits on a number line
  • Whole-number multiplication read as repeated addition
  • Adding fractions with the same denominator
  • Mixed fractions, and rewriting one as a single fraction (Class 6, reinforced in Part I, §8.1, p.176)
  • A fraction of a whole understood as: cut into equal parts, then take some
  • Area as the amount of surface a region covers, and the area of a rectangle as length times breadth for whole-number sides
  • Equivalent fractions, so that 6/20 and 3/10 can be recognised as one number
  • Reading a number written as a mixed fraction, such as one and a half

It builds directly on Answering "could this possibly fit?" by estimating in stages.

Where people usually slip up

Sentences students actually say, taken from the notes the videos were made from. Each one is answered on the page of the video it belongs to.

  • "You cannot multiply by a fraction, because you cannot add something a fractional number of times."
  • "Multiplying makes a number bigger."
  • "The number under the multiplier's bar is something you multiply by."
  • "3 × 1/4 and 1/4 × 3 are different problems."
  • "One and a quarter means one times a quarter."
  • "A fractional speed is a special case needing a special formula."
  • "'Of' means add, or means divide."
  • "You multiply the denominators because that is the rule."