3. Proportional Reasoning-2

Part II, printed Chapter 36 topics59 min

Chapter 3 of NCERT Mathematics for Class 8 (Part II, printed Chapter 3): Proportional Reasoning-2. Three sections — Ratios with more than two terms, Dividing a whole, and picturing it and Inverse proportion. Six videos, 59 min in all.

Worked answers to the 22 exercise questions in this chapter →

0 of 6 done — sign in to track this chapter

Part 1

Ratios with more than two terms

10 minDirect proportion restated: the quotient that stays constantTwo cooks work from the same batter rule — 6 cups of flour to 3 of milk, and 4 to 2. Will it taste the same? The quotient answers before you cook.10 min · 12 partsहिंदी10 minMap scale as a ratio, and what it lets you computeEvery map has a number tucked in one corner and most people never read it. One to six million is not a date and not a code.10 min · 12 partsहिंदी9 minRatios of three or more quantities at onceA spice rub ground from four things at once. Written as a comparison, it is one claim, not three separate ones.9 min · 12 partsहिंदी

Part 2

Dividing a whole, and picturing it

9 minDividing a quantity in a given ratioMake more of this keeping the recipe, and cut this up keeping the recipe, sound like opposites. One builds outward, the other divides inward.9 min · 12 partsहिंदी10 minBuilding a pie chart: turning counts into anglesForty students across five grades, drawn as a circle cut into five slices. That is not really a picture of counts — it is a picture of angles.10 min · 12 partsहिंदी

Part 3

Inverse proportion

11 minWhen one quantity rises and the other falls by the inverse factorA road takes 3 hours at 30 km/h. Drive it at 60 and the rule that has served you all chapter gives the wrong answer.11 min · 12 partsहिंदी

What you will be able to do

  • Write a recipe or mixture stated in amounts as a ratio, and say what the ratio is claiming that the amounts alone do not
  • State what a representative fraction asserts about a drawing and the ground it represents
  • Write a mixture of three or more ingredients as a single multi-term ratio, in a stated order
  • Add the terms of a ratio and interpret the sum as a count of equal parts
  • Turn a table of counts into a ratio, and that ratio into a set of central angles summing to 360°
  • Read a table of paired values and decide, by multiplying each pair, whether the pairing is inverse

What this chapter assumes you already know

  • Multiplying and dividing whole numbers and simple decimals, and cancelling a common factor in a fraction
  • That a fraction with the same units above and below is a plain number with no unit left on it
  • The metric ladder for length: 100 cm in a metre, 1000 m in a kilometre
  • Measuring a straight-line distance with a ruler, to the nearest millimetre
  • Multiplying and dividing by powers of ten, and reading a number written in the Indian grouping such as 60,00,000
  • Multiplying and dividing by 2, 3 and by simple decimals such as 1.5 and 0.5
  • Halving a quantity that is an odd number of units, and being comfortable with the half that results
  • Adding decimals to a total

It builds directly on What a ratio claims, and why it is not a difference, Simplest form, and using it to test whether two ratios are proportional, Solving a proportion problem, and the Trairasika rule of three, Unit conversion is a proportion in disguise and Sharing a whole in a given ratio.

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.

  • "Proportional means equal."
  • "Cross-multiplication is a rule about fractions I learnt somewhere."
  • "You can keep a ratio by adding the same amount to both terms."
  • "Same difference, same ratio."
  • "If the ratio checks out, the two dishes are identical."
  • "The fraction form must be first-over-second."
  • "You can always divide, so use the fraction form."
  • "The bigger the second number, the bigger the map."