7. Proportional Reasoning-1

Part I, printed Chapter 76 topics58 min

Chapter 7 of NCERT Mathematics for Class 8 (Part I, printed Chapter 7): Proportional Reasoning-1. Three sections — What proportional change looks like, Ratios and Using proportions. Six videos, 58 min in all.

Worked answers to the 26 exercise questions in this chapter →

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Part 1

What proportional change looks like

10 minWhy some resized images look right and others look stretchedYour eye sorts the stretched photographs from the good ones instantly, and cannot tell you what it just used to do it.10 min · 12 partsहिंदी

Part 2

Ratios

9 minWhat a ratio claims, and why it is not a differenceA ratio is not a pair of numbers. It is a claim, and the pair of numbers is only one of many ways of stating it.9 min · 12 partsहिंदी10 minSimplest form, and using it to test whether two ratios are proportionalSimplest form is not a tidier ratio. It is a name, and every ratio making the same claim carries it.10 min · 12 partsहिंदी

Part 3

Using proportions

9 minSolving a proportion problem, and the Trairasika rule of threeIf two quantities are locked together by a single factor, three of the four numbers decide the fourth. India wrote that rule down as Trairāśika.9 min · 12 partsहिंदी9 minSharing a whole in a given ratioA ratio counts groups, not objects. Share twelve counters as 3 : 1 and you have been told about groups, not counters.9 min · 12 partsहिंदी10 minUnit conversion is a proportion in disguiseA conversion is a ratio agreed once that never changes. So converting units is the rule of three with three numbers already filled in.10 min · 12 partsहिंदी

What you will be able to do

  • Read a table of widths and heights and decide, from the numbers alone, which of several rectangles have the same shape
  • Write the comparison of two quantities as a ratio with a colon, in the order the question asks for
  • Reduce a given ratio to its simplest form by dividing both terms by their HCF
  • Model a "three known, one unknown" situation as a proportion, putting the two quantities in the same order in both ratios
  • Divide a given quantity between two shares in a stated ratio, showing the group size as a separate step
  • Rewrite a ratio's terms in a common unit before comparing two ratios

What this chapter assumes you already know

  • Multiplying and dividing whole numbers, and multiplying by a fraction such as one half or three halves
  • Reading a fraction as an instruction to scale — "half of 60"
  • Measuring lengths in millimetres and centimetres with a ruler
  • Comparing two fractions or two quotients to see which is bigger
  • That a rectangle has four right angles whatever its width and height
  • Multiplying and dividing whole numbers, including by a fraction
  • Comparing two quotients to decide which is larger
  • Reading a unit off a measurement, and knowing that 1 kg is 1000 g

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.

  • "The big one and the small one must look different."
  • "They look different because one is a square."
  • "Same difference, same change."
  • "Subtracting from both makes it more square."
  • "Only whole-number factors count."
  • "Every rectangle is similar to every other rectangle."
  • "Width is the horizontal one."
  • "A ratio is a fraction of the whole."