1. Fractions in Disguise

Part II, printed Chapter 19 topics2 h

Chapter 1 of NCERT Mathematics for Class 8 (Part II, printed Chapter 1): Fractions in Disguise. Three sections — A percentage is a fraction with denominator 100, Finding a percentage of a quantity and Using percentages. Nine videos, 2 h in all.

Worked answers to the 53 exercise questions in this chapter →

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Part 1

A percentage is a fraction with denominator 100

10 minWhy forcing every fraction onto a scale of 100 makes them comparableA percentage is not a new kind of number. It is an ordinary fraction wearing a bottom number that somebody fixed in advance.10 min · 12 partsहिंदी

Part 2

Finding a percentage of a quantity

10 minComputing a percentage in your head by splitting itMental percentage arithmetic is not a bag of tricks. It is one line reused, with the percentage sitting out in front as a plain multiplier.10 min · 12 partsहिंदी11 minThe FDP trio: fraction, decimal and percentage as one objectA fraction, a decimal and a percentage are not three things you convert between. They are three ways of writing one number.11 min · 12 partsहिंदी10 minWhat a percentage greater than 100 does and does not mean“A percentage cannot be more than a hundred” is a belief almost everybody holds, and it is wrong about half the time.10 min · 12 partsहिंदी

Part 3

Using percentages

11 minComparing two proportions that have different totalsTwo proportions sitting on different totals cannot be ranked by their counts. Rescaling both onto one base is the whole job a percentage does.11 min · 12 partsहिंदी10 minPercentage increase and decrease, and choosing the right baseEvery percentage change is a fraction, and the number underneath it is where you started — never where you ended up.10 min · 12 partsहिंदी10 minProfit, loss and taxes as percentages of a stated amountA profit is a fact about a sale. A profit percentage is a fact about a sale and a choice of what to measure it against.10 min · 12 partsहिंदी10 minCompounding: why repeated growth multiplies instead of addingEvery percentage change is worked out on the value at the start of the period. One question decides everything: has that value already moved?10 min · 12 partsहिंदी9 minTricky percentages: why a 50% margin followed by a 50% discount leaves a 25% lossEvery percentage quietly names a number underneath it. Fifty per cent of what? That missing half of the sentence is where the mistakes live.9 min · 12 partsहिंदी

What you will be able to do

  • State what the symbol % abbreviates, and rewrite any percentage as a fraction with denominator 100
  • Write "y% of a quantity" as (y/100) × quantity for a named or unnamed quantity
  • Write any percentage as a fraction over 100, as that fraction in lowest terms, and as a decimal, and go in the reverse direction from any of the three
  • Compute the percentage one amount is of another when the first is larger, and read the result as a multiple
  • Judge whether two given proportions can be compared directly, and say what makes the direct comparison invalid
  • Compute a percentage increase and a percentage decrease from two values, putting the earlier value in the denominator
  • Define cost price, marked price and selling price, and identify each in a stated situation
  • Read a rate given as "k% p.a." and compute one period's interest on a stated principal
  • Compute the percentage gain of two offers and rank them, then rank the same two offers by amount, and explain why the two orders can disagree

What this chapter assumes you already know

  • Equivalent fractions: that multiplying numerator and denominator by the same non-zero number leaves the fraction unchanged
  • Comparing two fractions by putting them over a common denominator
  • Multiplying a fraction by a whole number, and dividing a whole number by a whole number to get a decimal
  • Reading a number line on which the labelled points are fractions
  • Solving a one-step equation of the shape a/b = x/100 by multiplying both sides by the same number
  • That a decimal like 0.31 means thirty-one hundredths
  • Multiplying and dividing a whole number by 10 and by 100
  • Halving numbers, including numbers that halve to a decimal

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.

  • "Per cent is a unit, like kilogram."
  • "Converting to a percentage changes the number."
  • "3/4 = 75% is a fact you memorise."
  • "7/14 must be 7% or 14%."
  • "Any common denominator would do, so 100 is arbitrary."
  • "Percentages are whole numbers."
  • "Two percentages can be compared, full stop."
  • "The bigger the percentage, the bigger the amount."