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Lesson 14 of 15

9 min

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Ten ideas, ten checks. The table comes first. You can read it while you answer.

Ten ideas for comparing two amounts by dividing
IdeaHow it goes
Two questionsSubtract for how much more. Divide for how many times.
A ratioA comparison made by dividing, written 3 : 2.
What it namesBoys : girls names two groups. Girls : class names a group and the whole.
EquivalentMultiply both parts by the same number (not 0).
Simplest formMatch units. Divide by the highest shared factor.
SharingAdd the parts. Find one. Then hand out.
ProportionTwo equal ratios. Multiply across to check.
Value of oneIf each is worth the same, divide to one. Multiply for many.
Growing togetherDirect proportion gives the same division every row.
Rates and scalesA rate keeps its units. A scale compares paper to world.

A report says a town had twice the rainfall of last year. Which question does that answer?

  • How much more
  • How many times
  • Neither

A shelf holds 9 novels and 6 textbooks. What is the ratio of novels to all the books?

  • 3 : 2
  • 3 : 5
  • 9 : 6

Which ratio makes the same comparison as 7 : 3?

  • 10 : 6
  • 21 : 9
  • 14 : 9

Write 750 g to 1 kg as a ratio in simplest form.

  • 750 : 1
  • 3 : 4
  • 4 : 3

₹5,400 is shared in the ratio 2 : 3 : 4. What are the shares?

  • ₹2,000, ₹3,000 and ₹4,000
  • ₹1,200, ₹1,800 and ₹2,400
  • ₹1,800 each

Fill the gap: 5 : 8 = ? : 24.

  • 21
  • 15
  • 12

Six chairs cost ₹2,340. What do nine cost?

  • ₹2,343
  • ₹3,510
  • ₹1,560

A stall charges ₹10 to enter and ₹30 a game. Two games cost ₹70. Four cost ₹130. Is the bill in direct proportion to the games?

  • Yes, because the bill rises with the games
  • No, because 70 ÷ 2 = 35 and 130 ÷ 4 = 32.5
  • Yes, because each game adds ₹30

A car covers 240 km in 4 hours. How far does it go in 7 hours at that rate?

  • 0.12 km
  • 420 km
  • 420 hours

A house plan has a scale of 1 : 150. A wall is 8 cm on the plan. How long is the real wall?

  • 150 cm
  • 12 m
  • 1,200 m

Chapter 7 of Part I is Proportional Reasoning-1. Open it and see what it does with these ideas.

Next: Fractions in Disguise. It uses the same habit. This time the second part is fixed at a hundred.

Reveal every answer to finish this lesson.