Five copies of one photograph
Three look right, two do not
Three of the five printed tigers look correct, one looks stretched tall and one looks squashed.
📚 Chapter Learning Kit
Proportional Reasoning – 1 · Class 8 Mathematics · Ganita Prakash
English 3 topics 105 leveled MCQs 51 flashcards 5 games Free
Shared by a Veda teacher · Generated with Veda AI · Oct 2026
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Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. Here's a taste from this kit; the app has the full deck.
The five measurements
Take a ruler to them
They run 60 by 40, 40 by 20, 30 by 20, 90 by 60, and 60 by 60 millimetres.
The test that fails
Equal differences prove nothing
From 60 by 40 to 40 by 20, both measurements dropped by exactly 20 millimetres.
The shape of the problem
Three known, one missing
Six glasses of lemonade took 10 spoons of sugar. How many does 18 take at the same sweetness?
The quickest route
Find the factor, apply the factor
The first term went from 6 to 18, so divide 18 by 6 to get the factor 3.
Adding instead of multiplying
Twenty-two is the trap
Twelve more glasses tempts an answer of 10 plus 12, which is 22 spoons.
📖 Smart notes
What you'll study, topic by topic
1
Same factor, not same difference
Resize a picture and it stays recognisable only if both sides change by the same factor. Subtracting the same amount from each distorts it. That is what a ratio measures and what proportion means.
- Two quantities change alike when both are multiplied by one factor.
- Taking the same amount off both does NOT keep them alike.
- A ratio a to b says that for every a of the first there are b of the second.
~30 min · full explanation, examples & memory tricks in the app
2
Finding the fourth number
Three numbers and a proportion are enough to find the fourth. The factor of change does it in one step, cross multiplication does it in general, and the units must agree before either is used.
- Both terms of a ratio must take the same factor.
- Divide the new first term by the old one to find that factor.
- Two ratios are in proportion when their cross products agree.
~35 min · full explanation, examples & memory tricks in the app
3
Sharing in a ratio, and changing units
To split a quantity in a given ratio, count the groups first. The ratio tells you how many groups each share takes, and the total divided by that count gives the size of one group.
- Dealing out by hand works but is slow for large totals.
- A ratio of m to n means m plus n groups in all.
- The size of one group is the total divided by that number of groups.
~35 min · full explanation, examples & memory tricks in the app
❓ Leveled MCQ practice
Try the smart MCQs from this kit
105 questions laddered from warm-up to topper-level, each with an explanation. A taste:
Five copies of one photograph are printed at different sizes, and two of them look wrong. The cause lies in
Beginner
A the size of the paper used
B the colour of the printing
C the ratio of width to height
D the shape of the frame
Show answer & explanation
the ratio of width to height
Only the ratio of the two measurements decides whether the shape survives.
One picture measures 60 by 40 millimetres and another measures 30 by 20. Both measurements have been
Beginner
A reduced by 30 millimetres
B multiplied by a half
C multiplied by different factors
D left unchanged
Show answer & explanation
multiplied by a half
Halving both terms keeps the two ratios in proportion.
A third picture measures 40 by 20. Compared with 60 by 40, each measurement has dropped by
Intermediate
A 10 millimetres
B half its value
C a third of its value
D 20 millimetres
Show answer & explanation
20 millimetres
Sixty to 40 is a drop of 20, and 40 to 20 is a drop of 20 as well.
That picture is the stretched one, even though both measurements dropped equally. What this shows is that
Advanced
A equal factors do not keep a shape
B equal differences do not keep a shape
C only squares keep their shape
D only rectangles keep their shape
Show answer & explanation
equal differences do not keep a shape
What the eye notices is the factor, and here the height halved while the width did not.
🃏 Flashcards
Tap a card to flip it
51 flashcards in this kit — the app reviews them with spaced repetition so the right card returns on the right day.
🎮 Learning games
Play your way through this kit
Every game is built from this kit's own content — scores feed your mastery, so playing counts as studying.
Memory Match
Word Match
Categorization
Fact Or Myth
Sequence Builder
Playable in the app
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