Two batters compared
The matching test
Mixtures of 6 to 3 and 4 to 2 are checked by cross multiplying.
📚 Chapter Learning Kit
Proportional Reasoning – 2 · 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
⚡ Veda Bites
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✏️ Example
✏️ Example
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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.
For any a, b, c and d
Writing it down
The ratios a to b and c to d match exactly when a times d equals b times c.
The representative fraction
The ratio in the map corner
A map carries a ratio such as 1 to 60,00,000 in one corner.
Add, divide, multiply
The old method, unchanged
Splitting 12 at 2 to 1 added the terms for 3 parts, then divided and multiplied.
Concrete at 1 to 1.5 to 3
A total of 110 units
The terms add to 5.5, so the whole breaks into 5.5 parts.
Twenty, 30 and 60
Reading off the amounts
Multiplying each term by 20 gives 20 of cement, 30 of sand and 60 of gravel.
📖 Smart notes
What you'll study, topic by topic
1
Ratios with many terms, and on a map
A ratio is not limited to two terms. A recipe with four ingredients or a map that shrinks the world both work the same way: every term is scaled by one factor.
- Two ratios a to b and c to d match when a times d equals b times c.
- A map scale is a ratio between a map distance and a real one.
- A scale of 1 to 60,00,000 puts 1 cm on the map at 60 km on the ground.
~35 min · full explanation, examples & memory tricks in the app
2
Dividing a whole, and the pie chart
To split any quantity in a ratio, each share is the quantity times that term over the sum of all the terms. A pie chart is that rule applied to the 360 degrees of a circle.
- Add every term of the ratio to get the number of parts.
- Each share is the quantity times its own term over that sum.
- A total of 110 at 1 to 1.5 to 3 splits into 20, 30 and 60.
~40 min · full explanation, examples & memory tricks in the app
3
Inverse proportion
Some pairs of quantities change by the same factor but in opposite directions. More workers means fewer days, and what stays fixed is not their quotient but their product.
- In a direct proportion both quantities change the same way.
- In an inverse proportion they change in opposite directions.
- Both kinds still change by the same FACTOR.
~40 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:
Two cooks mix rice and urad dal as 6 to 3 and as 4 to 2, and the quickest way to tell whether the two batters match is to
Beginner
A add the terms of each ratio
B cross multiply the two ratios
C subtract the terms of each ratio
D compare only the first terms
Show answer & explanation
cross multiply the two ratios
Six times 2 and 3 times 4 both give 12.
Carrying out that test on 6 to 3 against 4 to 2, the two products come to
Beginner
A 12 and 12
B 18 and 8
C 12 and 8
D 9 and 6
Show answer & explanation
12 and 12
Six times 2 is 12, and 3 times 4 is 12 as well.
Written for any four numbers, the ratios a to b and c to d are proportional exactly when
Intermediate
A a times b equals c times d
B a plus d equals b plus c
C a minus b equals c minus d
D a times d equals b times c
Show answer & explanation
a times d equals b times c
The same test reads as a over c equal to b over d.
The ratio printed in the corner of a map, comparing paper distance with ground distance, is called
Beginner
A the geographical fraction
B the proportional fraction
C the representative fraction
D the reduced fraction
Show answer & explanation
the representative fraction
It is usually 1 against a very large number.
🃏 Flashcards
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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
Study it properly — free, in the app
The full Veda Bites deck, complete notes, spaced-repetition flashcards, leveled MCQs, tests and games for this kit — plus Daily Facts and the Arena, every day.