Divide by the bottom, multiply by the top
Three quarters of eight metres
Split 8 metres into four equal parts of 2 metres, then take three of them.
📚 Chapter Learning Kit
Working with Fractions · Class 7 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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It is an instruction, not a decoration
The word of means multiply
Three quarters OF 8 is written 3/4 x 8.
The bottom number sets the piece size
The top number does the counting
In 3/4 the bottom number says how big each piece is and the top says how many to take.
A tailor cutting masks
How many halves in six metres
Each metre of cloth gives 2 masks needing half a metre, and there are 6 metres.
Fractions change nothing about that
Division asks how many fit
Division always asks how many of one amount fit inside another.
Small pieces mean a big count
The answer can come out larger
Twelve is larger than the 6 we started with, which feels wrong when dividing is meant to shrink things.
📖 Smart notes
What you'll study, topic by topic
1
Multiplying fractions, and what the product does
The word of means multiply: three quarters of 8 is 6, found by dividing by the bottom and multiplying by the top. Two cuts across a unit square show why two fractions multiply top by top over bottom by bottom. A product…
- The word of between a fraction and a quantity means multiply.
- The bottom number sets the piece size and the top number counts pieces.
- So 3/4 of 8 is 3 x 8 divided by 4, which is 6.
~40 min · full explanation, examples & memory tricks in the app
2
Dividing fractions, and why you turn one over
A division asks how many of one amount fit inside another, and fractions change none of that. One whole holds as many pieces as its bottom number says, so dividing by a fraction means multiplying by its reciprocal. A div…
- A division asks how many of one amount fit inside another.
- Six divided by 1/2 is 12, because each whole holds two halves.
- A quotient can be larger than the dividend, since small pieces fit often.
~40 min · full explanation, examples & memory tricks in the app
3
Fraction problems, and reading what is asked
A fraction says nothing about size until you know its whole, so units must match before comparing. Mixed numbers become fractions before multiplying, and a row of posts has one gap fewer than posts. Fractions of the same…
- Units must match before two fractional amounts can be compared.
- Four fifths of 600 grams is 480, and an eighth of 5 kilograms is 625.
- So a larger fraction can give the smaller amount, if the wholes differ.
~45 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:
A question asks for a fraction of a quantity, with the word of standing between the two of them. In such a question of means
Beginner
A add
B multiply
C subtract
D compare
Show answer & explanation
multiply
So three quarters of 8 is 3/4 x 8.
A rope 8 metres long is to be cut so that three quarters of its whole length is used. The piece used measures
Beginner
A 4 metres
B 2 metres
C 6 metres
D 11 metres
Show answer & explanation
6 metres
Four parts of 2 metres, and take three.
To find three quarters of 8, what do you do first, and why?
Advanced
A Divide 8 into four parts, because the bottom sets the piece size
B Multiply 8 by four, because the bottom number counts the pieces
C Divide 8 into three equal parts, because the top number is three
D Add 3 and 8, because the word of joins the two numbers given
Show answer & explanation
Divide 8 into four parts, because the bottom sets the piece size
The bottom number says how big a piece is, so the 8 is cut into four. The top number then says to take three of those pieces.
A box holds 10 marbles and two fifths of them are taken out and put to one side. Taken out that way, the marbles number
Beginner
A 5
B 2
C 4
D 20
Show answer & explanation
4
Five parts of 2, and take two.
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