The integers carry a direction
Numbers that run both ways
A temperature can be above or below zero, and a balance can be in credit or in debt.
📚 Chapter Learning Kit
Operations with Integers · 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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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.
One blue and one red together
A pair worth nothing
Take blue counters for positives and red for negatives. One of each is worth nothing at all.
Cancel, then read what is left
Adding with counters
Put out counters for each number, then cancel every zero pair you can see.
And that reading survives a negative
Multiplying is repeated adding
For whole numbers, 3 times 4 means three lots of 4, which is 12.
There is no doing something minus three times
The other order is awkward
Taking -3 times 4, the repeated adding reading breaks down.
It never did for whole numbers
The order should not matter
Three times 4 and 4 times 3 both give 12, and swapping never changes a product.
📖 Smart notes
What you'll study, topic by topic
1
Adding and subtracting integers with counters
A blue counter and a red counter make a zero pair, worth nothing, so adding or removing pairs changes no total. To add, cancel every zero pair and read what is left. To subtract something absent, add zero pairs first, wh…
- The integers are the whole numbers together with their negatives.
- Zero takes neither a plus nor a minus sign.
- One blue counter with one red counter is a zero pair, worth nothing.
~40 min · full explanation, examples & memory tricks in the app
2
Multiplying integers, and why two negatives give a positive
Multiplying by a negative extends repeated adding, and a pattern running past zero forces every value, including the one where both numbers are negative. Removing groups of red counters agrees. A product is negative exac…
- Three lots of -4 is -12, so repeated adding survives one negative.
- Swapping the two numbers never changes a product, which settles -3 times 4.
- In the column from 3 times 2, each answer is 3 less than the one above.
~45 min · full explanation, examples & memory tricks in the app
3
Dividing integers, and the sign rule they share
A division asks which number multiplies the divisor to give the dividend, so it is a multiplication question in disguise and needs no second sign rule. A quotient is negative when the signs differ. Dividing may give no i…
- A division asks which number multiplies the divisor to give the dividend.
- So every division is a multiplication question with a gap in it.
- Minus 12 divided by 3 is -4, and 12 divided by -3 is -4 as well.
~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:
A set of numbers is built by taking the whole numbers and then adding something to the collection. The integers are the whole numbers together with
Beginner
A their negatives
B the fractions
C the decimals
D their halves
Show answer & explanation
their negatives
And zero takes neither sign.
A number is written down with a minus sign standing in front of it rather than a plus sign. Such a number is
Beginner
A negative
B positive
C zero
D a fraction
Show answer & explanation
negative
So -8 is eight in the downward direction.
Among all the integers there is one that is neither above nor below the dividing point. The number taking neither sign is
Beginner
A one
B minus one
C zero
D every whole number
Show answer & explanation
zero
It has no direction at all.
One blue counter is placed on the table and one red counter is placed beside it, and the two are valued together. Together they are worth
Beginner
A two units
B nothing at all
C one unit
D minus one unit
Show answer & explanation
nothing at all
They pull opposite ways by the same amount.
🃏 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.
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Memory Match
Categorization
Fact Or Myth
Sequence Builder
Word Match
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