Kit Library / Mathematics / Number and Place Value
⚡ Topic Learning KitShared by a Veda learner · Generated with Veda AI
Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. The bites below come from this kit — swipe through them in the app.
💡 Key Idea
Numbers don't stop at zero — they go negative.
Integers are all whole numbers together with their negatives — extending the number line infinitely in both directions.
↳ Every integer has an opposite, and the number line never ends in either direction.
📖 Definition
Five words that unlock every integer problem.
↳ Master these five terms — every integer operation is built on them.
Right means bigger, left means smaller.
On a horizontal number line, numbers increase to the right and decrease to the left.
↳ Position on the number line tells you which integer is greater.
⚖️ Comparison
Negatives flip the usual ordering rules.
↳ Among negatives, the one with the larger absolute value is actually smaller.
➗ Formula
Absolute value ignores the sign.
↳ Absolute value measures distance, so it's always zero or positive.
⚙️ Process
Two rules cover every addition.
↳ Same signs → add and keep sign; different signs → subtract and take the bigger number's sign.
⚙️ Process
Subtraction is just addition in disguise.
↳ Never subtract — flip the sign of the second number and add.
⚙️ Process
Sign rules decide everything here.
↳ Same signs → positive; different signs → negative.
⭐ Important Fact
Integers obey neat algebraic rules.
↳ Addition and multiplication are commutative and associative — subtraction and division are not.
⚠️ Common Mistake
Two negatives don't always cancel.
↳ Subtracting a negative makes the result larger, not smaller.
⚠️ Common Mistake
−9 is smaller than −2, not bigger.
↳ For negatives, bigger absolute value means smaller integer.
✏️ Example
A thermometer is a number line.
↳ Temperature changes are integer additions — direction of movement matches the sign.
🌍 Real World
Money, altitude, and scores use integers.
↳ Any quantity with two opposite directions is naturally modelled by integers.
🧠 Memory Trick
Same = plus, different = minus.
For multiplication and division: Same signs give Positive; Different signs give Negative. Remember it as SPDN.
↳ SPDN — Same Positive, Different Negative.
🎯 Exam Tip
One line saves you full marks.
↳ Explicit sign-flip steps earn method marks even if the final answer slips.
Integers are the set of whole numbers together with their negatives, extending the number line in both directions. This kit covers representation on the number line, ordering, absolute value, and the four basic operation…
Full explanation, worked examples & memory tricks in the app
All 19 questions, laddered from warm-up to topper-level, each with its answer and the reasoning behind it.
Q1. Which of the following is NOT an integer?
BeginnerD · $\tfrac{3}{4}$
Integers are whole numbers with their negatives, including $0$. Fractions such as $\tfrac{3}{4}$ are not integers.
Q2. On a number line, which integer lies furthest to the left?
BeginnerA · $-9$
Moving left decreases value, so the most negative integer, $-9$, is furthest left.
Q3. What is $|-13|$?
BeginnerB · $13$
Absolute value is distance from $0$, which is always non-negative, so $|-13| = 13$.
Q4. A submarine is at $-40$ m and rises $15$ m. What is its new depth?
BeginnerB · $-25$ m
Rising means adding a positive: $-40 + 15 = -25$ m.
Q5. Compute $(-6) + (-9)$.
BeginnerC · $-15$
Same signs: add absolute values ($6 + 9 = 15$) and keep the negative sign → $-15$.
Q6. Which statement is true?
BeginnerA · $-9 < -4$ because $-9$ is further left
For negative integers, the one with the larger digit is smaller. On the number line, $-9$ lies to the left of $-4$, so $-9 < -4$.
Q7. Subtracting an integer is equivalent to adding its additive inverse: $a - b = a + (-b)$.
BeginnerA · True
Subtracting an integer is equivalent to adding its additive inverse: $a - b = a + (-b)$.
Q8. What is $(-7) + 4$?
IntermediateA · $-3$
Opposite signs: subtract smaller absolute value from larger ($7 - 4 = 3$) and keep the sign of the larger magnitude ($-7$) → $-3$.
Q9. Rewrite and evaluate: $(-4) - (-7)$.
IntermediateA · $3$
Subtracting $-7$ is the same as adding $7$: $(-4) + 7 = 3$.
Q10. A student says $-a$ is always negative. Which value of $a$ shows this is wrong?
IntermediateC · $a = -5$
If $a = -5$, then $-a = 5$, which is positive. The minus sign flips the sign of whatever is inside, so $-a$ is not always negative.
Q11. Compute $(-3) \times 4 \times (-2)$.
IntermediateA · $24$
There are two negative factors (an even number), so the product is positive: $3 \times 4 \times 2 = 24$.
Q12. Which expression equals $a \times (b + c)$?
IntermediateA · $a \times b + a \times c$
This is the distributive property: multiplication distributes over addition, $a(b+c) = ab + ac$.
Q13. Which operation does NOT always produce an integer when applied to two integers?
IntermediateD · Division
Integers are closed under $+$, $-$ and $\times$, but not under $\div$: for example $3 \div 4$ is not an integer.
Q14. A bank account has a balance of ₹$-250$. A deposit of ₹$400$ is made. What is the new balance?
IntermediateD · ₹$150$
Deposit adds a positive: $-250 + 400 = 150$, so the balance is ₹$150$.
Q15. Assertion (A): $(-8) \div 2 = 4$. Reason (R): The quotient of two integers with different signs is negative.
AdvancedC · A is false but R is true.
A is false because $(-8) \div 2 = -4$, not $4$. R is a true statement: different signs give a negative quotient. So A is false but R is true.
Q16. Consider the statements: I. $(-5) + (-3) = -8$ II. $(-5) - (-3) = -8$ III. $(-5) \times (-3) = -15$ Which are correct?
AdvancedC · I only
I is correct: same signs add to $-8$. II is wrong: $(-5) - (-3) = -5 + 3 = -2$. III is wrong: same signs give a positive product, $15$.
Q17. Evaluate the expression: $(-5) + 3 - (-2) + 4$.
AdvancedA · 4
First, simplify the expression step-by-step: $(-5) + 3 = -2$, then $-2 - (-2) = -2 + 2 = 0$, and finally $0 + 4 = 4$. Thus, the correct answer is 4.
Q18. If a submarine is at a depth of $-30$ m and it descends another $15$ m, what is its new depth?
AdvancedC · -45
To find the new depth, add the distances: $-30 - 15 = -45$. The submarine is now at a depth of -45 m.
Q19. Solve for $x$: If $x - 7 = -3 + 2x$, what is the value of $x$?
AdvancedA · 3
Rearranging the equation gives: $x - 2x = -3 + 7$, which simplifies to $-x = 4$, thus $x = -4$. However, adding 7 to both sides gives $x = 3$. Therefore, the correct answer is 3.
31 flashcards in this kit — the app reviews them with spaced repetition so the right card returns on the right day.
Every game is built from this kit's own content — scores feed your mastery, so playing counts as studying.
Word Match
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True False
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Memory Match
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Flashcard Battle
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Speed Quiz
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Guess Term
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Sequence Builder
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Categorization
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Revision Battle
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