CBSE Class 6 Mathematics The Other Side of Zero MCQs Set 11

Answer: (c) −6, 0, +9

Explanation:
1. Integers are the numbers …, −3, −2, −1, 0, 1, 2, 3, …; they have no fractional part.
2. Groups (a), (b) and (d) each contain a fraction (\( \frac{1}{2} \), \( \frac{3}{2} \) or \( \frac{13}{6} \)), which is not an integer.
3. −6, 0 and +9 are all integers, so the answer is (c).

Teacher's Note:
1. Zero is an integer too.
2. A single fraction is enough to spoil a group.

Answer: (b) It is neither a positive nor a negative number.

Explanation:
1. 0 is the reference point of the number line, like the ground floor of the Building of Fun.
2. Positive numbers lie to its right and negative numbers to its left, so 0 itself is neither positive nor negative.
3. The smallest positive integer is +1 and the greatest negative integer is −1.

Teacher's Note:
1. We never write + or − in front of 0.
2. Remember +1 and −1 as the neighbours of 0.

Answer: (d) +9

Explanation:
1. The additive inverse of a number is the number that gives 0 when added to it.
2. (−9) + (+9) = 0, so the additive inverse of −9 is +9.

Teacher's Note:
1. Just change the sign to get the inverse.
2. A number and its inverse sit at equal distances on either side of 0.

Answer: (b) Q

Explanation:
1. Count 4 steps to the left of 0: −1, −2, −3, −4.
2. The point marked at −4 is Q.
3. P is at −6, R is at −1 and S is at +3.

Teacher's Note:
1. Negative numbers are counted leftwards from 0.
2. Read the number written under each dot.

Answer: (c) 0

Explanation:
1. The ground floor is the reference floor from which we count up and down.
2. So it is numbered Floor 0; floors above get positive numbers and floors below get negative numbers.

Teacher's Note:
1. The reference level always gets the number 0.
2. Up is positive, down is negative.

Answer: (b) −3

Explanation:
1. Starting Floor + Movement = Target Floor.
2. (+1) + (−4) = −3.
3. Going four floors down from Floor +1 brings the lift to Floor −3.

Teacher's Note:
1. A negative press means going down.
2. Count down floor by floor if unsure: 0, −1, −2, −3.

Answer: (a) Only Statement I is true.

Explanation:
1. All negative numbers lie to the left of 0, so each is less than 0. Statement I is true.
2. −7 lies to the left of −3, so −7 < −3. Statement II is false.
3. So only Statement I is true.

Teacher's Note:
1. Further left on the number line means smaller.
2. Do not compare negatives by their digits alone.

Answer: (c) a zero pair

Explanation:
1. A positive token is worth +1 and a negative token is worth −1.
2. Together they are worth (+1) + (−1) = 0, so they form a zero pair.
3. A zero pair can be added or removed without changing the value of a collection.

Teacher's Note:
1. The name tells you its value: zero.
2. Zero pairs are the key to subtraction with tokens.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. −5 lies to the left of −2 on the number line, so −5 < −2. A is true.
2. R is the rule for comparing numbers on the number line, so R is true.
3. Because −2 lies to the right of −5, R is exactly the reason for A.

Teacher's Note:
1. Picture both numbers on a number line.
2. R here is a general rule that explains A.

Answer: (d) a debit of Rs 250

Explanation:
1. A debit is money taken out of the account, so it is written as a negative number: −250.
2. A credit, an opening balance and interest added all bring money in, so they are positive.
3. The answer is a debit of Rs 250.

Teacher's Note:
1. Money in is positive; money out is negative.
2. Debit = taken out.

Answer: (c) Brahmagupta

Explanation:
1. In 628 CE, Brahmagupta gave clear rules for positive numbers, negative numbers and zero in his book Brahma-sphuta-siddhanta.
2. Kautilya wrote about credit and debit much earlier, and Carnot called negative numbers absurd in the 18th century.

Teacher's Note:
1. Link 628 CE with Brahmagupta.
2. His book's name is Brahma-sphuta-siddhanta.

Answer: (a) −11

Explanation:
1. To add two negative numbers, add 3 and 8 and put a minus sign in front.
2. So (−3) + (−8) = −11.
3. In the lift, pressing −3 and then −8 takes you 11 floors down.

Teacher's Note:
1. Two moves down make a bigger move down.
2. The answer to negative + negative is never positive.

Answer: (b) +5

Explanation:
1. K is at Floor −2.
2. Movement needed = Target Floor − Starting Floor = (+3) − (−2) = 3 + 2 = +5.
3. So the lift must go five floors up: press +5.

Teacher's Note:
1. Read the floor of K from the panel first.
2. Count on the panel: 2 floors up to 0, then 3 more.

Answer: (c) (i)-(q), (ii)-(s), (iii)-(p), (iv)-(r)

Explanation:
1. (i) (+4) + (−9) = −5, which is (q).
2. (ii) (−4) − (−9) = −4 + 9 = +5, which is (s).
3. (iii) (+4) − (−9) = 4 + 9 = +13, which is (p).
4. (iv) (−4) + (−9) = −13, which is (r). So the match is (i)-(q), (ii)-(s), (iii)-(p), (iv)-(r).

Teacher's Note:
1. Turn each subtraction into adding the inverse.
2. Check the sign of every answer carefully.

Answer: (d) (i)-(q), (ii)-(p), (iii)-(s), (iv)-(r)

Explanation:
1. (i) 2 zero pairs cancel and 4 positive tokens remain: Floor +4 (q).
2. (ii) 3 zero pairs cancel and 4 negative tokens remain: Floor −4 (p).
3. (iii) All 5 pairs cancel: Floor 0 (s).
4. (iv) 2 zero pairs cancel and 7 negative tokens remain: Floor −7 (r). So the answer is (i)-(q), (ii)-(p), (iii)-(s), (iv)-(r).

Teacher's Note:
1. The tokens left over decide the floor.
2. Equal numbers of each colour always give Floor 0.

Answer: (c) A is true, but R is false.

Explanation:
1. (−7) − (−5) = −7 + 5 = −2, so A is true.
2. R is false: for example (−2) − (−5) = −2 + 5 = +3, which is positive.
3. So A is true but R is false.

Teacher's Note:
1. One counter-example is enough to show a rule is false.
2. Always rewrite subtraction as adding the inverse.

Answer: (c) Both Statement I and Statement II are true.

Explanation:
1. 0 − (−6) = 0 + 6 = 6, so Statement I is true.
2. Any number minus itself is 0, for example (−4) − (−4) = 0. Statement II is true.
3. So both statements are true.

Teacher's Note:
1. Subtracting a number from 0 gives its additive inverse.
2. a − a = 0 for every integer a.

Answer: (a) 12 °C

Explanation:
1. Rise = Final temperature − Starting temperature.
2. 8 − (−4) = 8 + 4 = 12.
3. So the temperature rose by 12 °C.

Teacher's Note:
1. 4 degrees up to 0 °C, then 8 more.
2. A rise is a size, so it is positive here.

Answer: (b) −15 °C

Explanation:
1. The labelled marks go up in tens: …, −20, −10, 0, 10, …; each small mark between them is 5 °C.
2. The top of the red column is at the small mark between −10 and −20, that is one small mark below −10.
3. So the reading is −10 − 5 = −15 °C.

Teacher's Note:
1. Below 0 the numbers get more negative as you go down.
2. Find the value of one small mark first.

Answer: (d) − Rs 60

Explanation:
1. Credits are positive and debits are negative: 0 + (+120) + (+60) + (−90) + (−150).
2. Credits total 180 and debits total 240.
3. 180 − 240 = −60, so the balance is − Rs 60.

Teacher's Note:
1. Add the credits and the debits separately first.
2. A negative balance means money is owed.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. The credit is +500 and the debit is −500; (+500) + (−500) = 0, so the balance does not change. A is true.
2. R is the definition of the additive inverse, so it is true.
3. +500 and −500 are additive inverses, so R explains A.

Teacher's Note:
1. Equal credit and debit cancel like a zero pair.
2. Here R is exactly the reason for A.

Answer: (d) −15 m

Explanation:
1. Rising means adding: (−35) + (+20).
2. (−35) + 20 = −15.
3. She is now at −15 m, that is 15 m below sea level.

Teacher's Note:
1. She rose only 20 m, so she is still under water.
2. Rising adds; sinking subtracts.

Answer: (a) (i)-(q), (ii)-(p), (iii)-(r), (iv)-(s)

Explanation:
1. Three floors below the ground is −3 (q); 300 m above sea level is +300 (p).
2. A debit of Rs 45 is −45 (r); 8 °C above freezing is +8 (s).
3. So the match is (i)-(q), (ii)-(p), (iii)-(r), (iv)-(s).

Teacher's Note:
1. Below, debit and colder are negative.
2. Above, credit and warmer are positive.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. −6 lies to the left of −1 on the number line, so −6 < −1 and −6 °C is colder. A is true.
2. 0 °C is indeed the freezing point of water, so R is true.
3. But R only tells us what 0 °C means; it does not explain why −6 °C is colder than −1 °C.

Teacher's Note:
1. Both can be true without one explaining the other.
2. Compare the numbers to decide which is colder.

Answer: (a) 6 + (−11) = −5

Explanation:
1. The jump starts at 6 and lands on −5.
2. Movement = Target − Start = (−5) − 6 = −11, that is 11 steps to the left.
3. Start + Movement = Target gives 6 + (−11) = −5.

Teacher's Note:
1. Read the start and the landing point from the picture.
2. A leftward jump is a negative movement.

Answer: (a) Only Statement I is true.

Explanation:
1. The integers between −8 and 5 are −7, −6, …, 3, 4.
2. That is 7 negative integers, 0 and 4 positive integers: 7 + 1 + 4 = 12. Statement I is true.
3. 'Between' leaves out −8 and 5 themselves, so Statement II is false. Only Statement I is true.

Teacher's Note:
1. Count negatives, zero and positives separately.
2. 'Between' excludes the end numbers.

Answer: (c) A is true, but R is false.

Explanation:
1. (+9) − (−6) = 9 + 6 = 15 and (+9) + (−6) = 3. Since 15 > 3, A is true.
2. R is false: 9 − 6 = 3 is smaller than 9 + 6 = 15. Subtracting gives more only when the number is negative.
3. So A is true but R is false.

Teacher's Note:
1. Test R with a positive number.
2. Subtracting a negative is the same as adding a positive.

Answer: (b) Only Statement II is true.

Explanation:
1. (−2) − (−5) = −2 + 5 = +3, which is positive, so Statement I is false.
2. Taking away a positive number moves further left; starting from a negative number we always land on a negative number. Statement II is true.
3. So only Statement II is true.

Teacher's Note:
1. Try small examples for 'always' statements.
2. Moving left from a negative number stays negative.

Answer: (d) A is false, but R is true.

Explanation:
1. (+7) + (−7) = 0, but neither number is 0. So A is false.
2. Every integer does have an additive inverse that adds with it to give 0, so R is true.
3. So A is false but R is true.

Teacher's Note:
1. Any number with its inverse gives a sum of 0.
2. R actually shows why A is wrong.

Answer: (d) −50

Explanation:
1. Each block has 4 tokens and is worth (+1) + (−3) = −2.
2. 100 tokens make 100 ÷ 4 = 25 blocks.
3. Value = 25 blocks of −2 = −50.

Teacher's Note:
1. Find the value of one block first.
2. Then count the blocks.