NCERT Solutions for Class 6 Maths Chapter 10 - The Other Side of Zero Exercise 10.2

Exercise 10.2

1. Complete the additions using tokens.

a. (+6)+(+4) 

Ans: For (+6), we use 6 positive tokens 

And for (+4), we use 4 positive tokens

Therefore, by combining we will get 

(+6) + ( +4) = (+10)

Hence, Counting all the positive tokens we get (+10)

b. (−3)+(−2)

Ans: For (-3) we use 3 negative tokens

For (-2) we use 2 negative tokens

Token

Now combining them we will get

(-3) + (-2) = -5

Hence, counting all the negative tokens we get (-5)

c. (+5)+(−7)

Ans: For (+5) we use 5 positive tokens

For (-7) we use 7 negative tokens

Now, combining them we will get 

Therefore, remaining tokens -= -2

d. (−2)+(+6)

Ans: For (-2) we use 2 negative tokens

For (+6) we use 6 positive tokens

Now, combining we will get 

(-2) +(+6) = +4

Hence, Remaining tokens are (+4)

2. Cancel the zero pairs in the following two sets of tokens. On what floor is the lift attendant in each case? What is the corresponding addition statement in each case?

Ans: 

a. From the given image we can remove 3 pairs 

Therefore the remaining are 2 negative tokens 

The lift attendant is on the second floor below the ground floor.

The corresponding addition statement = (+3)+(-5) = (-2)

b. From the given image we can remove 3 pairs.

The remaining are 3 positive tokens.

The lift attendant is on the third floor above the ground floor.

The corresponding addition statement = (+6) + (-3) = (+3)

3. Evaluate the following differences using tokens. Check that you get the same result as with other methods you now know: 

a. (+10) –(+7) b. (–8)– (–4) c. (–9) –(–4) 

d. (+9) –(+12) e. (–5)– (–7) f. (–2) –(–6)

Ans:

a. Here there are 10 positive tokens take away 7 positive tokens

Therefore, (+10)-(+7) = (+3)

b. Here there are -8 negative tokens take away -4 negative tokens

Therefore, (-8) -( - 4) = (-4)

c. Here there are -9 negative tokens take away -4 negative tokens

Therefore, (-9) -( - 4) = (-5)

d. There are not enough tokens to take out 12 positive tokens from 9 positive tokens.

So we put an extra 3 zero pairs ( 1 pair = a positive and a negative token)

Now we can take out 12 positive tokens 

Therefore, (+9) - (+12) = (-3)

e. There are ot enough tokens to take out -7 negative tokens from -5 negative tokens.

So, we put extra 2 zero pairs( 1 pair = a positive and a negative token)

Now, we can take out -7 negative tokens.

Hence, (-5)-(-7) = +2

f. There are not enough tokens to take out -6 negative tokens from -2 negative tokens

So, we put extra 4 zero pairs (1 pair = a negative and a positive token)

Now we can take out -6 negative tokens 

Hence, (-2)-(-6) = (+4)

4. Complete the subtractions: 

a. (–5) –(–7) b. (+10) –(+13) c. (–7) –(–9) 

d. (+3) – (+8) e. (–2) –(–7) f. (+3)–(+15) 

Ans:

a. There are not enough tokens to take out -7 negative tokens from -5 negative tokens.

So, we take an extra 2 Zero pairs (1 pair = a positive and a negative token) 

Now, we can take out -7 negative tokens.

Hence, (-5)-(-7) = +2

b. There are not enough tokens to take out +10 positive tokens from +13 positive tokens.

So, we take an extra 3 Zero pairs (1 pair = a positive and a negative token) 

Now, we can take out +13 positive tokens.

Hence, (+10)-(+13) = -3

c. There are not enough tokens to take out -9 negative tokens from -7 negative tokens.

So, we take an extra 2 Zero pairs (1 pair = a positive and a negative token) 

Now, we can take out -9 negative tokens.

Hence, (-7)-(-9) = +2

d. There are not enough tokens to take out +8 positive tokens from +3 positive tokens.

So, we take an extra 5 Zero pairs (1 pair = a positive and a negative token) 

Now, we can take out +8 positive tokens.

Hence, (+3) -(+8) = -5

e.  There are not enough tokens to take out -7 negative tokens from -2 negative tokens.

So, we take an extra 2 Zero pairs (1 pair = a positive and a negative token) 

Now, we can take out -7 negative tokens.

Hence, (-2) - (-7) = +5

f. There are not enough tokens to take out +15 positive tokens from +3 positive tokens.

So, we take an extra 12 Zero pairs (1 pair = a positive and a negative token) 

Now, we can take out +15 positive tokens.

Hence, (+3) - (+15) = -12

5. Try to subtract: –3– (+5). 

How many zero pairs will you have to put in? What is the result?

Ans: Here we have to take out 5 positives from -3 negatives. But there are not enough positive tokens.

So, we put down an extra 5 zero pairs (1 pair = a negative and positive token)

Now, we can take out 5 positive tokens

Hence, -3-(+5) = - 8

6. Evaluate the following using tokens. 

a. (–3)–(+10) b. (+8)– (–7) c. (–5)–(+9) 

d. (–9) – (+10) e. (+6) –(–4) f. (–2)–(+7)

Ans:

a. Here we have to take 10 positive tokens from -3 negative tokens. But there are not enough positive tokens.

So, we put down an extra 10 zero pairs (1 pair = a positive and a negative token)

Now, we can take out 10 positive tokens 

Hence (-3) - (+10) = -13

b. Here we have to take out -7 negative tokens from 8 positives. But there are not enough negative tokens.

So, we put down an extra 10 zero pairs.(1 pair = a negative and a positive pair)

Now, we can take out 10 positive tokens.

Hence, (-3)-(+10) = -13

b. Here we have to take out -7 negative tokens from 8 positive tokens. Butu there are not enough negative tokens.

So, we put down an extra 7 zero pairs (1 pair = a negative and a positive pair)

Now we can take out -7 negatives tokens

Hence, -5-(+9) = - 14

c. Here we have to take out 9 positives from -5 negative tokens. But there are not enough positive tokens.

So, we put extra 9 zero pairs (1 pair = a positive and a negative token)

Now we can take out 9 positive tokens.

Hence -5 - (-9) = =-14

d. Here we have to take out 10 positive tokens from -9 negative tokens. Butu there are not enough positive tokens.

So, we put down an extra 10 zero pairs (1 pair = a negative and a positive pair)

Now we can take out 10 positive tokens

Hence, -9-(+10) = -19

e. Here we have to take out -4 negative tokens from 6 positive tokens. But there are not enough negative tokens.

So, we put down an extra 4 zero pairs (1 pair = a negative and a positive pair)

Now we can take out -4 negative tokens

Hence, (+6)-(-4) =10

f. Here we have to take out 7 positive tokens from -2 negative tokens. Butu there are not enough positive tokens.

So, we put down an extra 7 zero pairs (1 pair = a negative and a positive pair)

Now we can take out 7 positive tokens

Hence, (-2) - (+7) = -9

Benefits of NCERT Solutions for Class 6 Maths Chapter 10 Exercise 10.2 The Other Side of Zero

• Provides clear explanations of the token model, helping students understand positive and negative numbers.

• Utilises visual aids to represent numbers, making it easier for students to grasp abstract concepts.

• Provides real-life examples where positive and negative numbers are applicable, making the learning relevant.

• Encourages students to think critically about how numbers interact on the number line, fostering deeper mathematical reasoning.

• The solutions are based on the NCERT curriculum, ensuring that all the important topics are covered thoroughly.

Class 6 Maths Chapter 10: Exercises Breakdown

Important Study Material Links for Class 6 Maths Chapter 10 - The Other Side of Zero

Conclusion

The NCERT Solutions for Class 6 Maths Chapter 10, "The Other Side of Zero," particularly Exercise 10.2 "The Token Model," plays an important role in enhancing students' understanding of numbers. By introducing the token model, students can visualise positive and negative numbers more clearly, making abstract concepts easier to understand. The detailed solutions and structured exercises build confidence and promote critical thinking skills. This chapter not only reinforces foundational math concepts but also prepares students for future topics involving integers. Overall, Vedantu’s solutions provide essential support for students to master these key ideas, ensuring a solid base for their ongoing mathematical journey.

Chapter-Specific NCERT Solutions for Class 6 Maths

The chapter-wise NCERT Solutions for Class 6 Maths are given below. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

Related Important Links for Maths Class 6

Along with this, students can also download additional study materials provided by Vedantu for Maths Class 6.