Free access of the complete Ganita Prakash Book Class 6 Solutions and Chapter 10 The Other Side of Zero Class 6 NCERT Solutions Question Answer are crafted in simple format to align with the latest CBSE syllabus.

## Class 6 Maths Chapter 10 The Other Side of Zero Solutions

### The Other Side of Zero Class 6 Solutions Questions and Answers

**10.1 Bela’s Building of Fun Figure it Out (Page No. 245)**

Question 1.

You start from Floor +2 and press -3 in the lift. Where will you reach? Write an expression for this movement.

Solution:

Do it yourself.

Question 2.

Evaluate these expressions (you may think of them as Starting Floor + Movement by referring to the Building of Fun).

(a) (-1) + (+ 4) = _______________

(b) (+4) + (+1) = _______________

(c) (+ 4) + (- 3) = _______________

(d) (-1) + (+ 2) = _______________

(e) (-1) + (+1) = _______________

(f) 0 + (+ 2) = _______________

(g) 0 + (-2) = _______________

Solution:

(a) (-1) + (+ 4) = + 5

(b) (+4) + (+1) = +5

(c) (+ 4) + (- 3) = +1

(d) (-1) + (+ 2) = +1

(e) (-1) + (+1) = 0

(f) 0 + (+ 2) = +2

(g) 0 + (-2) = -2

Question 3.

Starting from different floors, find the movements required to reach.Floor – 5.

For example, if I start at Floor +2, I must press -7 to reach Floor -5.

The expression is (+2) + (-7) = -5.

Find more such starting positions and the movements needed to reach Floor -5 and write the expressions.

Solution:

Do it yourself.

InText Questions

Question 1.

What do you press to go four floors up? What do you press to go three floors down? (Page 243)

Solution:

We press +4 (+ + + + ) to go four floors up and we press -3 (- – -) to go three floors down.

Question 2.

Number all the floors in the Building of Fun. (Page 244)

Solution:

Space is on Floor +6

Sports is on Floor +5

Ice Cream is on Floor +4

Books is on Floor +3

Art Centre is on Floor +2

Food court is on Floor +1

Welcome Hall is on Floor +0

Toys Shop is on Floor -1

Video Games is on Floor -2

Cinema is on Floor -3

Ghost House is on Floor -4

Dinosaur is on Floor -5

**10.1 Bela’s Building of Fun Figure it Out (Page No. 246)**

Question 1.

Evaluate these expressions by thinking of them as the resulting movement of combining button presses:

(a) (+1) + (+4) = __________

(b) (+ 4) + (+ 1) = __________

(c) (+ 4) + (- 3) + (- 2) = __________

(d) (-1) + (+2) + (-3) = __________

Solution:

(a) (+ 1) + (+4) = +5

(b) (+ 4) + (+ 1) = +5

(c) (+ 4) + (- 3) + (- 2) = {(+ 4) + (- 3)} + (- 2)

= (+1) + (- 2) = -1

(d) (-1) + (+2) + (-3) = {(-1) + (+2)} + (-3)

= (+1) + (-3) = -2

InText Questions

Back to Zero!

Question 1.

Write the inverses of these numbers: (Page 246)

+4, -4, -3, 0, +2, -1.

Solution:

The inverse of+4 is -4, the inverse of-4 is +4, the inverse of-3 is +3, the inverse of 0 is 0, the inverse of +2 is -2, and the inverse of-1 is +1. it Connect the inverses by drawing lines.

Question 2.

Connect the inverses by drawing lines.

Solution:

The inverses are connected with their respective numbers by the lines as shown below.

Question 3.

Comparing numbers using floors

Question 4.

Who is on the lowest floor?

1. Jay is in the Art Centre. So, he is on Floor +2.

2. Asin is in the Sports Centre. So, she is on Floor __________.

3. Binnu is in the Cinema Centre. So, she is on Floor __________

4. Aman is in the Toys Shop. So, he is on Floor __________.

Solution:

1. Jay is in the Art Centre. So, he is on Floor +2.

2. Asin is in the Sports Centre. So, she is on Floor +5.

3. Binnu is in the Cinema Centre. So, she is on Floor-3.

4. Aman is in the Toys Shop. So, he is on Floor -1.

Among the four children, Binnu on the lowest floor.

**10.1 Bela’s Building of Fun Figure it Out (Page No. 247)**

Question 1.

Compare the following numbers using the Building of Fun and fill in the boxes with < or >.

(a) -2 __________ + 5

(b) -5 __________ + 4

(c) -5 __________ – 3

(d) +6 __________ – 6

(e) 0 __________ – 4

(f) 0 __________ +4

Solution:

(a) Floor -2 is lower than Floor +5.

So, -2 < +5.

(b) Floor -5 is lower than Floor +4.

So, -5 < +4.

(c) Floor -5 is lower than Floor -3.

So, -5 < -3.

(d) Floor +6 is higher than Floor -6.

So, +6 > -6.

(e) Floor 0 is higher than Floor -4.

So, 0 > -4.

(f) Floor 0 is lower than Floor +4.

So, 0 < +4.

Question 2.

Imagine the Building of Fun with more floors.

Compare the numbers and fill in the boxes with < or >:

(a) -10 __________ -12

Solution:

Floor-10 is higher .than Floor-12.

So,-10 > -12.

(b) +17 __________ -10

Solution:

Floor +17 is higher than Floor -10.

So, +17 > -10.

(c) 0 __________ -20

Solution:

Floor 0 is higher than Floor -20.

So, 0 > -20.

(d) +9 __________ – 9

Solution:

Floor +9 is higher than Floor-9.

So, +9 > -9.

(e) -25 __________ -7

Solution:

Floor -25 is lower than Floor -7.

So,-25 < -7.

(f) +15 __________ -17

Solution:

Floor +15 is higher than Floor -17.

So, +15 > -17.

Question 3.

If Floor A = -12, Floor D = -1 and Floor E = +1 in the building shown on the right as a line, find the numbers of Floors B, C, F, G and H.

Solution:

Floor B is 9 floors lower than Floor 0.

So, the number of Floor B is -9.

Floor C is 6 floors lower than Floor 0.

So, the number of Floor C is -6.

Floor F is 2 floors higher than Floor 0.

So, the number of Floor F is +2.

Floor G is 6 floors higher than Floor 0.

So, the number of Floor G is +6.

Floor H is 11 floors higher than Floor 0.

So, the number of Floor H is +11.

Question 4.

Mark the following floors of the building shown on the right.

(a) -7

(b) -4

(c) +3

(d) -10

Solution:

Floors -7, -4, +3, and -10 of the building are marked on the line given on previous page.

InText Questions

Question 1.

Evaluate 15-5, 100 – 10 and 74 – 34 from this perspective. (Page 248)

Solution:

15-5 means 5 taken away from 15 is 10.

∴ 15 – 5 = 10

100 – 10 means 10 taken away from 100 is 90.

∴ 100 – 10 = 90

74 – 34 means 34 taken away from 74 is 40.

∴ 74 – 34 = 40

**10.1 Bela’s Building of Fun Figure it Out (Page No. 249)**

Complete these expressions. You may think of them as finding the movement needed to reach the Target Floor from the Starting Floor.

(a) (+1) – (+4) = ________________

(b) (0) – (+2) = ________________

(c) (+4) – (+1) = ________________

(d) (0) – (-2) = ________________

(e) (+4)-(-3) = ________________

(f) (-4) – (-3) = ________________

(g) (-1) – (+2) = ________________

(h) (-2) – (-2) = ________________

(i) (-1) – (+1) = ________________

(j) (+3)-(-3) = ________________

Solution:

(a) (+1) – (+4) = -3

(b) (0) – (-2) = -200

(c) (+4) – (+1) = +3

(d) (o) – (-2) = +2

(e) (+4) – (-3) = +7

(f) (-4) – (-3) = -1

(g) (-1) – (+2) = -3

(h) (-2) – (-2) = 0

(i) (-1) – (+1) = -2

(j) (+3) – (3) = +6

**10.1 Bela’s Building of Fun Figure it Out (Page No. 251)**

Complete these expressions.

(a) (+40) + ____ = +200

(b) (+40) + ____ = -200

(c) (-50) +____ = +200

(d) (-50) + ____ = -200

(e) (-200) – (-40) = ____

(f) (+200) – (+40) = ____

(g) (-200) -(+40) = ____

Check your answers by thinking about the movement in the mineshaft.

Solution:

(a) (+200) – (+40) = +160.

Therefore, (+40) + (+160) = +200

(b) (-200) – (+40) = -240.

Therefore, (+40) + (-240) = -200

(c) (+200) – (-50) = +250.

Therefore, (-50) + (+250) = +200

(d) (-200) – (-50) = -150.

Therefore, (-50) + (-150) = -200

(e) (-200) -(-40) = -160

(f) (+200) – (+40) = +160

(g) (-200) – (+40) = -240

InText Questions

Question 1.

Try evaluating the following expressions by similarly drawing or imagining a suitable lift: (Page 251)

(a) -125 + (-30)

(b) +105 – (-55)

(c) +105 + (+55)

(d) +80 – (-150)

(e) +80 + (+150)

(f) -99 – (-200)

(g) -99 + (+200)

(h) + 1500 – (-1500)

Solution:

(a) -125 + (-30) = -155

(b) +105 – (-55) = +160

(c)+105 + (+55) = +160

(d) +80-(-150) = +230

(e) +80+ (+150) = +230

(f) -99-(-200) = +101

(g)-99+ (+200) = +101

(h) +1500- (-1500) = +3000

**10.1 Bela’s Building of Fun Figure it Out (Page No. 253 – 254)**

Question 1.

Mark 3 positive numbers and 3 negative numbers on the number line above.

Solution:

3 positive numbers are encircled on the right side of 0, and 3 negative numbers are encircled on the left side of the zero on the number line, as shown below.

Answers may vary.

Question 2.

Write down the above 3 marked negative numbers in the following boxes:

Solution:

Question 3.

Is 2 > -3? Why? Is -2 < 3? Why?

Solution:

Represent the numbers 2, -3, -2 and 3 on a number line.

2 is to the right of-3 on the number line.

So, 2 > -3.

And, -2 is to the left of 3 on the number line. So, -2 < 3.

Question 4.

(i) -5 + 0

Solution:

(ii) 7 +(-7)

Solution:

(iii) -10 + 20

Solution:

(iv) 10 – 20

Solution:

(v) 7 – (-7)

Solution:

(vi) -8 – (-10)?

Solution:

InText Questions

Question 1.

Use unmarked number lines to evaluate these expressions: (Page 255)

(a) -125 + (-30) = _______________

(b) +105 -(-55) = _______________

(c) +80 – (-150) = _______________

(d) -99 – (-200) = _______________

Solution:

(a) -125 + (-30) = -155

(b) Subtracting a negative number is the same as adding the corresponding positive number.

So, +105 – (-55) means +105 + (+55) = 160. That is,

+105 – (-55) = +160

Similarly,

(c) +80 – (-150) = +230

(d) -99 – (-200) = +101

**10.2 The Token Model Figure it Out (Page No. 257)**

Question 1.

Complete the additions using tokens.

(a) (+6) + (+4)

Solution:

∴ (+6) + (+4) = +10

(b) (-3) + (-2)

Solution:

∴ (-3) + (-2) = -5

(c) (+5) + (-7)

Solution:

∴ (+5) + (-7) = -2

(d) (-2) + (+6)

Solution:

∴ (-2) + (+6) = +4

Question 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?

Solution:

The lift attendant is on the floor -2.

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

Solution:

The lift attendant is on the floor +3.

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

**10.2 The Token Model Figure it Out (Page No. 258)**

Question 1.

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

(a) (+10) – (+7)

Solution:

(+10) – (+7) = 3

(b) (-8) – (-4)

Solution:

(-8) – (-4) = -4

(c) (-9) – (-4)

Solution:

(-9) – (-4) = -5

(d) (+9) – (+12)

Solution:

Start with 9 positives.

But there are not enough tokens to take out 12 positives. So, we will add 3 extra zero pairs and then take out 12 positives.

(+9) – (+12) = -3

(e) (-5) – (-7)

Solution:

Start with 5 negatives.

But there are not enough tokens to take out 7 negatives. So, we will add 2 extra zero pairs and then take out 7 negatives.

(-5) – (-7) = +2

(f) (-2) – (-6)

Solution:

Start with 2 negatives.

But there are not enough tokens to take out 6 negatives. So, we will add 4 extra zero pairs and then take out 6 negatives.

(-2) – (-6) = +4

Question 2.

2. Complete the subtractions:

(a)

(-5) – (-7)

(b) (+10) – (+13)

(c) (-7) – (-9)

(d) (+3) – (+8)

(e) (-2) – (-7)

(f) (+3) – (+15)

Solution:

(a) (-5) – (-7) = +2

(b) (+10) – (+13) =-3

(c) (-7) – (-9) = +2

(d) (+3) – (+8) = -5

(e) (-2) – (-7) = +5

(f) (+3) – (+15) = -12

**10.2 The Token Model Figure it Out (Page No. 259)**

Question 1.

Try to subtract: -3 – (+5).

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

Solution:

Start with 3 negatives.

Since, we need to take out 5 positives. So, we will add 5 extra zero pairs and then take out 5 positives.

-3 – (+ 5) = -8

Question 2.

Evaluate the following using tokens.

(a) (-3) – (+10)

Solution:

Start with 3 negatives.

Since, we need to take out 10 positives. So, we will add 10 extra zero pairs and then take out 10 positives.

∴ (-3) – (+10) = -13

(b) (+8) – (-7)

Solution:

Start with 8 positives.

Since we need to take out 7 negatives. So, we will add 7 extra zero pairs and then take out 7 negatives.

∴ (+8) – (-7) = + 15

(c) (-5) – (+9)

Solution:

Start with 5 negatives.

Add 9 extra zero pairs and then take out 9 positives.

∴ (-5) – (+9) = -14

(d) (-9) – (+10)

Solution:

Start with 9 negatives.

Add 10 extra zero pairs and then take out 10 positives.

∴ (-9) – (+10) = -19

(e) (+6) – (-4)

Solution:

Start with 6 positives.

Add 4 extra zero pairs and then take out 4 negatives.

∴ (+6) – (-4) = +10

(f) (-2) – (+7)

Solution:

Start with 2 negatives.

Add 7 extra zero pairs and then take out 7 positives.

∴ (-2) – (+7) = – 9

**10.3 Integers in Other Places Figure it Out (Page No. 260)**

Question 1.

Suppose you start with 0 rupees in your bank account, and then you have crediip of ₹ 30, ₹ 40, and ₹ 50, and debits of ₹ 40, ₹ 50, and ₹ 60. What is your bank account balance now?

Solution:

Consider ‘credits’ as positive numbers and ‘debits’ as negative numbers.

Total credits = (+30) + (+40) + (+50) = +120

Total debits = (-10) + (-50) + (-60) = -150

Account balance = Total credits + Total debits = (+120)+ (-150) = -30

Hence, the account balance is -₹30.

Question 2.

Suppose you start with 0 rupees in your bank account, and then you have debits of ₹1, 2, 4, 8, 16, 32, 64, and 128, and then a single credit of ₹ 256. What is your bank account balance now?

Solution:

Consider ‘credits’ as positive numbers and ‘debits’ as negative numbers.

Total credits = +256

Total debits = (-1) + (-2) + (-4) + (-8) + (-16) + (-32) + (-64)+ (-128) =-255

Account balance = Total credits + Total debits = (+256) + (-255) = +1

Hence, the account balance is ₹ 1.

Question 3.

Why is it generally better to try and maintain a positive balance in your bank account? What are circumstances under which it may be worthwhile to temporarily have a negative balance?

Solution:

It is usually better to keep a positive balance in our bank account because it helps us avoid extra fees and keeps our credit score good. We can withdraw money when we need it. A negative balance might be okay temporarily if we need to cover something urgent and are expecting money soon. Just make sure to fix the negative balance quickly to avoid extra Charges and to ensure we have funds available for emergencies.

(Note: It is an example solution. Answer may vary.)

**10.3 Integers in Other Places Figure it Out (Page No. 261)**

Question 1.

Looking at the geographical cross-section fill in the respective heights:

Solution:

A = 1500 m

B = -500 m

C = 300 m

D = -1200 m

E = 1200 m

F = -200m

G = 100 m

Question 2.

Which is the highest point in this geographical cross-section? Which is the lowest point?

Solution:

The highest point is point A, with a height of 1500 m, and the lowest point is point D with a height of -1200 m or we can say with a depth of 1200 m.

Question 3.

Can you write the points A, B, …, G in a sequence of decreasing order of heights? Can you write the points in a sequence of increasing order of heights?

Solution:

The sequence of decreasing order of heights: A, E, C, G, F, B, and D.

The sequence of increasing order of heights: D, B, F, G, C, E, and A.

Question 4.

What is the highest point above sea level on Earth? What is its height?

Solution:

The highest point above sea level on Earth is the peak of Mount Everest. It stands at approximately 29,032 feet or 8,848 metres above sea level.

Question 5.

What is the lowest point with respect to sea level on land or on the ocean floor? What is its height? (This height should be negative).

Solution:

The lowest point on land with respect to sea level is the shoreline of the Dead Sea, which is approximately 1,410 feet (430 metres) below sea level. In terms of height, we can write it as approximately -1,410 feet or -430 metres.

But the lowest point on the ocean floor is the Challenger Deep in the Mariana Trench, which is about 36,070 feet or 10,994 metres below sea level. In terms of height, we can write it as -36070 feet or -10994 metres.

**10.3 Integers in Other Places Figure it Out (Page No. 262)**

Question 1.

Do you know that there are some places in India where temperatures can go below 0°C? Find out the places in India where temperatures sometimes go below 0°C. What is common among these places? Why does it become colder there and not in other places?

Solution:

In India, some places experience temperatures that can drop below 0°C, especially in the northern regions. Drass in Ladakh, is knowmfor its extremely cold temperatures, particularly during winter. Similarly, Shimla and Manali in Himachal Pradesh also the temperatures fall below freezing in the winter months. The Siachen Glacier, located in the union territory of Ladakh, is one of the coldest places in India.

In such locations one thing is common which is their high altitude. Being situated in the Himalayas, these areas are at significant elevations where the air is thinner and less capable of holding heat. Additionally, their northern geographical location means they receive less direct sunlight during winter, which contributes to their colder temperatures.

Question 2.

Leh in Ladakh gets very cold during winter. The following is a table of temperature readings taken during different times of the day/night in Leh on a day in November. Match the temperature with the appropriate time of the day/night.

Solution:

**10.4 Explorations with Integers Figure it Out (Page No. 263 – 264)**

Question 1.

Do the calculations for the given grid and find the border sum.

Solution:

Top row: 5 + (-3) + (-5) = -3

Bottom row: (-8) + (-2) + 7 = -3

Left column: 5 + 0 + (-8) = -3

Right column: (-5) + (-5) + 7 = -3

Therefore, The border sum of the given grid is ‘-3’.

Question 2.

Complete the grids to make the required border sum:

Solution:

Question 3.

For the last grid above, find more than one way of filling the numbers to get border sum -4.

Solution:

We can fill up the above grids in so many ways.

Following are few ways to fill the last grid.

Question 4.

Which other grids can be filled in multiple ways? What could be the reason?

Solution:

We can also fill up the grid 1 in multiple ways. Any grid with 3 or fewer prefilled numbers can be filled in multiple ways.

Question 5.

Make a border integer square puzzle and challenge your classmates.

Solution:

Do it yourself.

**10.4 Explorations with Integers Figure it Out-1 (Page No. 265)**

Question 1.

Try afresh, choose different numbers this time. What sum did you get? Was it different from the first time? Try a few more times!

Solution:

Let’s circle the number -5.

Now as per the game, let’s strike out the row and column with the number -5.

Now try yourself.

Question 2.

Play the same game with the grids below. What answer did you get?

The Other Side of Zero Class 6 NCERT Solutions Ganita Prakash Maths Chapter 10 56

Solution:

(a) Let’s circle the number 1.

Now as per the game, let’s strike out the row and column with number 1.

Now try yourself.

(b) Let’s circle the number 0.

Now as per the game, let’s strike out the row and column with the number 0.

Now try yourself.

Now let’s add the circled numbers = 0 + (-5) + 1 + (-10) = -14 which is the required answer.

Question 3.

What could be so special about these grids? Is the magic in the numbers the way they are arranged or both? Can you make more such grids?

Solution:

Grids can be fascinating because of both the numbers and the way they are arranged. Here’s why:

Numbers: The numbers in a grid can follow specific patterns or sequences, such as magic squares where the sums of numbers in each row, column, and diagonal are the same.

Arrangement: The way elements are arranged in a grid can create visual balance and harmony.

**10.4 Explorations with Integers Figure it Out-2 (Page No. 265 – 266)**

Question 1.

Write all the integers between the given pairs, in increasing order.

(3) 0 and -7

(b) -4 and 4

(c) -8 and -15

(d) -30 and -23

Solution:

(a) The integers between 0 and -7 in increasing order are: -6, -5, -4, -3, -2, and -1.

(b) The integers between -4 and 4 in increasing order are: -3, -2, -1, 0, 1, 2, and 3.

(c) The integers between -8 and -15 in increasing order are: -14, -13, -12, -11, -10, and -9.

(d) The integers between -30 and -23 in increasing order are: -29, -28, -27, -26, -25, and -24.

Question 2.

Give three numbers such that their sum is -8.

Solution:

Three such numbers are: 0,1, and -9 as 0 + 1 + (-9) = -8 (Note: Answer my vary.)

Question 3.

There are two dice whose faces have these numbers: -1, 2, -3, 4, -5, 6. Tlje smallest possible sum upon rolling these dice is -10 = (-5) + (-5) and the largest possible sum is 12 = (6) + (6). Some numbers between (-10) and (+12) are not possible to get by adding numbers on these two dice. Find those numbers.

Solution:

All possible combinations of numbers on both dice will be: (-5, -5), (-5, -3), (-5, -1), (-5, 2), (-5, 4), (-5,6), (-3, -5), (-3, -3), (-3, -1), (-3,2), (-3,4), (-3,6), (-1, -5), (-1, -3), (-1, -1), (-1, 2), (-1, 4), (-1, 6), (2, -5), (2, -3), (2, -1), (2, 2), (2, 4), (2, 6), (4, -5), (4, -3), (4, -1), (4, 2), (4, 4), (4, 6), (6, -5), (6, -3), (6,-1), (6, 2), (6, 4), (6, 6).

Unique sums are: -10, -8, -6, -4, -3, -2, -1, 1, 3, 4, 5, 6, 8, 10, 12

So, the numbers between -10 and 12 that are not possible as a sum of the numbers on the dice are -9, -7, -5, 0, 2, 7, 9, and 11.

Question 4.

Solve these:

Solution:

Question 5.

Find the years below.

(a) From the present year, which year was it 150 years ago?

(b) From the present year, which year was it 2200 years ago?

(c) What will be the year 320 years after 680 BCE?

Solution:

(a) Do it yourself.

(b) Do it yourself.

(c) 680 BCE is the year -680.

Now, -680 + 320 = -360 So, it was 360 BCE.

Question 6.

Complete the following sequences:

(a) (-40), (-34), (-28), (-22), _______, _______, _______, _______

(b) 3, 4, 2, 5, 1, 6, 0, 7, _______, _______, _______, _______

(c) _______, _______, 12, 6, 1, (-3), (-6), _______, _______

Solution:

(a) (-40) + 6 = (-34); (-34) + 6 = (-28);

(-28) + 6 = (-22); (-22) + 6 = (-16);

(-16) + 6 = (-10), (-10) + 6 = (-4),

Therefore, (-40), (-34), (-28), (-22), (-16), (-10), (-4)

(b) 3 + 1 = 4; 4 – 2 = 2; 2 + 3 = 5; 5 – 4 = 1; 1 + 5 = 6; 6 – 6 = 0; 0 + 7 = 7; 7 – 8 = -1; -1 + 9 = 8; 8 – 10 = -2

3, 4, 2, 5, 1, 6, 0, 7, -1, 8, -2

(c) Since, 27 – 8 = 19; 19 – 7 = 12; 12 – 6 = 6; 6 – 5 = 1; 1 – 4 =-3; -3 – 3 = -6; -6-2 = -8; -8 – 1 = -9

27, 19, 12, 6, 1, (-3), (-6), -8, -9

Question 7.

Flere are six integer cards: (+1), (+7), (+18), (-5), (-2), (-9).

You can pick any of these and make an expression using addition(s) and subtraction(s).

Here is an expression: (+18) + (+1) – (+7) – (-2) which gives a value (+14).

Now, pick cards and make an expression such that its value is closer to (-30).

Solution:

(-9) – (+18) + (-2) = -29, which is closer to -30 Answers may vary.

Question 8.

The sum of two positive integers is always positive but a (positive integer) – (positive integer) can be positive or negative. What about

(a) (positive) – (negative)

(b) (positive) + (negative)

(c) (negative) + (negative)

(d) (negative) – (negative)

(e) (negative) – (positive)

(f) (negative) + (positive)

Solution:

(a) (positive) – (negative) is always positive.

(b) (positive) + (negative) can be positive ornegative.

(c) (negative) + (negative) is always negative.

(d) (negative) – (negative) can be positive or negative.

(e) (negative) – (positive) is always negative.

(f) (negative) + (positive) can be negative or positive.

Question 9.

This string has a total of 100 tokens arranged in a particular pattern. What is the value of the string?

Solution:

The group of 5 tokens hasthe value, (+3) + (-2) = +1

There will be 20 such groups in a string of 100 tokens.

So, the total value will be +20.

**10.5 A Pinch of History Figure it Out (Page No. 268)**

Question 1.

Can you explain each of Brahmagupta’s rules in terms of Bela’s Building of Fun, or in terms of a number line?

Solution:

Do it yourself

Question 2.

Give your own examples of each rule.

Solution:

Do it yourself