Class 6
Dashboard
Mathematics
The Other Side Of Zero
NCERT Solutions
NCERT Solutions
The Other Side Of Zero
64 Solutions
Exercise:
All Exercises
Chapter 10 Questions
Chapter 10 Questions (Page 248)
Chapter 10 Questions (Page 252)
Chapter 10 Questions (Page 255)
Chapter 10 Questions (Pages 259-260)
Figure it Out (Page 245)
Figure it Out (Page 247)
Figure it Out (Page 249)
Figure it Out (Page 253)
Figure it Out (Page 257)
Figure it Out (Page 258)
Figure it Out (Page 260)
Figure it Out (Page 261)
Figure it Out (Page 262)
Figure it Out (Page 263)
Figure it Out (Page 265 - Amazing Grid)
Figure it Out (Page 265 - Final Section)
Figure it Out (Page 267)
Figure it out (Page 246)
Figure it out (Page 251)
Figure it out (Page 259)
Q1
Chapter 10 Questions
What do you press to go four floors up? What do you press to go three floors down?
Q2
Chapter 10 Questions
Number all the floors in the Building of Fun.
Q1
Chapter 10 Questions (Page 248)
Evaluate 15-5, 100-10 and 74-34 from this perspective.
Q1
Chapter 10 Questions (Page 252)
In the other exercises that you did above, did you notice that subtracting a negative number was the same as adding the corresponding positive number?
Q2
Chapter 10 Questions (Page 252)
If, from 5 you wish to go over to 9, how far must you travel along the number line?
Q3
Chapter 10 Questions (Page 252)
Now, from 9, if you wish to go to 3, how much must you travel along the number line?
Q4
Chapter 10 Questions (Page 252)
Now, from 3, if you wish to go to -2, how far must you travel?
Q1
Chapter 10 Questions (Page 255)
Use unmarked number lines to evaluate these expressions: a.
−
125
+
(
−
30
)
=
-125+(-30)=
−
125
+
(
−
30
)
=
b.
+
105
−
(
−
55
)
=
+105-(-55)=
+
105
−
(
−
55
)
=
c.
+
80
−
(
−
150
)
=
+80-(-150)=
+
80
−
(
−
150
)
=
d. $-99-(-200)=
Q1
Chapter 10 Questions (Pages 259-260)
Your new bank balance is _____.
Q2
Chapter 10 Questions (Pages 259-260)
Your bank balance is now _____.
Q3
Chapter 10 Questions (Pages 259-260)
What is your bank balance now? _____ Is this possible?
Q4
Chapter 10 Questions (Pages 259-260)
What is your balance now？ _____
Q1
Figure it Out (Page 245)
You start from Floor +2 and press -3 in the lift. Where will you reach? Write an expression for this movement.
Q2
Figure it Out (Page 245)
Evaluate these expressions (you may think of them as Starting Floor + Movement by referring to the Building of Fun). a.
(
+
1
)
+
(
+
4
)
=
(+1)+(+4)=
(
+
1
)
+
(
+
4
)
=
b.
(
+
4
)
+
(
+
1
)
=
(+4)+(+1)=
(
+
4
)
+
(
+
1
)
=
c.
(
+
4
)
+
(
−
3
)
=
(+4)+(-3)=
(
+
4
)
+
(
−
3
)
=
d.
(
−
1
)
+
(
+
2
)
=
(-1)+(+2)=
(
−
1
)
+
(
+
2
)
=
e.
(
−
1
)
+
(
+
1
)
=
(-1)+(+1)=
(
−
1
)
+
(
+
1
)
=
f.
0
+
(
+
2
)
=
0+(+2)=
0
+
(
+
2
)
=
g.
0
+
(
−
2
)
=
0+(-2)=
0
+
(
−
2
)
=
Q3
Figure it Out (Page 245)
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
(+2)+(-7)=-5
(
+
2
)
+
(
−
7
)
=
−
5
. Find more such starting positions and the movements needed to reach Floor -5 and write the expressions.
Q1
Figure it out (Page 246)
Evaluate these expressions by thinking of them as the resulting movement of combining button presses: a.
(
+
1
)
+
(
+
4
)
=
(+1)+(+4)=
(
+
1
)
+
(
+
4
)
=
b.
(
+
4
)
+
(
+
1
)
=
(+4)+(+1)=
(
+
4
)
+
(
+
1
)
=
c.
(
+
4
)
+
(
−
3
)
+
(
−
2
)
=
(+4)+(-3)+(-2)=
(
+
4
)
+
(
−
3
)
+
(
−
2
)
=
d.
(
−
1
)
+
(
+
2
)
+
(
−
3
)
=
(-1)+(+2)+(-3)=
(
−
1
)
+
(
+
2
)
+
(
−
3
)
=
Q2
Figure it out (Page 246)
Write the inverses of these numbers:
+
4
,
−
4
,
−
3
,
0
,
+
2
,
−
1.
+4, -4, -3, 0, +2, -1.
+
4
,
−
4
,
−
3
,
0
,
+
2
,
−
1.
Q3
Figure it out (Page 246)
Connect the inverses by drawing lines.
Q4
Figure it out (Page 246)
Who is on the lowest floor?
Jay is in the Art Centre. So, he is on Floor +2.
Asin is in the Sports Centre. So, she is on Floor _____.
Binnu is in the Cinema Centre. So, she is on Floor _____.
Aman is in the Toys Store. So, he is on Floor _____.
Q1
Figure it Out (Page 247)
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
Q2
Figure it Out (Page 247)
Imagine the Building of Fun with more floors. Compare the numbers and fill in the boxes with < or >: a. -10 □ -12 b. +17 □ -10 c. 0 □ -20 d. +9 □ -9 e. -25 □ -7 f. +15 □ -17
Q3
Figure it Out (Page 247)
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.
Q4
Figure it Out (Page 247)
Mark the following floors of the building shown on the right. a. -7 b. -4 c. +3 d. -10
Q1
Figure it Out (Page 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
)
=
(+1)-(+4)=
(
+
1
)
−
(
+
4
)
=
b.
(
0
)
−
(
+
2
)
=
(0)-(+2)=
(
0
)
−
(
+
2
)
=
c.
(
+
4
)
−
(
+
1
)
=
(+4)-(+1)=
(
+
4
)
−
(
+
1
)
=
d.
(
0
)
−
(
−
2
)
=
(0)-(-2)=
(
0
)
−
(
−
2
)
=
e.
(
+
4
)
−
(
−
3
)
=
(+4)-(-3)=
(
+
4
)
−
(
−
3
)
=
f.
(
−
4
)
−
(
−
3
)
=
(-4)-(-3)=
(
−
4
)
−
(
−
3
)
=
g.
(
−
1
)
−
(
+
2
)
=
(-1)-(+2)=
(
−
1
)
−
(
+
2
)
=
h.
(
−
2
)
−
(
−
2
)
=
(-2)-(-2)=
(
−
2
)
−
(
−
2
)
=
i.
(
−
1
)
−
(
+
1
)
=
(-1)-(+1)=
(
−
1
)
−
(
+
1
)
=
j. $(+3)-(-3)=
Q1
Figure it out (Page 251)
Complete these expressions. a.
(
+
40
)
+
□
=
+
200
(+40)+\square=+200
(
+
40
)
+
□
=
+
200
b.
(
+
40
)
+
□
=
−
200
(+40)+\square=-200
(
+
40
)
+
□
=
−
200
c.
(
−
50
)
+
□
=
+
200
(-50)+\square=+200
(
−
50
)
+
□
=
+
200
d.
(
−
50
)
+
□
=
−
200
(-50)+\square=-200
(
−
50
)
+
□
=
−
200
e.
(
−
200
)
−
(
−
40
)
=
(-200)-(-40)=
(
−
200
)
−
(
−
40
)
=
f.
(
+
200
)
−
(
+
40
)
=
(+200)-(+40)=
(
+
200
)
−
(
+
40
)
=
g. $(-200)-(+40)=
Q1
Figure it Out (Page 253)
Mark 3 positive numbers and 3 negative numbers on the number line above.
Q2
Figure it Out (Page 253)
Write down the above 3 marked negative numbers in the following boxes: □ □ □
Q3
Figure it Out (Page 253)
Is
2
>
−
3
2 > -3
2
>
−
3
? Why? Is
−
2
<
3
-2 < 3
−
2
<
3
? Why?
Q4
Figure it Out (Page 253)
What are a.
−
5
+
0
-5+0
−
5
+
0
b.
7
+
(
−
7
)
7+ (-7)
7
+
(
−
7
)
c.
−
10
+
20
-10+20
−
10
+
20
d.
10
−
20
10-20
10
−
20
e.
7
−
(
−
7
)
7-(-7)
7
−
(
−
7
)
f.
−
8
−
(
−
10
)
-8-(-10)
−
8
−
(
−
10
)
?
Q1
Figure it Out (Page 257)
Complete the additions using tokens. a.
(
+
6
)
+
(
+
4
)
(+6)+(+4)
(
+
6
)
+
(
+
4
)
b.
(
−
3
)
+
(
−
2
)
(-3)+(-2)
(
−
3
)
+
(
−
2
)
c.
(
+
5
)
+
(
−
7
)
(+5)+(-7)
(
+
5
)
+
(
−
7
)
d.
(
−
2
)
+
(
+
6
)
(-2)+(+6)
(
−
2
)
+
(
+
6
)
Q2
Figure it Out (Page 257)
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?
Q1
Figure it Out (Page 258)
Evaluate the following differences using tokens. Check that you get the same result as with other methods you now know: a.
(
+
10
)
−
(
+
7
)
(+10)-(+7)
(
+
10
)
−
(
+
7
)
b.
(
−
8
)
−
(
−
4
)
(-8)-(-4)
(
−
8
)
−
(
−
4
)
c.
(
−
9
)
−
(
−
4
)
(-9)-(-4)
(
−
9
)
−
(
−
4
)
d.
(
+
9
)
−
(
+
12
)
(+9)-(+12)
(
+
9
)
−
(
+
12
)
e.
(
−
5
)
−
(
−
7
)
(-5)-(-7)
(
−
5
)
−
(
−
7
)
f.
(
−
2
)
−
(
−
6
)
(-2)-(-6)
(
−
2
)
−
(
−
6
)
Q2
Figure it Out (Page 258)
Complete the subtractions: a.
(
−
5
)
−
(
−
7
)
(-5)-(-7)
(
−
5
)
−
(
−
7
)
b.
(
+
10
)
−
(
+
13
)
(+10)-(+13)
(
+
10
)
−
(
+
13
)
c.
(
−
7
)
−
(
−
9
)
(-7)-(-9)
(
−
7
)
−
(
−
9
)
d.
(
+
3
)
−
(
+
8
)
(+3)-(+8)
(
+
3
)
−
(
+
8
)
e.
(
−
2
)
−
(
−
7
)
(-2)-(-7)
(
−
2
)
−
(
−
7
)
f.
(
+
3
)
−
(
+
15
)
(+3)-(+15)
(
+
3
)
−
(
+
15
)
Q1
Figure it out (Page 259)
Try to subtract:
−
3
−
(
+
5
)
-3-(+5)
−
3
−
(
+
5
)
.
How many zero pairs will you have to put in? What is the result?
Q2
Figure it out (Page 259)
Evaluate the following using tokens. a.
(
−
3
)
−
(
+
10
)
(-3)-(+10)
(
−
3
)
−
(
+
10
)
b.
(
+
8
)
−
(
−
7
)
(+8)-(-7)
(
+
8
)
−
(
−
7
)
c.
(
−
5
)
−
(
+
9
)
(-5)-(+9)
(
−
5
)
−
(
+
9
)
d.
(
−
9
)
−
(
+
10
)
(-9)-(+10)
(
−
9
)
−
(
+
10
)
e.
(
+
6
)
−
(
−
4
)
(+6)-(-4)
(
+
6
)
−
(
−
4
)
f.
(
−
2
)
−
(
+
7
)
(-2)-(+7)
(
−
2
)
−
(
+
7
)
Q1
Figure it Out (Page 260)
Suppose you start with ₹ 0 in your bank account, and then you have credits of ₹30, ₹40, and ₹50, and debits of ₹40, ₹50, and ₹60. What is your bank account balance now?
Q2
Figure it Out (Page 260)
Suppose you start with ₹ 0 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?
Q3
Figure it Out (Page 260)
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?
Q1
Figure it Out (Page 261)
Looking at the geographical cross section, fill in the respective heights: a. □ b. □ c. □ d. □ e. □ f. □ g. □
Q2
Figure it Out (Page 261)
Which is the highest point in this geographical cross section? Which is the lowest point?
Q3
Figure it Out (Page 261)
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?
Q4
Figure it Out (Page 261)
What is the highest point above sea level on Earth? What is its height?
Q5
Figure it Out (Page 261)
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).
Q1
Figure it Out (Page 262)
Do you know that there are some places in India where temperatures can go below
0
∘
C
0^\circ C
0
∘
C
? Find out the places in India where temperatures sometimes go below
0
∘
C
0^\circ C
0
∘
C
. What is common among these places? Why does it become colder there and not in other places?
Q2
Figure it Out (Page 262)
Leh in Ladakh gets very cold during the winter. The following is a table of temperature readings taken during different times of the day and night in Leh on a day in November. Match the temperature with the appropriate time of the day and night.
Temperature:
14
∘
C
,
8
∘
C
,
−
2
∘
C
,
−
4
∘
C
14^\circ C, 8^\circ C, -2^\circ C, -4^\circ C
1
4
∘
C
,
8
∘
C
,
−
2
∘
C
,
−
4
∘
C
Time: 02:00 a.m., 11:00 p.m., 02:00 p.m., 11:00 a.m.
Q1
Figure it Out (Page 263)
Do the calculations for the second grid above and find the border sum.
Q2
Figure it Out (Page 263)
Complete the grids to make the required border sum.
Q3
Figure it Out (Page 263)
For the last grid above, find more than one way of filling the numbers to get border sum -4.
Q4
Figure it Out (Page 263)
Which other grids can be filled in multiple ways? What could be the reason?
Q5
Figure it Out (Page 263)
Make a border integer square puzzle and challenge your classmates.
Q1
Figure it Out (Page 265 - Amazing Grid)
Try afresh, choose different numbers this time. What sum did you get? Was it different from the first time? Try a few more times!
Q2
Figure it Out (Page 265 - Amazing Grid)
Play the same game with the grids below. What answer did you get?
Q3
Figure it Out (Page 265 - Amazing Grid)
What could be so special about these grids? Is the magic in the numbers or the way they are arranged or both? Can you make more such grids?
Q1
Figure it Out (Page 265 - Final Section)
Write all the integers between the given pairs, in increasing order. a. 0 and -7 b. -4 and 4 c. -8 and -15 d. -30 and -23
Q2
Figure it Out (Page 265 - Final Section)
Give three numbers such that their sum is -8.
Q3
Figure it Out (Page 265 - Final Section)
There are two dice whose faces have these numbers:
−
1
,
2
,
−
3
,
4
,
−
5
,
6
-1, 2, -3, 4, -5, 6
−
1
,
2
,
−
3
,
4
,
−
5
,
6
. The smallest possible sum upon rolling these dice is -10
=
(
−
5
)
+
(
−
5
)
=(-5)+(-5)
=
(
−
5
)
+
(
−
5
)
and the largest possible sum is
12
=
(
6
)
+
(
6
)
12=(6)+(6)
12
=
(
6
)
+
(
6
)
. Some numbers between ( -10 ) and ( +12 ) are not possible to get by adding numbers on these two dice. Find those numbers.
Q4
Figure it Out (Page 265 - Final Section)
Solve these:
|
8
−
13
8-13
8
−
13
|
(
−
8
)
−
(
13
)
(-8)-(13)
(
−
8
)
−
(
13
)
|
(
−
13
)
−
(
−
8
)
(-13)-(-8)
(
−
13
)
−
(
−
8
)
|
(
−
13
)
+
(
−
8
)
(-13)+(-8)
(
−
13
)
+
(
−
8
)
| |
8
+
(
−
13
)
8+(-13)
8
+
(
−
13
)
|
(
−
8
)
−
(
−
13
)
(-8)-(-13)
(
−
8
)
−
(
−
13
)
|
(
13
)
−
8
(13)-8
(
13
)
−
8
|
13
−
(
−
8
)
13-(-8)
13
−
(
−
8
)
|
Q5
Figure it Out (Page 265 - Final Section)
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? Hint: Recall that there was no year 0. c. What will be the year 320 years after 680 BCE?
Q6
Figure it Out (Page 265 - Final Section)
Complete the following sequences: a. (-40), (-34), (-28), (-22), _____, _____, _____ b. 3, 4, 2, 5, 1, 6, 0, 7, _____, _____, _____ c. _____, _____, 12, 6, 1, (-3), (-6), _____, _____, _____
Q7
Figure it Out (Page 265 - Final Section)
Here 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
)
(+18)+(+1)-(+7)-(-2)
(
+
18
)
+
(
+
1
)
−
(
+
7
)
−
(
−
2
)
which gives a value
(
+
14
)
(+14)
(
+
14
)
. Now, pick cards and make an expression such that its value is closer to (-30).
Q8
Figure it Out (Page 265 - Final Section)
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)
Q9
Figure it Out (Page 265 - Final Section)
This string has a total of 100 tokens arranged in a particular pattern. What is the value of the string?
Q1
Figure it Out (Page 267)
Can you explain each of Brahmagupta's rules in terms of Bela's Building of Fun, or in terms of a number line?
Q2
Figure it Out (Page 267)
Give your own examples of each rule.
More from this chapter
Chapter overview
Important Points
Practice Questions
Flashcards