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

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Solution sheet 1

Page no. 243

NCERT Class 6 Maths Chapter 10, question 1 — Source question

What do you press to go four floors up? What do you press to go three floors down?

Show solution

• + + + + or + 4 • - - - or – 3 Page No. 244

Source worked solution for Class 6 Chapter 10, question 1, part 1 — Source worked answer · part 1

Page no. 243 · Page No. 244

NCERT Class 6 Maths Chapter 10, question 2 — Source question

Number all the floors in the Building of Fun.

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+3: Book Store +2: Art Centre +1: Food Court 0: Welcome Hall -1: Toy Store -2: Video Game. Page No. 245 Figure it out

Source worked solution for Class 6 Chapter 10, question 2, part 1 — Source worked answer · part 1

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NCERT Class 6 Maths Chapter 10, question 3 — Source question

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

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(+2) + (-3) = -1; Toy store.

Source worked solution for Class 6 Chapter 10, question 3, part 1 — Source worked answer · part 1

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NCERT Class 6 Maths Chapter 10, question 4 — Source 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) = _____

Show solution

a. (+5) b. (+5) c. (+1) d. (+1) e. 0 f. (+2) g. (-2) [1]

Source worked solution for Class 6 Chapter 10, question 4, part 1 — Source worked answer · part 1

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Solution sheet 2

Source solution page 45

NCERT Class 6 Maths Chapter 10, question 5 — Source 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.

Show solution

Starting floor + Movement = Target Floor +1 + (-6) = (-5) -2 + (-3) = (-5) 0 + (-5) = (-5) (Try more possibilities) Page No. 246 Figure it out

Source worked solution for Class 6 Chapter 10, question 5, part 1 — Source worked answer · part 1

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NCERT Class 6 Maths Chapter 10, question 6 — Source question

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) = _____

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a. (+5) b. (+5) c. (-1) d. (-2)

Source worked solution for Class 6 Chapter 10, question 6, part 1 — Source worked answer · part 1

Source solution page 45

NCERT Class 6 Maths Chapter 10, question 7 — Source question

Write the inverses of these numbers: +4, –4, –3, 0, +2, –1.

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Inverse of +4 = -4 Inverse of -4 = +4 Inverse of -3 = +3 Inverse of 0 = 0 Inverse of +2 = (-2) Inverse of -1 = +1

Source worked solution for Class 6 Chapter 10, question 7, part 1 — Source worked answer · part 1

Source solution page 45

NCERT Class 6 Maths Chapter 10, question 8 — Source question

Connect the inverses by drawing lines. (+5) (-7) (–8) (+9) (–9) (+8) (-5) (+7) [2]

Show solution

(+5) (-7) (–8) (+9) (–9) (+8) (-5) (+7)

Source worked solution for Class 6 Chapter 10, question 8, part 1 — Source worked answer · part 1

Source worked solution for Class 6 Chapter 10, question 8, part 2 — Source worked answer · part 2

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Solution sheet 3

Source solution page 46

NCERT Class 6 Maths Chapter 10, question 9 — Source question

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 __.

Show solution

Binnu is on the lowest floor. 1. +2 2. +5 3. -3 4. -1 Page No. 247 Figure it out

Source worked solution for Class 6 Chapter 10, question 9, part 1 — Source worked answer · part 1

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NCERT Class 6 Maths Chapter 10, question 10 — Source question

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

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a. (–2) +5 b. (–5) + 4 c. (–5) – 3 d. + 6 – 6 e. 0 – 4 f. 0 + 4 Ans. a. < b. < c. < d. > e. > f. <

Source worked solution for Class 6 Chapter 10, question 10, part 1 — Source worked answer · part 1

Source solution page 46

NCERT Class 6 Maths Chapter 10, question 11 — Source question

2. Imagine the Building of Fun with more floors. Compare the numbers and fill in the boxes with < or >: a. a. (–10) (–12) b. + 17 (–10) c. 0 (–20) d. + 9 (–9) e. (–25) (–7) f. + 15 (–17)

Show solution

a. > b. > c. > d. > e. < f. > [3] +8 +7

Source worked solution for Class 6 Chapter 10, question 11, part 1 — Source worked answer · part 1

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Solution sheet 4

Source solution page 47

NCERT Class 6 Maths Chapter 10, question 12 — Source 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. +6 G

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B = -9 C = -6 F = +2 G = +6 H = +11 +5

Source worked solution for Class 6 Chapter 10, question 12, part 1 — Source worked answer · part 1

Source solution page 47

NCERT Class 6 Maths Chapter 10, question 13 — Source question

4. Mark the following floors of the building shown on the right. +4 a. -7 b. -4 c. +3 d. -10 +3 R

Show solution

+2 a. P = -7 b. Q = - 4 c. R = +3 d. S = -10 +1 E 0 Page 248 -1 D

Source worked solution for Class 6 Chapter 10, question 13, part 1 — Source worked answer · part 1

Page 248

NCERT Class 6 Maths Chapter 10, question 14 — Source question

Evaluate 15 – 5, 100 – 10 and 74 – 34 from this perspective.

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-2 -3 -4 Q • 15 -5 can be expressed as 5 + ? = 15 . So, ? = 10 • 100 – 10 can be expressed as 10 + ? = 100. So, ? = 90 • 74 – 34 can be expressed as 34 + ? = 74. So, ? = 40 -5 Page No. 249 -6 C Figure it out -7 P

Source worked solution for Class 6 Chapter 10, question 14, part 1 — Source worked answer · part 1

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NCERT Class 6 Maths Chapter 10, question 15 — Source question

Complete these expressions. You may think of them as finding the movement needed -8 to reach the Target Floor from the Starting Floor. -9 B a. (+ 1) – (+ 4) = ___ b. (0) – (+ 2) = _ -10 S c. (+ 4) – (+ 1) = _ d. (0) – (– 2) = ___ -11 e. (+ 4) – (– 3) = _ f. (– 4) – (– 3) = __ A -12 g. (– 1) – (+ 2) = _ h. (– 2) – (– 2) = __ i. (– 1) – (+1) = _ j. (+ 3) – (– 3) = ______

Show solution

a. (-3) b. (-2) c. (+3) d. (+2) e. (+7) f. (-1) g. (-3) h. (0) i. (-2) j. (+6) [4] Page No. 251 Figure it out

Source worked solution for Class 6 Chapter 10, question 15, part 1 — Source worked answer · part 1

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Solution sheet 5

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NCERT Class 6 Maths Chapter 10, question 16 — Source question

Complete these expressions. a. (+ 40) + __ = + 200 b. (+ 40) + _ = – 200 c. (– 50) + = + 200 d. (– 50) + _ = – 200 e. (– 200) – (– 40) = _ f. (+ 200) – (+ 40) = _ g. (– 200) – (+ 40) = _____

Show solution

a. (+160) b. (-240) c. (+250) d. (-150) e. (-160) f. (+160) g. (-240) Page No. 252

Source worked solution for Class 6 Chapter 10, question 16, part 1 — Source worked answer · part 1

Page No. 252

NCERT Class 6 Maths Chapter 10, question 17 — Source question

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?

Show solution

Yes. The infinite lift reminds us of a number line.

Source worked solution for Class 6 Chapter 10, question 17, part 1 — Source worked answer · part 1

Page No. 252

NCERT Class 6 Maths Chapter 10, question 18 — Source question

If, from 5 you wish to go over to 9, how far must you travel along the number line?

Show solution

4 steps.

Source worked solution for Class 6 Chapter 10, question 18, part 1 — Source worked answer · part 1

Page No. 252

NCERT Class 6 Maths Chapter 10, question 19 — Source question

Now, from 9, if you wish to go to 3, how much must you travel along the number line?

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One must travel 6 steps backward or move (-6) from 9 to go to 3.

Source worked solution for Class 6 Chapter 10, question 19, part 1 — Source worked answer · part 1

Source solution page 48

NCERT Class 6 Maths Chapter 10, question 20 — Source question

Now, from 3, if you wish to go to – 2, how far must you travel?

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One must travel 5 steps backward or move (-5) from 3 to go to -2. Page No. 253 Figure it out B A C P Q R -10 6 1 3 4 -9 -8 -7 -6 -4 -3 -2 -1 0 5 7 8 9 10 -5 2

Source worked solution for Class 6 Chapter 10, question 20, part 1 — Source worked answer · part 1

Source solution page 48

NCERT Class 6 Maths Chapter 10, question 21 — Source question

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

Show solution

Mark A = 2, B = 5, C = 8 P = -1, Q = -3, R = -7 (Try other possibilities) [5]

Source worked solution for Class 6 Chapter 10, question 21, part 1 — Source worked answer · part 1

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Solution sheet 6

Source solution page 49

NCERT Class 6 Maths Chapter 10, question 22 — Source question

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

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-7, -3, -1

Source worked solution for Class 6 Chapter 10, question 22, part 1 — Source worked answer · part 1

Source solution page 49

NCERT Class 6 Maths Chapter 10, question 23 — Source question

3. Is 2 > – 3? Why? Is – 2 < 3? Why?

Show solution

Yes, 2 > -3. On the number line 2 is on the right side of (-3). Yes, -2 < 3, as 3 is on the right of -2.

Source worked solution for Class 6 Chapter 10, question 23, part 1 — Source worked answer · part 1

Source solution page 49

NCERT Class 6 Maths Chapter 10, question 24 — Source question

4. What are (i) – 5 + 0 (ii) 7 + (– 7) (iii) – 10 + 20 (iv) 10 – 20 (v) 7 – (– 7) (vi) – 8 – (– 10)?

Show solution

(i) – 5 + 0 = -5 (ii) 7 + (– 7) = 0 (iii) – 10 + 20 =10 (iv) 10 – 20 = -10 (v) 7 – (– 7) = 14 (vi) – 8 – (– 10) = 2 Page No. 255

Source worked solution for Class 6 Chapter 10, question 24, part 1 — Source worked answer · part 1

Page No. 255

NCERT Class 6 Maths Chapter 10, question 25 — Source question

Use unmarked number lines to evaluate these expressions: a. – 125 + (– 30) = ___ b. + 105 – (– 55) = _ c. + 80 – (– 150) = _ d. – 99 – (– 200) = ___

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a. – 125 + (– 30) = -155 b. + 105 – (– 55) = 160 c. + 80 – (– 150) = 230 d. – 99 – (– 200) = 101 Page No. 257 Figure it out

Source worked solution for Class 6 Chapter 10, question 25, part 1 — Source worked answer · part 1

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NCERT Class 6 Maths Chapter 10, question 26 — Source question

1. Complete the additions using tokens. a. (+ 6) + (+ 4) b. (– 3) + (– 2) c. (+ 5) + (– 7) d. (– 2) + (+ 6)

Show solution

a. +10 b. -5 [6] c. (-2) d. (+4)

Source worked solution for Class 6 Chapter 10, question 26, part 1 — Source worked answer · part 1

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Solution sheet 7

Source solution page 50

NCERT Class 6 Maths Chapter 10, question 27 — Source 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? a. b.

Show solution

a. (+3) + (-5) = (-2) b. (+6) + (-3) = (+3) Attendant is at (-2) Floor Attendant is at (+3) Floor Page No. 258 Figure it out

Source worked solution for Class 6 Chapter 10, question 27, part 1 — Source worked answer · part 1

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NCERT Class 6 Maths Chapter 10, question 28 — Source 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) b. (– 8) – (– 4) c. (– 9) – (– 4) d. (+ 9) – (+ 12) e. (– 5) – (– 7) f. (– 2) – (– 6)

Show solution

a. (+10) – (+7) = (+3) b. (-8) – (-4) = (-8) + (+4) = (-4) c. (-9) – (-4) = (-9) + (+4) = (-5) d. (+9) – (+12) = (-3) e. [7] (-5) - (-7) = (+2) f. (-2) – (-6) = +4 Try for other methods.

Source worked solution for Class 6 Chapter 10, question 28, part 1 — Source worked answer · part 1

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Solution sheet 8

Source solution page 51

NCERT Class 6 Maths Chapter 10, question 29 — Source question

2. Complete the subtractions: a. (– 5) – (– 7) b. (+ 10) – (+ 13) c. (– 7) – (– 9) d. (+ 3) – (+ 8) e. (– 2) – (– 7) f. (+ 3) – (+ 15)

Show solution

a. +2 b. -3 c. +2 d. (-5) e. +5 f. (-12) Section 10.2 Page No. 259 Figure it out

Source worked solution for Class 6 Chapter 10, question 29, part 1 — Source worked answer · part 1

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NCERT Class 6 Maths Chapter 10, question 30 — Source question

1. Try to subtract: – 3 – (+ 5). How many zero pairs will you have to put in? What is the result?

Show solution

-8 We have to put five zero pairs.

Source worked solution for Class 6 Chapter 10, question 30, part 1 — Source worked answer · part 1

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NCERT Class 6 Maths Chapter 10, question 31 — Source question

2. Evaluate the following using tokens. a. (– 3) – (+ 10) b. (+ 8) – (– 7) c. (– 5) – (+ 9) d. (– 9) – (+ 10) e. (+ 6) – (– 4) f. (– 2) – (+ 7)

Show solution

a. -13 b. +15 c. -14 d. -19 e. +10 f. -9 [8] Section 10.3 Page No. 259

Source worked solution for Class 6 Chapter 10, question 31, part 1 — Source worked answer · part 1

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Solution sheet 9

Section 10.3 · Page No. 259

NCERT Class 6 Maths Chapter 10, question 32 — Source question

Your new bank balance is _______.

Show solution

₹ 100 + ₹ 60 = ₹ 160

Source worked solution for Class 6 Chapter 10, question 32, part 1 — Source worked answer · part 1

Section 10.3 · Page No. 259

NCERT Class 6 Maths Chapter 10, question 33 — Source question

Your bank balance is now ______.

Show solution

₹ 160 - ₹ 30 = ₹ 130

Source worked solution for Class 6 Chapter 10, question 33, part 1 — Source worked answer · part 1

Section 10.3 · Page No. 259

NCERT Class 6 Maths Chapter 10, question 34 — Source question

What is your bank balance now? ______ Is this possible?

Show solution

₹ 130 - ₹ 150 = - ₹ 20 Page No. 260

Source worked solution for Class 6 Chapter 10, question 34, part 1 — Source worked answer · part 1

Page No. 260

NCERT Class 6 Maths Chapter 10, question 35 — Source question

What is your balance now? ______

Show solution

₹ 180 Section 10.3 Page 260 Figure it Out

Source worked solution for Class 6 Chapter 10, question 35, part 1 — Source worked answer · part 1

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NCERT Class 6 Maths Chapter 10, question 36 — Source question

1. Suppose you start with 0 rupees 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?]

Show solution

(+30) + (+40) + (+50) – (40) – (50) – (60) Balance amount in Bank Account = ₹ (-30)

Source worked solution for Class 6 Chapter 10, question 36, part 1 — Source worked answer · part 1

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NCERT Class 6 Maths Chapter 10, question 37 — Source 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?

Show solution

(1) – (2) – (4) – (8) – (16) – (32) – (64) – (128) + (256) Balance amount in the Bank Account = ₹ 1 [9] Figure it Out Page 261

Source worked solution for Class 6 Chapter 10, question 37, part 1 — Source worked answer · part 1

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Solution sheet 10

Figure it Out · Page 261

NCERT Class 6 Maths Chapter 10, question 38 — Source question

1. Looking at the geographical cross section fill in the respective heights: A B C D E. F. G.

Show solution

Approximate heights are: A. (+1500) m B. (-500) m C. (+300) m D. (-1200) m E. (+1200) m F. (-200) m G. (+100) m

Source worked solution for Class 6 Chapter 10, question 38, part 1 — Source worked answer · part 1

Source solution page 53

NCERT Class 6 Maths Chapter 10, question 39 — Source question

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

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Highest point is A & the lowest point is D.

Source worked solution for Class 6 Chapter 10, question 39, part 1 — Source worked answer · part 1

Q.2. Which is the highest point in this geographical cross-section? Which is the lowest

NCERT Class 6 Maths Chapter 10, question 40 — Source question

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

Show solution

A, E, C, G, F, B, D. (Decreasing order) D, B, F, G, C, E, A. (Increasing order)

Source worked solution for Class 6 Chapter 10, question 40, part 1 — Source worked answer · part 1

Source solution page 53

NCERT Class 6 Maths Chapter 10, question 41 — Source question

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

Show solution

Mount-Everest. Its height above sea level is 8848m.

Source worked solution for Class 6 Chapter 10, question 41, part 1 — Source worked answer · part 1

Source solution page 53

NCERT Class 6 Maths Chapter 10, question 42 — Source 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).

Show solution

The lowest know point on the Earth is the challenger deep, located in the Mariana trench in the Pacific Ocean. Its depth is approximately -10994 m. [10] Page 262 Figure it Out

Source worked solution for Class 6 Chapter 10, question 42, part 1 — Source worked answer · part 1

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Solution sheet 11

Page 262 · Figure it Out

NCERT Class 6 Maths Chapter 10, question 43 — Source question

2 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.

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Temperature Time 14°C 02:00 p.m. 8°C 11:00 a.m –2°C 11:00 p.m. –4°C 02:00 a.m. Section 10.4 Page 263 Figure it Out

Source worked solution for Class 6 Chapter 10, question 43, part 1 — Source worked answer · part 1

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NCERT Class 6 Maths Chapter 10, question 44 — Source question

1 Do the calculations for the second grid above and find the border sum.

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-3, -3, -3, -3

Source worked solution for Class 6 Chapter 10, question 44, part 1 — Source worked answer · part 1

Page 263 · Figure it Out

NCERT Class 6 Maths Chapter 10, question 45 — Source question

2 Complete the grids to make the required border sum:

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One of the ways: -10 10 4 5 -5 9 -10 5 Border sum +4 6 8 -16 11 -5 -19 -2 19 Border sum -2 7 -2 -9 -3 -5 -8 -6 10 Border sum -4 Think of other ways. [11] Page 265 Figure it Out

Source worked solution for Class 6 Chapter 10, question 45, part 1 — Source worked answer · part 1

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Solution sheet 12

Page 265 · Figure it Out

NCERT Class 6 Maths Chapter 10, question 46 — Source question

2

Show solution

-8 -14 Figure it Out

Source worked solution for Class 6 Chapter 10, question 46, part 1 — Source worked answer · part 1

Figure it Out · Figure it Out

NCERT Class 6 Maths Chapter 10, question 47 — Source question

1 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

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a. -6,-5,-4,-3,-2,-1 b. -3,-2,-1,0,1,2,3 c. -14,-13,-12,-11,-10,-9 d. -29,-28,-27,-26,-25,-24

Source worked solution for Class 6 Chapter 10, question 47, part 1 — Source worked answer · part 1

Source solution page 55

NCERT Class 6 Maths Chapter 10, question 48 — Source question

2 Give three numbers such that their sum is –8.

Show solution

One of the combinations is -5,7,-10. Think of other combinations.

Source worked solution for Class 6 Chapter 10, question 48, part 1 — Source worked answer · part 1

Think of other combinations.

NCERT Class 6 Maths Chapter 10, question 49 — Source question

3 There are two dice whose faces have these numbers: –1, 2, –3, 4, –5, 6. The 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.

Show solution

-9,-7,-5,0,2,7,9,11

Source worked solution for Class 6 Chapter 10, question 49, part 1 — Source worked answer · part 1

Think of other combinations.

NCERT Class 6 Maths Chapter 10, question 50 — Source question

4 Solve these:

Show solution

-5 -21 -5 -21 -5 5 5 21 [12]

Source worked solution for Class 6 Chapter 10, question 50, part 1 — Source worked answer · part 1

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Solution sheet 13

Source solution page 56

NCERT Class 6 Maths Chapter 10, question 51 — Source 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? _ Hint: Recall that there was no year 0. c. What will be the year 320 years after 680 BCE? ______

Show solution

c. -360 BCE

Source worked solution for Class 6 Chapter 10, question 51, part 1 — Source worked answer · part 1

Source solution page 56

NCERT Class 6 Maths Chapter 10, question 52 — Source 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), _, , __

Show solution

a. -16, -10, -4 b. -1,8, -2 c. 27, 19, … -8,-9,-9

Source worked solution for Class 6 Chapter 10, question 52, part 1 — Source worked answer · part 1

Source solution page 56

NCERT Class 6 Maths Chapter 10, question 53 — Source question

7 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) which gives a value (+14). Now, pick cards and make an expression such that its value is closer to (– 30).

Show solution

One of the ways is (-2) + (-9) – (+18) – (+1) = -30

Source worked solution for Class 6 Chapter 10, question 53, part 1 — Source worked answer · part 1

Source solution page 56

NCERT Class 6 Maths Chapter 10, question 54 — Source 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)

Show solution

a. positive b. can be positive or negative c. negative d. can be positive or negative e. negative f. can be positive or negative

Source worked solution for Class 6 Chapter 10, question 54, part 1 — Source worked answer · part 1

Source solution page 56

NCERT Class 6 Maths Chapter 10, question 55 — Source question

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

Show solution

20 [13]

Source worked solution for Class 6 Chapter 10, question 55, part 1 — Source worked answer · part 1

Match, attempt, then check

What do you press to go four floors up? What do you press to go three floors down?

Number all the floors in the Building of Fun.

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

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) = _______

Write the inverses of these numbers: +4, –4, –3, 0, +2, –1.

Connect the inverses by drawing lines. (+5) (-7) (–8) (+9) (–9) (+8) (-5) (+7) [2]

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 ____.

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

2. Imagine the Building of Fun with more floors. Compare the numbers and fill in the boxes with < or >: a. a. (–10) (–12) b. + 17 (–10) c. 0 (–20) d. + 9 (–9) e. (–25) (–7) f. + 15 (–17)

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. +6 G

4. Mark the following floors of the building shown on the right. +4 a. -7 b. -4 c. +3 d. -10 +3 R

Evaluate 15 – 5, 100 – 10 and 74 – 34 from this perspective.

Complete these expressions. a. (+ 40) + ______ = + 200 b. (+ 40) + _______ = – 200 c. (– 50) + ______ = + 200 d. (– 50) + _______ = – 200 e. (– 200) – (– 40) = _______ f. (+ 200) – (+ 40) = _______ g. (– 200) – (+ 40) = _______

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?

If, from 5 you wish to go over to 9, how far must you travel along the number line?

Now, from 9, if you wish to go to 3, how much must you travel along the number line?

Now, from 3, if you wish to go to – 2, how far must you travel?

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

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

3. Is 2 > – 3? Why? Is – 2 < 3? Why?

4. What are (i) – 5 + 0 (ii) 7 + (– 7) (iii) – 10 + 20 (iv) 10 – 20 (v) 7 – (– 7) (vi) – 8 – (– 10)?

Use unmarked number lines to evaluate these expressions: a. – 125 + (– 30) = _______ b. + 105 – (– 55) = _______ c. + 80 – (– 150) = _______ d. – 99 – (– 200) = _______

1. Complete the additions using tokens. a. (+ 6) + (+ 4) b. (– 3) + (– 2) c. (+ 5) + (– 7) d. (– 2) + (+ 6)

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? a. b.

1. 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)

2. Complete the subtractions: a. (– 5) – (– 7) b. (+ 10) – (+ 13) c. (– 7) – (– 9) d. (+ 3) – (+ 8) e. (– 2) – (– 7) f. (+ 3) – (+ 15)

1. Try to subtract: – 3 – (+ 5). How many zero pairs will you have to put in? What is the result?

2. Evaluate the following using tokens. a. (– 3) – (+ 10) b. (+ 8) – (– 7) c. (– 5) – (+ 9) d. (– 9) – (+ 10) e. (+ 6) – (– 4) f. (– 2) – (+ 7)

Your new bank balance is _______.

Your bank balance is now ______.

What is your bank balance now? ______ Is this possible?

What is your balance now? ______

1. Suppose you start with 0 rupees 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?]

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?

1. Looking at the geographical cross section fill in the respective heights: A B C D E. F. G.

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

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

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

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).

2 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.

1 Do the calculations for the second grid above and find the border sum.

2 Complete the grids to make the required border sum:

2

1 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

2 Give three numbers such that their sum is –8.

4 Solve these:

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? _______ Hint: Recall that there was no year 0. c. What will be the year 320 years after 680 BCE? ________

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), _____, ______, ______

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

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) = _____

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 __.

Complete these expressions. a. (+ 40) + __ = + 200 b. (+ 40) + _ = – 200 c. (– 50) + = + 200 d. (– 50) + _ = – 200 e. (– 200) – (– 40) = _ f. (+ 200) – (+ 40) = _ g. (– 200) – (+ 40) = _____

Use unmarked number lines to evaluate these expressions: a. – 125 + (– 30) = ___ b. + 105 – (– 55) = _ c. + 80 – (– 150) = _ d. – 99 – (– 200) = ___

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? _ Hint: Recall that there was no year 0. c. What will be the year 320 years after 680 BCE? ______

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), _, , __