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NCERT Solutions · Maths Ch 10
The Other Side of Zero
51 questions · 5 exercises
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Ex 10.1
Ex 10.2
Ex 10.3
Ex 10.4
Ex 10.5
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
EXERCISE 10.1 · 15 QUESTIONS
Building of Fun
Q1
Building of Fun: number all the floors (Welcome Hall, Toy Store, Video Game, Food Court, Art Centre, Book Store).
(3 marks)
Q2
You start from Floor +2 and press −3 in the lift. Where will you reach? Write an expression for this movement.
(2 marks)
Q3
Evaluate: (a) (+1) + (+4) (b) (+4) + (+1) (c) (+4) + (−3) (d) (−1) + (+2) (e) (−1) + (+1) (f) 0 + (+2) (g) 0 + (−2)
(3 marks)
Q4
Starting from different floors, find the movements required to reach Floor −5. Write the expressions.
(2 marks)
Q5
Evaluate by combining the button presses: (a) (+1) + (+4) (b) (+4) + (+1) (c) (+4) + (−3) + (−2) (d) (−1) + (+2) + (−3)
(3 marks)
Q6
Gurmit was in the Toy Store and wanted to go down two floors, but he pressed '+' two times and then '−' three times. How many floors below or above the Toy Store will he reach?
(1 mark)
Q7
Write the inverses of these numbers: +4, −4, −3, 0, +2, −1. Connect the inverses among +5, −7, −8, +9, −9, +8, −5, +7.
(3 marks)
Q8
Who is on the lowest floor? Jay is in the Art Centre (Floor +2), Asin in the Sports Centre, Binnu in the Cinema Centre, Aman in the Toys Shop.
(2 marks)
Q9
Compare using the Building of Fun and fill in : (a) −2 __ +5 (b) −5 __ +4 (c) −5 __ −3 (d) +6 __ −6 (e) 0 __ −4 (f) 0 __ +4
(2 marks)
Q10
Imagine more floors. Compare and fill in : (a) −10 __ −12 (b) +17 __ −10 (c) 0 __ −20 (d) +9 __ −9 (e) −25 __ −7 (f) +15 __ −17
(2 marks)
Q11
If Floor A = −12, Floor D = −1 and Floor E = +1 in the building shown as a line, find the numbers of Floors B, C, F, G and H.
(2 marks)
Q12
Mark the following floors on the building shown as a line: (a) −7 (b) −4 (c) +3 (d) −10
(2 marks)
Q13
Evaluate 15 − 5, 100 − 10 and 74 − 34 using the meaning of subtraction as 'finding the missing number to be added'.
(2 marks)
Q14
Complete these expressions (Target Floor − Starting Floor = Movement): (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)
(3 marks)
Q15
Examples: (a) Target −1, start −2: which button? (b) Target −1, start +3? (c) Target +2, start −2?
(2 marks)
2
EXERCISE 10.2 · 9 QUESTIONS
The Mine, Infinite Lift and Number Line
Q1
Mine: complete the expressions. (a) (+40) + __ = +200 (b) (+40) + __ = −200 (c) (−50) + __ = +200 (d) (−50) + __ = −200 (e) (−200) − (−40) (f) (+200) − (+40) (g) (−200) − (+40)
(3 marks)
Q2
Evaluate by imagining a suitable lift: (a) −125 + (−30) (b) +105 − (−55) (c) +105 + (+55) (d) +80 − (−150) (e) +80 + (+150) (f) −99 − (−200) (g) −99 + (+200) (h) +1500 − (−1500)
(3 marks)
Q3
In the exercises above, did you notice that subtracting a negative number was the same as adding the corresponding positive number?
(2 marks)
Q4
If, from 5, you wish to go to 9, how far must you travel? From 9 to 3? From 3 to −2? Write the subtraction statements.
(2 marks)
Q5
Mark 3 positive numbers and 3 negative numbers on the number line from −10 to 10. Write the three negative numbers in increasing order.
(2 marks)
Q6
Is 2 > −3? Why? Is −2 (1 mark)
Q7
What are (a) −5 + 0 (b) 7 + (−7) (c) −10 + 20 (d) 10 − 20 (e) 7 − (−7) (f) −8 − (−10)?
(2 marks)
Q8
Use unmarked number lines to evaluate: (a) −125 + (−30) (b) +105 − (−55) (c) +80 − (−150) (d) −99 − (−200)
(2 marks)
Q9
Convert subtraction to addition: write (+7) − (+5), (−3) − (+8), (+8) − (−2), (+6) − (−9) as additions.
(3 marks)
3
EXERCISE 10.3 · 7 QUESTIONS
The Token Model
Q1
Tokens: the lift attendant finds 5 positive and 3 negative tokens in his pocket. On which floor is he? Add +5 and −8 using tokens.
(2 marks)
Q2
Complete the additions using tokens: (a) (+6) + (+4) (b) (−3) + (−2) (c) (+5) + (−7) (d) (−2) + (+6)
(3 marks)
Q3
Cancel the zero pairs in the two sets of tokens (a: 3 positive and 5 negative; b: 6 positive and 3 negative). On what floor is the lift attendant in each case? Write the addition statement.
(2 marks)
Q4
Evaluate the following differences using tokens: (a) (+10) − (+7) (b) (−8) − (−4) (c) (−9) − (−4) (d) (+9) − (+12) (e) (−5) − (−7) (f) (−2) − (−6)
(3 marks)
Q5
Complete the subtractions: (a) (−5) − (−7) (b) (+10) − (+13) (c) (−7) − (−9) (d) (+3) − (+8) (e) (−2) − (−7) (f) (+3) − (+15)
(3 marks)
Q6
Try to subtract −3 − (+5). How many zero pairs will you have to put in? What is the result?
(2 marks)
Q7
Evaluate using tokens: (a) (−3) − (+10) (b) (+8) − (−7) (c) (−5) − (+9) (d) (−9) − (+10) (e) (+6) − (−4) (f) (−2) − (+7)
(3 marks)
4
EXERCISE 10.4 · 10 QUESTIONS
Integers in Other Places and Explorations
Q1
Bank account: you open an account with ₹100, deposit ₹60, then pay a bill of ₹30, then make a purchase of ₹150, then earn ₹200. What is the balance after each step? Is a negative balance possible?
(2 marks)
Q2
Start with ₹0. Credits of ₹30, ₹40, ₹50 and debits of ₹40, ₹50, ₹60. What is the bank balance now?
(2 marks)
Q3
Start with ₹0. Debits of ₹1, 2, 4, 8, 16, 32, 64 and 128, then a single credit of ₹256. What is the balance?
(2 marks)
Q4
Why is it generally better to maintain a positive balance in your bank account? When may it be worthwhile to have a temporary negative balance?
(1 mark)
Q5
Geographical cross-section: fill in the heights (approximate) of points A to G and say which is the highest and the lowest. Write the points in decreasing order of height.
(3 marks)
Q6
What is the highest point above sea level on Earth? What is its height? What is the lowest point with respect to sea level on land or on the ocean floor? What is its height?
(1 mark)
Q7
Leh in Ladakh: match the temperatures 14°C, 8°C, −2°C, −4°C with the times 02:00 a.m., 11:00 p.m., 02:00 p.m., 11:00 a.m.
(3 marks)
Q8
Hollow integer grid: for the second grid (top row 5, −3, −5; left column 5, 0, −8; right column −5, −5, 7; bottom row −8, −2, 7), find the border sum.
(3 marks)
Q9
Complete the grids to make the border sums +4, −2 and −4. Find more than one way for −4.
(5 marks)
Q10
An amazing grid of numbers: choose any number, strike out its row and column, choose any unstruck number, and so on; add the circled numbers. Try with different choices and the grids given. What do you notice?
(2 marks)
5
EXERCISE 10.5 · 10 QUESTIONS
End of Chapter
Q1
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 marks)
Q2
Give three numbers such that their sum is −8.
(2 marks)
Q3
Two dice have faces −1, 2, −3, 4, −5, 6. The smallest possible sum is −10 and the largest is 12. Which numbers between −10 and 12 cannot be obtained?
(3 marks)
Q4
Solve these: 8 − 13, (−8) − (13), (−13) − (−8), (−13) + (−8), 8 + (−13), (−8) − (−13), 13 − 8, 13 − (−8).
(3 marks)
Q5
Find the years: (a) which year was it 150 years ago (from the present year)? (b) 2200 years ago? (Recall there was no year 0.) (c) What will be the year 320 years after 680 BCE?
(2 marks)
Q6
Complete the sequences: (a) −40, −34, −28, −22, __, __, __ (b) 3, 4, 2, 5, 1, 6, 0, 7, __, __, __ (c) __, __, 12, 6, 1, −3, −6, __, __, __
(3 marks)
Q7
Six integer cards: (+1), (+7), (+18), (−5), (−2), (−9). Make an expression using addition(s) and subtraction(s) such that its value is closer to −30.
(2 marks)
Q8
The sum of two positive integers is always positive, but positive − positive 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?
(3 marks)
Q9
A string has a total of 100 tokens arranged in a particular pattern. What is the value of the string?
(1 mark)
Q10
Brahmagupta's rules: explain with examples (a) addition rule: −5 + 3 (b) subtraction rule: 2 − (−3).
(2 marks)