NCERT Exemplar solutions for Mathematics [English] Class 7 chapter 1 - Integers [Latest edition]

When the integers 10, 0, 5, –5, –7 are arranged in descending or ascending order, them find out which of the following integers always remains in the middle of the arrangement.

By observing the number line, state which of the following statements is not true.

By observing the above number line, state which of the following statements is true?

Next three consecutive numbers in the pattern 11, 8, 5, 2 are ______.

The next number in the pattern –62, –37, –12 is ______.

Which of the following statements is not true?

On the following number line value ‘Zero’ is shown by the point

If ⊗, O, ✓ and • represent some integers on number line, then descending order of these numbers is ______.

On the number line, the value of (–3) × 3 lies on right hand side of ______.

The value of 5 ÷ (–1) does not lie between ______.

Water level in a well was 20 m below ground level. During rainy season, rain water collected in different water tanks was drained into the well and the water level rises 5 m above the previous level. The wall of the well is 1 m 20 cm high and a pulley is fixed at a height of 80 cm. Raghu wants to draw water from the well. The minimum length of the rope that he can use is ______.

(– 11) × 7 is not equal to ______.

(–10) × (–5) + (–7) is equal to ______.

Which of the folllowing is not the additive inverse of a ?

Which of the following is the multiplicative identity for an integer a?

[(–8) × (–3)] × (–4) is not equal to ______.

(–25) × [6 + 4] is not same as ______.

–35 × 107 is not same as ______.

(–43) × (–99) + 43 is equal to ______.

(–16) ÷ 4 is not same as ______.

Which of the following does not represent an integer?

Which of the following is different from the others?

Which of the following shows the maximum rise in temperature?

If a and b are two integers, then which of the following may not be an integer?

For a non-zero integer a which of the following is not defined?

Encircle the odd one of the following.

Encircle the odd one of the following.

Encircle the odd one of the following.

Encircle the odd one of the following.

Encircle the odd one of the following.

(–a) + b = b + Additive inverse of ______.

______ ÷ (–10) = 0.

(–157) × (–19) + 157 = ______.

[(–8) + ______] + ______ = ______ + [(–3) + ______] = –3

On the following number line, (–4) × 3 is represented by the point ______.

If x, y and z are integers then (x + ______) + z = ______ + (y + ______).

(–43) + ______ = –43

(–8) + (–8) + (–8) = _____ × (–8)

11 × (–5) = – (_____ × _____) = _____.

(–9) × 20 = _____.

(–23) × (42) = (–42) × _____.

While multiplying a positive integer and a negative integer, we multiply them as ______ numbers and put a ______ sign before the product.

If we multiply ______ number of negative integers, then the resulting integer is positive.

If we multiply six negative integers and six positive integers, then the resulting integer is ______.

If we multiply five positive integers and one negative integer, then the resulting integer is ______.

______ is the multiplicative identity for integers.

We get additive inverse of an integer a when we multiply it by ______.

(–25) × (–2) = ______.

(–5) × (–6) × (–7) = ______.

3 × (–1) × (–15) = ______.

[12 × (–7)] × 5 = ______ × [(–7) × ______]

23 × (–99) = ______ × (–100 + ______) = 23 × ______ + 23 × ______.

______ × ( – 1) = –35

______ × (–1) = 47

88 × ______ = –88

______ × (–93) = 93

(–40) × ______ = 80

______ × (–23) = –920

When we divide a negative integer by a positive integer, we divide them as whole numbers and put a ______ sign before quotient.

When –16 is divided by ______ the quotient is 4.

Division is the inverse operation of ______.

65 ÷ (–13) = ______.

(–100) ÷ (–10) = ______.

(–225) ÷ 5 = ______.

______ ÷ (–1) = –83

______ ÷ (–1) = 75

51 ÷ _____ = – 51

113 ÷ _____ = –1

(–95) ÷ ______ = 95

(–69) ÷ (69) = ______.

(–28) ÷ (–28) = ______.

5 – (–8) is same as 5 + 8.

(–9) + (–11) is greater than (–9) – (–11).

Sum of two negative integers always gives a number smaller than both the integers.

Difference of two negative integers cannot be a positive integer.

We can write a pair of integers whose sum is not an integer.

Integers are closed under subtraction.

(–23) + 47 is same as 47 + (–23).

When we change the order of integers, their sum remains the same.

When we change the order of integers their difference remains the same.

Going 500 m towards east first and then 200 m back is same as going 200 m towards west first and then going 500 m back.

(–5) × (33) = 5 × (–33)

(–19) × (–11) = 19 × 11

(–20) × (5 – 3) = (–20) × (– 2)

4 × (–5) = (–10) × (–2)

(–1) × (–2) × (–3) = 1 × 2 × 3

–3 × 3 = –12 – (–3)

Product of two negative integers is a negative integer.

Product of three negative integers is a negative integer.

Product of a negative integer and a positive integer is a positive integer.

When we multiply two integers their product is always greater than both the integers.

Integers are closed under multiplication.

(–237) × 0 is same as 0 × (–39).

Multiplication is not commutative for integers.

(–1) is not a multiplicative identity of integers.

99 × 101 can be written as (100 – 1) × (100 + 1)

If a, b, c are integers and b ≠ 0 then, a × (b – c) = a × b – a × c

(a + b) × c = a × c + a × b

a × b = b × a

a ÷ b = b ÷ a

a – b = b – a

a ÷ (–b) = –(a ÷ b)

a ÷ (–1) = –a

Multiplication fact (–8) × (–10) = 80 is same as division fact 80 ÷ (–8) = (–10)

Integers are closed under division.

[(–32) ÷ 8] ÷ 2 = –32 ÷ [8 ÷ 2]

The sum of an integer and its additive inverse is zero (0).

The successor of 0 × (–25) is 1 × (–25)

–5 × 4 = –20

–5 × 3 = –15 = –20 – (–5)

–5 × 2 = ______ = –15 – (–5)

–5 × 1 = ______ = ______

–5 × 0 = 0 = ______

–5 × –1 = 5 = ______

–5 × – 2 = ______ = ______

7 × 4 = 28

7 × 3 = ______ = 28 – 7

7 × 2 = ______ = ______ – 7

7 × 1 = 7 = ______ – 7

7 × 0 = ______ = ______ – ______

7 × –1 = –7 = ______ – ______

7 × –2 = ______ = ______ – ______

7 × –3 ______ = ______ – ______

An atom consists of charged particles called electrons and protons. Each proton has a charge of +1 and each electron has a charge of –1. Remember number of electrons is equal to number of protons, while answering these questions:

What is the charge on an atom?

An atom consists of charged particles called electrons and protons. Each proton has a charge of +1 and each electron has a charge of –1. Remember number of electrons is equal to number of protons, while answering these questions:

What will be the charge on an atom if it loses an electron?

An atom consists of charged particles called electrons and protons. Each proton has a charge of +1 and each electron has a charge of –1. Remember number of electrons is equal to number of protons, while answering these questions:

What will be the charge on an atom if it gains an electron?

An atom changes to a charged particle called ion if it loses or gains electrons. The charge on an ion is the charge on electrons plus charge on protons. Now, write the missing information in the table given below:

Remembering that 1AD came immediately after 1BC, while solving these problems take 1BC as –1 and 1AD as +1.

The Greeco-Roman era, when Greece and Rome ruled Egypt started in the year 330 BC and ended in the year 395 AD. How long did this era last?

Remembering that 1AD came immediately after 1BC, while solving these problems take 1BC as –1 and 1AD as +1.

Bhaskaracharya was born in the year 1114 AD and died in the year 1185 AD. What was his age when he died?

Remembering that 1AD came immediately after 1BC, while solving these problems take 1BC as –1 and 1AD as +1.

Turks ruled Egypt in the year 1517 AD and Queen Nefertis ruled Egypt about 2900 years before the Turks ruled. In what year did she rule?

Remembering that 1AD came immediately after 1BC, while solving these problems take 1BC as –1 and 1AD as +1.

Greek mathematician Archimedes lived between 287 BC and 212 BC and Aristotle lived between 380 BC and 322 BC. Who lived during an earlier period?

The table shows the lowest recorded temperatures for each continent. Write the continents in order from the lowest recorded temperature to the highest recorded temperature.

Write a pair of integers whose product is –12 and there lies seven integers between them (excluding the given integers).

From given integers in Column I match an integer of Column II so that their product lies between –19 and –6:

Write a pair of integers whose product is –36 and whose difference is 15.

You have ₹ 500 in your savings account at the beginning of the month. The record below shows all of your transactions during the month. How much money is in your account after these transactions?

Write a positive integer and a negative integer whose sum is a negative integer.

Write a positive integer and a negative integer whose sum is a positive integer.

Write a positive integer and a negative integer whose difference is a negative integer.

Write a positive integer and a negative integer whose difference is a positive integer.

Write two integers which are smaller than –5 but their difference is –5.

Write two integers which are greater than –10 but their sum is smaller than –10.

Write two integers which are greater than – 4 but their difference is smaller than –4.

Write two integers which are smaller than –6 but their difference is greater than –6.

Write two negative integers whose difference is 7.

Write two integers such that one is smaller than –11, and other is greater than –11 but their difference is –11.

Write two integers whose product is smaller than both the integers.

Write two integers whose product is greater than both the integers.

Ramu evaluated the expression –7 – (–3) and came up with the answer –10. What did Ramu do wrong?

Reeta evaluated –4 + d for d = –6 and gave an answer of 2. What might Reeta have done wrong?

The table given below shows the elevations relative to sea level of four locations. Taking sea level as zero, answer the following questions:

1. Which location is closest to sea level?
2. Which location is farthest from sea level?
3. Arrange the locations from the least to the greatest elevation.

You are at an elevation 380 m above sea level as you start a motor ride. During the ride, your elevation changes by the following metres: 540 m, –268 m, 116 m, –152 m, 490 m, –844 m, 94 m. What is your elevation relative to the sea level at the end of the ride

Evaluate the following, using distributive property.

–39 × 99

Evaluate the following, using distributive property.

(–85) × 43 + 43 × (–15)

Evaluate the following, using distributive property.

53 × (–9) –  (–109) × 53

Evaluate the following, using distributive property.

68 × (–17) + (–68) × 3

If * is an operation have, such that for integers a and b. We have a * b = a × b + (a × a + b × b), then find (–3) * (–5)

If * is an operation have, such that for integers a and b. We have a * b = a × b + (a × a + b × b), then find (–6) * 2

If Δ is an operation such that for integers a and b we have a Δ b = a × b – 2 × a × b + b × b (–a) × b + b × b then find 4 Δ (–3) Also show that 4 ∆ (–3) ≠ (–3) ∆ 4.

If Δ is an operation such that for integers a and b we have a Δ b = a × b – 2 × a × b + b × b (–a) × b + b × b then find (–7) Δ (–1). Also show that (–7) Δ (–1) ≠ (–1) Δ (–7).

Below u, v, w and x represent different integers, where u = –4 and x ≠ 1. By using following equations, find each of the values:
u × v = u
x × w = w
u + x = w

1. v
2. w
3. x

Explain your reasoning using the properties of integers.

Height of a place A is 1800 m above sea level. Another place B is 700 m below sea level. What is the difference between the levels of these two places?

The given table shows the freezing points in °F of different gases at sea level. Convert each of these into °C to the nearest integral value using the relation and complete the table,

C = `5/9 (F - 32)`

Sana and Fatima participated in an apple race. The race was conducted in 6 parts. In the first part, Sana won by 10 seconds. In the second part she lost by 1 minute, then won by 20 seconds in the third part and lost by 25 seconds in the fourth part, she lost by 37 seconds in the fifth part and won by 12 seconds in the last part. Who won the race finally?

A green grocer had a profit of ₹ 47 on Monday, a loss of ₹ 12 on Tuesday and loss of ₹ 8 on Wednesday. Find his net profit or loss in 3 days.

In a test, +3 marks are given for every correct answer and –1 mark are given for every incorrect answer. Sona attempted all the questions and scored +20 marks though she got 10 correct answers.

1. How many incorrect answers has she attempted?
2. How many questions were given in the test?

In a true-false test containing 50 questions, a student is to be awarded 2 marks for every correct answer and –2 for every incorrect answer and 0 for not supplying any answer. If Yash secured 94 marks in a test, what are the possibilities of his marking correct or wrong answer?

A multistorey building has 25 floors above the ground level each of height 5 m. It also has 3 floors in the basement each of height 5 m. A lift in building moves at a rate of 1 m/s. If a man starts from 5 0m above the ground, how long will it take him to reach at 2nd floor of basement?

Taking today as zero on the number line, if the day before yesterday is 17 January, what is the date 3 days after tomorrow?

The highest point measured above sea level is the summit of Mt. Everest which is 8,848 m above sea level and the lowest point is challenger Deep at the bottom of Mariana Trench which is 10911 m below sea level. What is the vertical distance between these two points?