#### Chapters

## Chapter 1: Number System

### Tamil Nadu Board Samacheer Kalvi solutions for Class 7th Mathematics Term 1 Answers Guide Chapter 1 Number SystemExercise 1.1 [Pages 9 - 10]

#### Fill in the blanks

(−30) + ____ = 60

(−5) + ___ = −100

(−52) + (−52) = ____

____ + (−22) = 0

____ + (−70) = 70

20 + 80 + ____ = 0

75 + (−25) = _____

171 + _____ = 0

[(−3) + (−12)] + (−77) = ______ + [(−12) + (−77)]

(−42) + [ ____ + (−23)] = [ ____ + 15] + ____

#### Say true or false

The additive inverse of (−32) is (−32)

True

False

(−90) + (−30) = 60

True

False

(−125) + 25 = −100

True

False

Add the following

8 and −12 using number line

Add the following

(−3) and (−5) using number line

Add the following

(−100) + (−10)

Add the following

20 + (−72)

Add the following

82 + (−75)

Add the following

−48 + (−15)

Add the following

−225 + (−63)

Thenmalar appeared for competitive exam which has negative scoring of 1 mark for each incorrect answer. In paper I she answered 25 questions incorrectly and in paper II, 13 questions incorrectly. Find the total reduction of marks

In a quiz competition, Team A scored +30, −20, 0 and team B scored −20, 0, +30 in three successive rounds. Which team will win? Can we say that we can add integers in any order?

Are (11 + 7) + 10 and 11 + (7 + 10) equal? Mention the property.

Find 5 pairs of integers that add up to 2

#### Objective type questions

The temperature at 12 noon at a certain place was 18° above zero. If it decreases at the rate of 3° per hour at what time if would be 12° below zero?

12 midnight

12 noon

10 am

10 pm

Identify the problem with negative numbers as its answer:

−9 + (−5) + 6

18 + (–12) – 6

−4 + 2 + 10

10 + (– 4) + 8

(−10) + (+7) = _____

+3

−3

−17

+17

(−8) + 10 + (−2) = _____

2

8

0

20

20 + (−9) + 9 = _____

20

29

11

38

### Tamil Nadu Board Samacheer Kalvi solutions for Class 7th Mathematics Term 1 Answers Guide Chapter 1 Number SystemExercise 1.2 [Pages 14 - 15]

#### Fill in the blanks

−44 + ____ = −88

_____ – 75 = – 45

_____ – (+50) = – 80

#### Say true or false

(– 675) – (– 400) = –1075

True

False

15 – (–18) is the same as 15 + 18

True

False

(– 45) – (– 8) = (– 8) – (– 45)

True

False

Find the value of –3 – (– 4) using number line

Find the value of 7 – (–10) using number line

Find the value of 35 – (– 64)

Find the value of –200 – (+100)

Kabilan was having 10 pencils with him. He gave 2 pencils to Senthil and 3 to Karthik. Next day his father gave him 6 more pencils, from that he gave 8 to his sister. How many pencils are left with him?

A lift is on the ground floor. If it goes 5 floors down and then moves up to 10 floors from there. Then in which floor will the lift be?

When Kala woke up, her body temperature was 102°F. She took medicine for fever. After 2 hours it was 2°F lower. What was her temperature then?

What number should be added to (−17) to get −19?

A student was asked to subtract (−12) from −47. He got −30. Is he correct? Justify.

#### Objective type questions

(–5) – (–18) = _____

23

– 13

13

– 23

(–100) – 0 + 100 = _____

200

0

100

– 200

### Tamil Nadu Board Samacheer Kalvi solutions for Class 7th Mathematics Term 1 Answers Guide Chapter 1 Number SystemExercise 1.3 [Pages 21 - 22]

#### Fill in the blanks

−80 × ____ = −80

(−10) × ____ = 20

100 × ___ = −500

____ × (−9) = −45

_____ × 75 = 0

#### Say true or false

(−15) × 5 = 75

True

False

(−100) × 0 × 20 = 0

True

False

8 × (−4) = 32

True

False

What will be the sign of the product of the following:

16 times of negative integer

What will be the sign of the product of the following:

29 times of negative integer

Find the product of (−35) × 22

Find the product of (−10) × 12 × (−9)

Find the product of (−9) × (−8) × (−7) × (−6)

Find the product of (−25) × 0 × 45 × 90

Find the product of (−2) × (+50) × (−25) × 4

Check the following for equality and if they are equal, mention the property.

(8 – 13) × 7 and 8 – (13 × 7)

Check the following for equality and if they are equal, mention the property.

[(– 6) – (+8)] × (– 4) and (– 6) – [8 × (– 4)]

Check the following for equality and if they are equal, mention the property.

3 × [(−4) + (−10)] and [3 × (−4) + 3 × (−10)]

During summer, the level of the water in a pond decreases by 2 inches every week due to evaporation. What is the change in the level of the water over a period of 6 weeks?

Find all possible pairs of integers that give a product of −50

#### Objective type questions

Which of the following expressions is equal to −30

−20 – (−5 × 2)

(6 × 10) – (6 × 5)

(2 × 5) + (4 × 5)

(−6) × (+5)

Which property is illustrated by the equation: (5 × 2) + (5 × 5) = 5 × (2 + 5)

commutative

closure

distributive

associative

11 × (−1) = ______

−1

0

+1

−11

(−12) × (−9) = _______

108

−108

+1

−1

### Tamil Nadu Board Samacheer Kalvi solutions for Class 7th Mathematics Term 1 Answers Guide Chapter 1 Number SystemExercise 1.4 [Pages 24 - 25]

#### Fill in the blanks

(−40) ÷ ____ = 40

25 ÷ _____ = −5

_____ ÷ (−4) = 9

(−62) ÷ (−62) = _____

#### Say true or false

(−30) ÷ (−6) = −6

True

False

(−64) ÷ (−64) is 0

True

False

Find the values of (−75) ÷ 5

Find the values of (−100) ÷ (−20)

Find the values of 45 ÷ (−9)

Find the values of (−82) ÷ 82

The product of two integers is −135. If one number is −15. Find the other integer

In 8 hours duration, with uniform decrease in temperature, the temperature dropped 24°C. How many degrees did the temperature drop each hour?

An elevator descends into a mine shaft at the rate of 5 m/min. If the descent starts from 15 m above the ground level, how long will it take to reach −250 m?

A person lost 4800 calories in 30 days. If the calory loss is uniform, calculate the loss of calory per day

Given 168 × 32 = 5376 then, find (−5376) ÷ (−32)

How many −4’s are there is (−20)?

(−400) divided into 10 equal parts gives _____

#### Objective type questions

Which of the following does not represent an integer?

0 ÷ (−7)

20 ÷ (−4)

(−9) ÷ 3

12 ÷ 5

(−16) ÷ 4 is the same as

−(−16 ÷ 4)

−(16) ÷ (−4)

16 ÷ (−4)

−4 ÷ −16

(−200) ÷ 10 is

20

−20

−190

210

The set of integers is not closed under

Addition

Subtraction

Multiplication

Division

### Tamil Nadu Board Samacheer Kalvi solutions for Class 7th Mathematics Term 1 Answers Guide Chapter 1 Number SystemExercise 1.5 [Pages 28 - 29]

One night in Kashmir, the temperature is −5°C. Next day the temperature is 9°C. What is the increase in temperature?

An atom can contain protons which have a positive charge (+) and electrons which have a negative charge (−). When an electron and a proton pair up, they become neutral (0) and cancel the charge at. Now determine the net charge:

5 electrons and 3 protons →

An atom can contain protons which have a positive charge (+) and electrons which have a negative charge (−). When an electron and a proton pair up, they become neutral (0) and cancel the charge at. Now determine the net charge:

6 protons and 6 electrons →

An atom can contain protons which have a positive charge (+) and electrons which have a negative charge (−). When an electron and a proton pair up, they become neutral (0) and cancel the charge at. Now determine the net charge:

9 protons and 12 electrons →

4 protons and 8 electrons →

7 protons and 6 electrons →

Scientists use the Kelvin scale (K) as an alternative temperature scale to degrees Celsius (°C) by the relation T°C = (T + 273)K. Convert the following to Kelvin:

−275°C

Scientists use the Kelvin scale (K) as an alternative temperature scale to degrees Celsius (°C) by the relation T°C = (T + 273)K. Convert the following to Kelvin:

45°C

Scientists use the Kelvin scale (K) as an alternative temperature scale to degrees Celsius (°C) by the relation T°C = (T + 273)K. Convert the following to Kelvin:

−400°C

−273°C

Find the amount that is left in the student’s bank account, if he has made the following transaction in a month. His initial balance is ₹ 690

**(i)** Deposit (+) of ₹ 485

**(ii)** Withdrawal (−) of ₹ 500

**(iii)** Withdrawal (−) of ₹ 350

**(iv)** Deposit (+) of ₹ 89

**(v)** If another ₹ 300 was withdrawn, what would the balance be?

A poet Tamizh Nambi lost 35 pages of his ‘lyrics’ when his file had got wet in the rain. Use integers, to determine the following.

If Tamizh Nambi wrote 5 pages per day, how many day’s work did he lose?

A poet Tamizh Nambi lost 35 pages of his ‘lyrics’ when his file had got wet in the rain. Use integers, to determine the following.

If four pages contained 1800 characters, (letters) how many characters were lost?

A poet Tamizh Nambi lost 35 pages of his ‘lyrics’ when his file had got wet in the rain. Use integers, to determine the following:

If Tamizh Nambi is paid ₹ 250 for each page produced, how much money did he lose?

A poet Tamizh Nambi lost 35 pages of his ‘lyrics’ when his file had got wet in the rain. Use integers, to determine the following:

If Kavimaan helps Tamizh Nambi and they are able to produce 7 pages per day, how many days will it take to recreate the work lost?

A poet Tamizh Nambi lost 35 pages of his ‘lyrics’ when his file had got wet in the rain. Use integers, to determine the following:

Tamizh Nambi pays Kavimann ₹ 100 per page for his help. How much money does Kavimaan receive?

Add 2 to me. Then multiply by 5 and subtract 10 and divide new by 4 and I will give you 15! Who am I?

Kamatchi, a fruit vendor sells 30 apples and 50 pomegranates. If she makes a profit of ₹ 8 per apple and loss ₹ 5 per pomegranate. What will be her overall profit or loss?

During a drought, the water level in a dam fell 3 inches per week for 6 consecutive weeks. What was the change in the water level in the dam at the end of this period?

Buddha was born in 563 BC (BCE) and died in 483 BC (BCE). Was he alive in 500 BC (BCE)? and find his life time. (Source: Compton’s Encyclopedia)

### Tamil Nadu Board Samacheer Kalvi solutions for Class 7th Mathematics Term 1 Answers Guide Chapter 1 Number SystemExercise 1.6 [Pages 29 - 31]

#### Miscellaneous Practice problems

What should be added to −1 to get 10?

−70 + 20 = `square` − 10

Subtract 94860 from (−86945)

Find the value of (−25) + 60 + (−95) + (−385)

Find the sum of (−9999) (−2001) and (−5999)

Find the product of (−30) × (−70) × 15

Divide (−72) by 8

Find two pairs of integers whose product is +15

Check the following for equality

(11 + 7) + 10 and 11 + (7 + 10)

Check the following for equality

(8 – 13) × 7 and 8 – (13 × 7)

Check the following for equality

[(−6) – (+8)] × (−4) and (−6) – [8 × (−4)]

Check the following for equality

3 × [(−4) + (−10)] and [3 × (−4) + 3 × (−10)]

Kalaivani had ₹ 5000 in her bank account on 01.01.2018. She deposited ₹ 2000 in January and withdrew ₹ 700 in February. What was Kalaivani’s bank balance on 01.04.2018, if she deposited ₹ 1000 and withdraw ₹ 500 in March?

The price of an item x increases by ₹ 10 every year and an item y decreases by ₹ 15 every year. If in 2018, the price of x is ₹ 50 and y is ₹ 90, then which item will be costlier in the year 2020.

**Match the statements in Column A and Column B**

S.No. |
Column A |
Column B |

1. |
For any two integers 72 and 108, 72 + 108 is also an integer. | (a) Distributive property of multiplication over addition. |

2. |
For any three integers 68, 25 and 99 68 × (25 + 99) = (68 × 25) + (68 × 99) |
(b) Multiplicative identity |

3. |
0 + (−138) = (−138) = (−138) + 0 | (c) Commutative property under |

4. |
For any two integers (−5) and 10 (−5) × 10 = 10 × (−5) |
(d) Closed under addition. |

5. |
1 × (−1098) = (–1098) = (–1098) × 1 | (e) Additive identity. |

#### Challenge Problems

Say true or false.

The sum of a positive integer and a negative integer is always a positive integer

True

False

Say true or false.

The sum of two integers can never be zero

True

False

Say true or false.

The product of two negative integers is a positive integer

True

False

Say true or false.

The quotient of two integers having opposite sign is a negative integer

True

False

Say true or false.

The smallest negative integer is −1

True

False

An integer divided by 7 gives a result −3. What is that integer?

Replace the question mark with suitable integer in the equation

72 + (−5) − **?** = 72

Can you give 10 pairs of single digit integers whose sum is zero?

If P = −15 and Q = 5 find (P – Q) ÷ (P + Q)

If the letters in the English alphabets A to M represent the number from 1 to 13 respectively and N represents 0 and the letters O to Z correspond from −1 to −12, find the sum of integers for the names given below.

For example,

MATH → Sum → 13 + 1 – 6 + 8 = 16

YOUR NAME

If the letters in the English alphabets A to M represent the number from 1 to 13 respectively and N represents 0 and the letters O to Z correspond from −1 to −12, find the sum of integers for the names given below.

For example,

MATH → Sum → 13 + 1 – 6 + 8 = 16

SUCCESS

From a water tank 100 litres of water is used every day. After 10 days there is 2000 litres of water in the tank. How much water was there in the tank before 10 days?

A dog is climbing down into a well to drink water. In each jump, it goes down 4 steps. The water level is in 20^{th} step. How many jumps does the dog take to reach the water level?

Kannan has a fruit shop. He sells 1 dozen bananas at a loss of ₹ 2 each because it may get rotten next day. What is his loss?

A submarine was situated at 650 feet below the sea level. If it descends 200 feet, what is its new position?

In a magic square given below each row, column and diagonal should have the same sum. Find the values of x, y, and z

1 | −10 | x |

y | −3 | −2 |

−6 | 4 | z |

## Chapter 1: Number System

## Tamil Nadu Board Samacheer Kalvi solutions for Class 7th Mathematics Term 1 Answers Guide chapter 1 - Number System

Tamil Nadu Board Samacheer Kalvi solutions for Class 7th Mathematics Term 1 Answers Guide chapter 1 (Number System) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Tamil Nadu Board of Secondary Education Class 7th Mathematics Term 1 Answers Guide solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 7th Mathematics Term 1 Answers Guide chapter 1 Number System are Concept of Integers, Representation of Integers on the Number Line, Concept for Ordering of Integers, Addition of Integers, Addition of Integers on Number line, Subtraction of Integers, Properties of Addition and Subtraction of Integers, Multiplication of a Positive and a Negative Integers, Multiplication of Two Negative Integers, Product of Three Or More Negative Integers, Properties of Multiplication of Integers, Closure Property of Multiplication of Integers, Closure Property of Multiplication of Integers, Associative Property of Multiplication of Integers, Distributive Property of Multiplication of Integers, Multiplicative Identity of Integers, Division of Integers, Properties of Division of Integers, Statement Problems on Integers Using All Fundamental Operations..

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