Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 1 Number System Intext Questions

Students can Download Maths Chapter 1 Number System Intext Questions and Answers, Notes Pdf, Samacheer Kalvi 7th Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 1 Number System Intext Questions

(Try These Textbook Page No. 1)

Question 1.
Write the following integers in ascending order: -5,0,2,4, -6,10, -10
Solution:
Plotting the points on the number line, we get
Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 1 Number System Intext Questions 1
The numbers are placed in an increasing order from left to right.
∴ Ascending order: -10 < -6 < -5 < 0 < 2 < 4 < 10

Question 2.
If the integers -15, 12, -17, 5, -1, -5, 6 are marked on the number line then the integer on the extreme left is _____ .
Solution:
The least number will be on the extreme left.
∴ -17 will be on the extreme left.

Question 3.
Complete the following pattern:
50, ___ 30, 20, _, 0, -10, _, _, -40, _, ___.
Solution:
The difference between the consecutive number is 10.
50, 40, 30,20, 10, 0, -10, -20, -30, -40, -50, -60

Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 1 Number System Intext Questions

Question 4.
Compare the given numbers and write “<”, “>” or in the boxes.
Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 1 Number System Intext Questions 2
Solution:
(a) Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 1 Number System Intext Questions 3 A positive number is greater than a negative number.
(b) Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 1 Number System Intext Questions 41000,0 is less than all positive integers.
(c) Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 1 Number System Intext Questions 5

Question 5.
Write the given integers in descending order, -27, 19, 0, 12, -4, -22, 47, 3, -9, -35.
Solution:
Separating positive and the negative integers, we get -27, -4, -22, -9, -35
Arranging the numbers in descending order -4 > -9 > -22 > -27 > -35
The positive numbers are 19,12,47, 3
Arranging in descending order, we get 47 > 19 > 12 > 3
0 stands in the middle.
∴ Descending order: 47 > 19 > 12 > 3 > 0 > -4 > -9 > -22 > -27 > -35

(Try This Text Book Page No. 3)

Question 1.
Find the value of the following using the number line activity.
(i) (-4) + (+3)
(ii) (-4) + (-3)
(iii) (+4) + (-3)
Solution:
(i) (-4) + (+3)
To find the sum of (-4) and (+3), we start at zero facing positive direction continuing in the same direction and move 4 units backward to represent (-4).
Since the operation is addition we maintain the same direction and move three units forward to represent (+3)
We land at -1
So (-4) + (+3) = -1
Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 1 Number System Intext Questions 6

(ii) (-4) + (-3)
From zero move 4 steps backward to represent (-4)
From the same direction again move 3 units backward to represent (-3)
We land at -7 So (-4) + (-3) = -7
Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 1 Number System Intext Questions 7

(iii) (+4) + (-3)
We start at zero facing positive direction and move 4 steps forward to represent (+4) Since the operation is addition we maintain the same direction and move three units backward to represent (-3).
We land at +1.
So (+4) + (-3) = +1
Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 1 Number System Intext Questions 8

(Properties of Addition Textbook Page No. 6)

Question 1.
Complete the given table and check whether the sum of two integers is an integer or not?
(i) 7 + (-5) = (+2)
(ii) (-6)+ (-13) = (-19)
(iii) 25 + 9 = 34
(iv) (-12) + 4 = -8
(v) 41 + 32 = 73
(vi) (-19) + (-15) = (-34)
(vii) 52 + (-15) = (+37)
(viii)(-7) + 0 = (-7)
(ix) 0 + 12 = 12
(x) 14 + 0 = 14
(xi) (-6) +(-6) = (-12)
(xii) (-27) + 0 = -27
Solution:
The sum of two integers is an integer.

(Try These Textbook Page No. 7)

Question 1.
Fill in the blanks:
(i) 20 + (-11) = -(11)+ 20 [∵ Addition is commutative]
(ii) (-5) + (-8) = (-8) + (-5) [∵ Addition is commutative]
(iii) (-3) +12 =12 + (-3) [∵ Addition is commutative]

Question 2.
Say True or False.
(i) (-11) + (-8) = (-8) + (-11)
(ii) -7 + 2 = 2 + (-7)
(iii) (-33) + 8 = 8 + (-33)
Solution:
(i) True, because addition is commutative for intergers
(ii) True, by commutative property on intergers
(iii) True, by commutative property on intergers

Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 1 Number System Intext Questions

Question 3.
Verify the following.
(i) [(-2) + (-9)] + 6 = (-2) + [(-9) + 6]
(ii) [7 + (-8)] + (-5) = 7 + [(-8) + (-5)]
(iii) [(-11) + 5]+ (-14) = (-11) + [5 + (-14)]
(iv) (-5) + [(-32) +(-2)] = [(-5) + (-32) + (-2)]
Solution:
(i) [(-2) + (-9)] + 6 = (-2) + [(-9) + 6]
[(-2) + (-9)] + 6 = (-11) + 6 = -5
Also (-2) + [(-9) + 6] = (-2) + (-3) = -5
Both the cases the sum is -5.
∴ – [(-2) + (-9)] + 6 = (-2) + [(-9) + 6]

(ii) [7 + (-8)] +(-5) = 7 + [(-8) + (-5)]
Here [7 + (-8)] + (-5) = (-1) + (-5) = -6
Also 7 + [(-8) + (-5)] = 7 + (-13) = 7 – 13 = -6
In both the cases the sum is -6.
∴ [7 + (-8)] + (-5) = 7 + [(-8) + (-5)]

(iii) [(-11) + 5] + (-14) = (-11) + [5 + (-14)]
Here [(-11) + 5] + (-14) = (-6) + (-14) = (-20)
(-11) + [5 + (-14)] = (-11) +(-9) = (-20)
In both the cases the sum is -20.
∴ [(-11) + 5] + (-14) = (-11) + [5 + (-14)]

(iv) (-5) + [(-32) + (-2)] = [(-5) + (-32)] + (-2)
(-5) + [(-32) + (-2)] = (-5) + (-34) = -39
Also [(-5) + (-32)] + (-2) = (-37) + (-2) = -39
In both the cases the sum is -39.
∴ (-5)+ [(-32) +(-2)] = [(-5)+ (-32)] +(-2)

Question 4.
Find the missing integers:
(i) 0 + (-95) = -95
(ii) -611 + 0 = -611
(iii) ____ + 0 = _____ Any integer; the same integer
(iv) 0 + (-140) = -140

Question 5.
Complete the following:
(i) -603 + 603 = 0
(ii) 9847+ (-9847) = 0
(iii) 1652 + (-1652) = 0
(iv) -777 + 777 = 0
(v) –5281 +5281 = 0

Exercise 1.2

Subtraction of Integers

(Try These Text book Page No. 11)

Question 1.
Do the following by using number line.
(i) (-4) – (+3)
Solution:
We start at zero facing positive direction move 4 units backward to represent (-4). Then turn towards negative side and move 3 units forward.
Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 1 Number System Intext Questions 9

We reach -7.
∴ (-4) – (+3) = -7.

(ii) (-4) – (-3)
Solution:
We start at zero facing positive direction. Move 4 units backward to represent -4. Then turn towards the negative side and move 3 units backwards.

Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 1 Number System Intext Questions 10
We reach at-1.
∴ (-4) – (-3) = -1.

Question 2.
Find the values and compare the answers.
(i) (-6) – (-2) and (-6) + 2
Solution:
(-6) – (-2) = -6 + (Additive inverse of-2)
= -6 + (+2) = -4
Also (-6)+ 2 = -4
∴ (-6) – (-2) = (-6) + 2

(ii) 35 – (-7) and 35 + 7.
Solution:
35 – (-7) = 35 + (Additive inverse of -7) = 35 + (+7) = 42
Also 35 + 7 = 42 ; 35 – (-7) =35 + 7

(iii) 26 – (+10) and 26 + (-10)
Solution:
26 – (+10) = 26 + (Additive inverse of +10) = 26 + (-10) = 16
Also 26 + (-10) = 16; 26 – (+10) = 26 + (-10)

Question 3.
Put the suitable symbol <, > or = in the boxes.
Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 1 Number System Intext Questions 11

Solution:
(i) -10 – 8 = -18 & -10 + 8 = – 2
(ii) (-20) + 10 = -10 & (-20) – (-10) = -10
(iii) -70 – 50 = (-70) + (-50) = -20
(iv) 100 – (+100) = 0 & 100 – (-100) = 100 + (+100) = 200
(v) -50 – 30 = -50 + (-30) = -80 Also -100 + 20 = – 80

(Try These Text book Page No. 14)

Question 1.
Fill in the blanks.
(i) (-7) – (-15) = +8
-7 – (-15) = -7 + (Additive inverse of-15)
= -7 + 15 = +8
(ii) 12 – (-7) = 19          12 – (-7) = 19
(iii) -4 – (-5) = 1

Question 2.
Find the values and compare the answers.
(i) 15 – 12 and 12 – 15
(ii) -21 – 32 and -32 – (-21)
Solution:
(i) 15 – 12 = 3 & 12-15 = 12 +(-15) = -3
Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 1 Number System Intext Questions 12

(ii) -21 – 32 = (-21) + (-32) = -53
Also -32 – (-21) = (-32) + (+21) = -11 ; -53 < -11

Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 1 Number System Intext Questions 13

Question 3.
Is associative property true for subtraction of integers. Take any three examples and check.
Solution:
Consider the numbers 1,2 and 3. Now (1 – 2) – 3 = -1 – 3 = -4
Also 1 – (2 – 3) = 1 – (-1) = 1 + 1 = 2
∴ (1 – 2) – ≠ 1 – (2 – 3)
∴ Associative property is not true for subtraction of integers.

Exercise 1.3

Multiplication of Integers

(Try These Textbook Page No. 16)

Question 1.
Find the product of the following
(i) (-20) × (-45) = +900 [As we know the product of two negative integers is positive, the answer is +900.]
(ii) (-9) × (-8) = 72 [ ∵ Product of two negative integers is positive]
(iii) (-30) × 40 × (-1) = (+1200) [Product of two integers with opposite sings is negative integer.
(-30) × 40 × (-1) = (-1200) × (-1) = +1200)]
(iv) (-50) × 2 × (-10) = -1000 [Product of two integers with opposite signs is negative.
(+50) × 2 × (-10) = 100 × (-10) = -1000)]

Question 2.
Complete the following table by multiplying the integers in the corresponding row and column headers.
Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 1 Number System Intext Questions 14
Solution:
We know that
(i) product of two positive integers is positive
(ii) product of two negative integers is
(ii) product of two negative integers is positive
(iii) product of integers with opposite sign is negative.
∴ The table will be as follows:
Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 1 Number System Intext Questions 15

Question 3.
Which of the following is incorrect?
(i) (-55) × (-22) × (-33) < 0
(ii) (-1521) × 2511 < 0
(iii) 2512 – 1525 < 0
(iv) (1981) × (+2000) < 0
Solution:
(iii) and (iv) are incorrect because 2512 – 1252 is a positive integer.
Also (+1981) × (+2000) is a positive integer.

(Try These Textbook Page No. 18)

Question 1.
Find the product and check for equality
(i) 18 × (-5) and (-5) × 18
Solution:
Here 18 × (-5) = -90 Also (-5) × 18 = -90
∴ 18 × (-5)= (-5) × 18

(ii) 31 × (-6) and (-6) × 31
Solution:
Here 31 × (-6) = -186 Also (-6) × 31 =-186
∴ 31 × (-6)= (-6) × 31

(iii) 4 × 51 and 51 × 4
Solution:
Here 4 × 51 = 204 Also 51 × 4 = 204
∴ 4 × 51 = 51 × 4

Samacheer Kalvi 7th Maths Solutions Term 1 Chapter 1 Number System Intext Questions

Question 2.
Prove the following.
(i) (-20) × (13 × 4) = [(-20) × 13] × 4
Solution:
LHS = (-20) × (13 × 4) = (-20) × 52 = -1040
RHS = [(-20) × 13] × 4 = (-260) × 4 = -1040
LHS = RHS
∴ (-20) × (13 × 4) = [(-20) × 13] × 4

(ii) [(-50) × (-2)] × (-3) = (-50) × [(-2) × (-3)]
Solution:
LHS = [(-50) × (-2)] × (-3) = 100 × (-3) = -300
RHS = (-50) × [(-2) × (-3)] = (-50) × 6 =-300
LHS = RHS
∴ [(-50) × (-2)] × (-3) = (-50) × [-2) × (-3)]

(iii) [(-4) × (-3)] × (-5) = (-4) × [(-3) × (-5)]
Solution:
LHS = [(-4) × (-3)] × (-5) = 12 × (-5) = -60
RHS = (-4) × [(-3) × (-5)] = (-4) × 15 = -60
LHS = RHS
∴ [(-4) × (-3)] × (-5) = (-4) × [(-3) × (-5)]

(Try These Textbook Page No. 19)

Question 1.
Find the values of the following and check for equality:
(i) (-6) × (4 + (-5)) and ((-6) × 4) + ((-6) × (-5))
Solution:
(-6) × (4 + (-5)) = (-6) × (-1) = 6 .
((-6) × 4) + ((-6) × (-5)) = (-24)+ 30 = 6
Hence (-6) × (4 + (-5)) = ((-6) × 4) + ((-6) × (-5))

(ii) (-3) × [2 + (-8)] and [(-3) × 2] + [(-3) × 8]
Solution:
(-3) × [2 + (-8)] = (-3) × (-6) = 18
Also [(-3) × 2] + [(-3) × 8] = (-6)+ (-24) = -30
(-3) × [2 + (-8)] ≠ [(-3) × 2] + [(-3) × 8]

Question 2.
Prove the following.
(i) [(-5) × (-76)] + [(-5) × 8]
Solution:
LHS = (-5) × [(-76) + 8] = (-5) × (-68)
= +340
RHS = [(-5) × (-76)] + [(-5) × 8]
= +380 + (-40) = +380 – 40
= +340
LHS = RHS
∴ (-5) × [(-76) + 8] = [(-5) × (-76)] + [(-5) × 8]

(ii) (42 × 7) + [42 × (-3)]
Solution:
LHS = 42 × [7 + (-3)]
= 168
RHS = (42 × 7) + [42 × (-3)] = 294 – 126
= 168
LHS = RHS
∴ 42 × [7 + (-3)] = (42 × 7) + [42 × (-3)]

(iii) [(-3) × (-4)] + [(-3) × (-5)]
Solution:
LHS = (-3) × [(-4) + (-5)] = (-3) × (-9)
= +27
RHS = [(-3) × (-4)] + [(-3) × (-5)] = 12 + 15 = 27
LHS = RHS
∴ (-3) × [(-4) + (-5)] = [(-3) × (-4)] + [(-3) × (-5)]

(iv) 103 × 25 = (100 + 3) × 25 = (100 × 25) + (3 × 25)
Solution:
First consider 103 × 25 = 2575
Now (100 + 3) × 25 = 103 × 25 = 2575
Also (100 × 25) + (3 × 25) = 2500 + 75
= 2575
∴ All the three are same. 103 × 25 = (100 + 3) × 25 = (100 × 25) +(3 × 25)

Exercise 1.4

Division of Integers

(Try These Text book Page No. 22)

Question 1.
(i) (-32) ÷ 4 = _____
(ii) (-50) ÷ 50 = ____
(iii) 30 ÷ 15 = ______
(iv) -200 ÷ 10 = _____
(v) -48 ÷ 6 = ______
Solution:
(i) -8
(ii) -1
(iii) 2
(iv) -20
(v) -8

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