SCERT AP 7th Class Maths Solutions Pdf Chapter 1 Integers Unit Exercise Questions and Answers.
AP State Syllabus 7th Class Maths Solutions 1st Lesson Integers Unit Exercise
Question 1.
Calculate the following.
(i) 8 × (-1)
Answer:
8 × (-1)
We know, a × (- b) = – (a × b)
= – (8 × 1) = – 8
(ii) (- 2) × 175
Answer:
(-2) × 175
We know, (- a) × b = – (a × b)
= – (2 × 175) = – 350
(iii) (- 3) × (-40)
Answer:
(- 3) × (-40)
We know, (- a) × (-b) = (a × b)
= (- 3) × (- 40)
= 3 × 40 = 120
(iv) (- 24) × (- 7)
Answer:
(- 24) × (- 7)
We know, (- a) × (- b) = (a × b)
= 24 × 7 = 168
(v) (- 7) ÷ (-1)
Answer:
(- 7) ÷ (-1)
We know, (- a) + (- b) = a ÷ b
= (- 7) ÷ (- 1)
= 7 ÷ 1 = 7
(vi) (- 12) ÷ (+ 6)
Answer:
(- 12) ÷ ( + 6)
We know, (- a) ÷ (- b) = – (a ÷ b)
= (- 12) ÷ 6 = – 2
(vii) (- 49) ÷ (-7 )
Answer:
(- 49) ÷ (-7)
We know, (- a) ÷ (- b) = a ÷ b
= (- 49) ÷ (- 7)
= 49 ÷ 7 = 7
(viii) (+ 63) ÷ (- 9)
Answer:
(+ 63) ÷ (- 9)
We know, a ÷ (- b) = – (a ÷ b)
= 63 ÷ (-9) = – (63 ÷ 9) = – 7
Question 2.
Replace the blank with an integer to make it a true statement.
(i) (- 7) × _______ = 21
Answer:
(- 7) × x = 21
× = 21 ÷ (-7)
We know, a ÷ (-b) = – (a ÷ b)
x = – (21 ÷ 7)
∴ x = – 3
(ii) 7 × _______= – 42
Answer:
7 × x = – 42
x = (- 42) ÷ 7
We know, (- a) ÷ b = – (a ÷ b)
x = – (42 ÷ 7)
∴ x = – 6
(iii) ________ × (-9) = – 72
Answer:
x × (- 9) = – 72
x = (- 72) ÷ (- 9)
We know, (- a) ÷ (-b) = (a ÷ b)
x = (72 ÷ 9)
∴ x = 8
(iv) ________ × (- 11) = 132
Answer:
x × (- 11) = 132
× = 132 ÷ (-11)
We know, a ÷ (- b) = – (a ÷ b)
x = – (132 ÷ 11)
∴ × = – 12
(v) (- 25) ÷ ________ = 1
Answer:
(- 25) ÷ x = 1
(- 25) = 1 × x
x = (- 25) ÷ 1
We know, (- a) ÷ b = – (a ÷ b)
x = – (25 ÷ 1)
∴ x = – 25
(vi) 42 ÷ ________ = – 6
Answer:
42 ÷ x = – 6
42 = (- 6) × x
x = 42 ÷ (- 6)
We know, a ÷ (- b) = – (a ÷ b)
x = – (42 ÷ 6)
∴ x = – 7
(vii) ______ ÷ 4 (- 15) = 6
Answer:
x × 4 (- 15) = 6
x = 6 × (- 15)
We know, a × (-b) = – (a × b)
x = – (6 × 15)
∴ x = – 90
(viii) ________ ÷ (- 9) = 16
Answer:
x ÷ (- 9) = 16
x = 16 × (- 9)
We know, a × (- b) = – (a × b)
x = – (16 × 9)
∴ x = – 144
Question 3.
Write all the possible pairs of integers that give a product of – 50.
Answer:
| a | b | a × b = – 50 |
| 41 | (-50) | 41 × (-50) = – 50 |
| (-D | (+50) | (-1) × (50) = – 50 |
| +2 | (-25) | 42 × (-25) = – 50 |
| (-2) | (+25) | (-2) × (25) = – 50 |
| +5 | (-10) | 45 × (-10) = – 50 |
| (-5) | (+10) | (-5) × (10) = – 50 |
| 450 | (-D | 50 × (-1) = – 50 |
| (-50) | (1) | (-50) × (1) = – 50 |
Question 4.
Sarikar, a fruit vendor sells 100 kg of oranges and 75 kg of pomegranates. If he makes a profit of ₹ 11 per one kg of pomegranates and loss of ₹ 8 per one kg oranges, what will be his overall profit or loss ?
Answer:
Given
Profit on 1 kg of pomegranates = ₹ 11
Profit on 75 kg of pomegranates
= 75 × 11
= ₹ 825
Loss on 1 kg of oranges = ₹ 8
Loss on 100 kg of oranges
= 100 × 8
= ₹ 800
Profit is greater than loss.
So, Sankar will get profit.
Overall profit = ₹ 825 – ₹ 800
= ₹ 25
Question 5.
Bhargavi lost 5700 calories in the month of June using yoga. If the calory loss is uniform, calculate the loss of calories per day ?
Answer:
Given number of calories Bhargavi lost in the month of June = 5700 calories June month has 30 days.
So, number of calories lost in 30 days = 5700
Number of calories lost in 1 day = 5700 ÷ 30
Number of calories lost per day = 190 Calories.
Question 6.
Simplify 625 × (-35) + 625 × 30 using suitable law.
Answer:
625 × (-35) + 625 × 30
Multiplication distributes over addition of integers.
We know, a × b + a × c = a(b + c)
= 625 [(- 35) + 30]
= 625 (- 35 + 30)
= 625 (- 5)
We know, a × (- b) = – (a × b)
= – (625 × 5)
= – 3125
Question 7.
Simplify the following using BODMAS.
(i) 12 – 36 ÷ 3
Answer:
12 – 36 = 3 (Division)
= 12 – 12 (Subtraction)
= 0
(ii) 6 × (-7) + (- 3) ÷ 3
Answer:
6 × (- 7) + (- 3) ÷ 3
We know, (- a) ÷ b = – (a ÷ b)
= 6 × (- 7) – 3 ÷ 3 (Division)
We know, a × (-b) = – (a × b)
= – (6 × 7) – 1 (Multiplication)
= – 42 – 1 (Subtraction)
= – 43
(iii) 38 – {35 – (36 – \(\overline{34-37}\))}
Answer:
38 – {35 – (36 – \(\overline{34-37}\))} (Vinculum)
= 38 – {35 – (36 – (-3)}
= 38 – {35 – (36 + 3)} (Simple bracket)
= 38 – {35 – 39} (Curly bracket)
= 38 – (-4)
= 38 + 4 (Addition)
= 42
Question 8.
Write the absolute values of following numbers.
(i) – 700
Answer:
We know, |- x| = x
|- 700| = 700
(ii) 150
Answer:
We know, | x | = + x
So, |150| = 150
(iii) – 150
Answer:
We know, | – x | = x
So, |- 150| = 150
(iv) – 35
Answer:
We know, | – x | = x
So, |- 35| = 35
(v) If p < 10, then |p – 10|
Answer:
We know, if × < a, then |x – a | = a – x
So, |p – 10| = 10 – p
(vi) If y > 7, then |7 – y|
Answer:
We know, if x > a, then |a – x| = x – a
So, |7 – y | = y – 7