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