7 th 1.4

7th Standard Mathematics — Chapter 1

Exercise 1.4 Solutions

1. Fill in the blanks

1. (-40) ÷ -1 = 40
   
   Working: (-40) ÷ 40 = -1
2. 25 ÷ -5 = -5
   
   Working: 25 ÷ (-5) = -5
3. -36 ÷ (-4) = 9
   
   Working: 9 × (-4) = -36
4. (-62) ÷ (-62) = 1
   
   Working: Any non-zero integer divided by itself gives 1.

2. Say True or False

1. (-30) ÷ (-6) = -6
   Answer: False
   Reason: (-30) ÷ (-6) = +5, not -6.
2. (-64) ÷ (-64) is 0
   Answer: False
   Reason: (-64) ÷ (-64) = 1, not 0.

3. Find the values of the following

1. (-75) ÷ 5
   = -(75 ÷ 5) = -15
2. (-100) ÷ (-20)
   = +(100 ÷ 20) = 5
3. 45 ÷ (-9)
   = -(45 ÷ 9) = -5
4. (-82) ÷ 82
   = -(82 ÷ 82) = -1

4. Integer Product Problem

The product of two integers is -135. If one number is -15, find the other integer.

Solution:

• Product of two integers = -135
• One integer = -15
• Other integer = (-135) ÷ (-15)

Calculation: (-135) ÷ (-15) = +9

Answer: The other integer is 9.

5. Temperature Change Problem

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

Solution:

• Total duration = 8 hours
• Total drop in temperature = 24°
• Drop in temperature per hour = 24° ÷ 8

Calculation: 24 ÷ 8 = 3°

Answer: The temperature dropped 3° each hour (or -3° per hour).

6. Elevator / Shaft Problem

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

Solution:

• Starting point = +15 m (above ground level)
• Ending point = -250 m (below ground level)
• Total distance to descend = 15 - (-250) = 15 + 250 = 265 m
• Speed of descent = 5 m/sec

Calculation: Time taken = Total Distance ÷ Speed = 265 ÷ 5 = 53 seconds

Answer: It will take 53 seconds.

7. Calorie Loss Problem

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

Solution:

• Total calorie loss in 30 days = 4800 calories
• Loss of calorie per day = 4800 ÷ 30

Calculation: 4800 ÷ 30 = 160 calories

Answer: The loss of calorie per day is 160 calories.

8. Division Property Problem

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

Solution:

Since 168 × 32 = 5376, we know 5376 ÷ 32 = 168.

Dividing two negative integers yields a positive result:

(-5376) ÷ (-32) = +(5376 ÷ 32) = 168

Answer: 168

9. Grouping Problem

How many (-4)'s are there in (-20)?

Solution:

To find how many (-4)'s make up (-20), divide (-20) by (-4):

(-20) ÷ (-4) = 5

Answer: There are 5 (-4)'s in (-20).

10. Equal Division

(-400) divided into 10 equal parts gives ______.

Solution:

(-400) ÷ 10 = -40

Answer: -40