7 th 1.3

7th Standard Mathematics — Chapter 1

Exercise 1.3 Solutions

1. Fill in the blanks

1. -80 × 1 = -80
2. (-10) × -2 = 20
3. (100) × -5 = -500
4. 5 × (-9) = -45
5. 0 × 75 = 0

2. Say True or False

1. (-15) × 5 = 75
   Answer: False
   Reason: A negative multiplied by a positive gives a negative result (-75).
2. (-100) × 0 × 20 = 0
   Answer: True
   Reason: Multiplying any number by 0 results in 0.
3. 8 × (-4) = 32
   Answer: False
   Reason: 8 × (-4) = -32, not +32.

3. What will be the sign of the product of the following

1. 16 times of negative integer:
   Answer: Positive (+)
   Reason: 16 is an even number. Multiplying a negative integer an even number of times gives a positive product.
2. 29 times of negative integer:
   Answer: Negative (-)
   Reason: 29 is an odd number. Multiplying a negative integer an odd number of times gives a negative product.

4. Find the product of

1. (-35) × 22
   = -(35 × 22) = -770
2. (-10) × 12 × (-9)
   = [(-10) × (-9)] × 12 = 90 × 12 = 1080
3. (-9) × (-8) × (-7) × (-6)
   = [(-9) × (-8)] × [(-7) × (-6)] = 72 × 42 = 3024
4. (-25) × 0 × 45 × 90
   = 0
   Reason: Since one factor is 0, the entire product is 0.
5. (-2) × (+50) × (-25) × 4
   = [(-2) × (+50)] × [(-25) × 4] = (-100) × (-100) = 10000

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

1. (8 - 13) × 7 and 8 - (13 × 7)
   LHS = (8 - 13) × 7 = -5 × 7 = -35
   RHS = 8 - (13 × 7) = 8 - 91 = -83
   LHS ≠ RHS
   Answer: Not Equal
2. [(-6) - (+8)] × (-4) and (-6) - [8 × (-4)]
   LHS = [-6 - 8] × (-4) = -14 × (-4) = 56
   RHS = (-6) - (-32) = -6 + 32 = 26
   LHS ≠ RHS
   Answer: Not Equal
3. 3 × [(-4) + (-10)] and [3 × (-4)] + [3 × (-10)]
   LHS = 3 × [-14] = -42
   RHS = (-12) + (-30) = -42
   LHS = RHS
   Answer: Equal
   
   Property: Distributive Property of Multiplication over Addition.

6. Word Problem 1

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?

Solution:

• Decrease in water level per week = -2 inches
• Number of weeks = 6
• Total change in water level = 6 × (-2) = -12 inches

Answer: The water level decreases by 12 inches (or -12 inches change).

7. Pairs of Integers

Find all possible pairs of integers that give a product of -50.

Solution:

Pairs of integers that multiply to -50:

1. 1 × (-50) = -50  →  (1, -50)
2. (-1) × 50 = -50  →  (-1, 50)
3. 2 × (-25) = -50  →  (2, -25)
4. (-2) × 25 = -50  →  (-2, 25)
5. 5 × (-10) = -50  →  (5, -10)
6. (-5) × 10 = -50  →  (-5, 10)