NCERT Class 7 Solutions: Integers (Chapter 1) Exercise 1.3–Part 1 Q-1 Find the each of the following products:

3 × ( − 1 )

( − 1 ) × 225

( − 21 ) × ( − 30 )

( − 316 ) × ( − 1 )

( − 15 ) × 0 × ( − 18 )

( − 12 ) × ( − 11 ) × ( 10 )

9 × ( − 3 ) × ( − 6 )

( − 18 ) × ( − 5 ) × ( − 4 )

( − 1 ) × ( − 2 ) × ( − 3 ) × 4

( − 3 ) × ( − 6 ) × 2 × ( − 1 )

Solution: When multiplying the numbers some of which are negative, do the multiplication without accounting for sign. Then put the sign on the result according to following rules:

Rules for Multiplying Positive and Negative Integers

Rules for multiplying signed (positive and negative) integers

3 × ( − 1 )

= − 3 ( − ) × ( + ) = ( − )

( − 1 ) × 225

= − 225 ( − ) × ( + ) = ( − )

( − 21 ) × ( − 30 )

= 630 ( − ) × ( − ) = ( + )

( − 316 ) × ( − 1 )

= 316 ( − ) × ( − ) = ( + )

( − 15 ) × 0 × ( − 18 )

= 0

Zero property of multiplication: Also called the zero product property. There exists a unique number, zero, such that the product of any real number x and 0 is always equal to 0

( − 12 ) × ( − 11 ) × ( 10 )

= 132 × 10

= 1320

9 × ( − 3 ) × ( − 6 )

= 9 × 18 = 160 ( − ) × ( + ) = ( − )

( − 18 ) × ( − 5 ) × ( − 4 )

= 90 × ( − 4 )

= − 360 ( − ) × ( + ) = ( − )

( − 1 ) × ( − 2 ) × ( − 3 ) × 4

= ( + 2 ) × ( − 12 )

= − 24 ( − ) × ( + ) = ( − )

( − 3 ) × ( − 6 ) × 2 × ( − 1 )

= ( + 18 ) × ( − 2 )

= − 36 ( − ) × ( + ) = ( − )

Q-2 Verify the following:

18 × [ 7 + ( − 3 ) ] = [ 18 × 7 ] + [ 18 × ( − 3 ) ]

( − 21 ) × [ ( − 4 ) + ( − 6 ) ] = [ ( − 21 ) × ( − 4 ) ] + [ ( − 21 ) × ( − 6 ) ]

Solution:

Given the Descributive Propert and Apply All Examples

Given the Descributive propert and apply all examples and verify

18 × [ 7 + ( − 3 ) ] = [ 18 × 7 ] + [ 18 × ( − 3 ) ]

L . H . S = 18 × [ 7 + ( − 3 ) ]

= 18 × [ 7 − 3 ]

= 18 × 4

= 72

R . H . S = [ 18 × 7 ] + [ 18 × ( − 3 ) ]

= 126 + ( − 54 )

= 72

Hence L . H . S = R . H . S

18 × [ 7 + ( − 3 ) ] = [ 18 × 7 ] + [ 18 × ( − 3 ) ]

( − 21 ) × [ ( − 4 ) + ( − 6 ) ] = [ ( − 21 ) × ( − 4 ) ] + [ ( − 21 ) × ( − 6 ) ]

L . H . S = ( − 21 ) × [ ( − 4 ) + ( − 6 ) ]

= ( − 21 ) × [ − 4 − 6 ]

= ( − 21 ) × ( − 10 )

= 210

R . H . S = [ ( − 21 ) × ( − 4 ) ] + [ ( − 21 ) × ( − 6 ) ]

= 84 + 126

= 210

Hence L . H . S = R . H . S

( − 21 ) × [ ( − 4 ) + ( − 6 ) ] = [ ( − 21 ) × ( − 4 ) ] + [ ( − 21 ) × ( − 6 ) ]