Question

(1)
Find the product, using suitable properties.
26 (48) + (48) * (-36) (ii) 8 x 53 (-125)
(ü15 (-25) * (-4) * (-10)
(iv) (41) × 102
(v) 625 * (-35) + (-625) * 65 (vi) 7 x (50 – 2)
(vii) (-17) * (-29)
(viii) (-57) × (-19) + 57
​

Answer 1

Find the product, using suitable properties.

(I) 26*(48) + (48)*(-36)

by using the reverse distributive property, (as both terms have 48 in common)

⟹ 48[ 26 + (-36)]

⟹ 48( 26 - 36)

⟹ 48( - 10 )

⟹ -480

(ii) 8 x 53 (-125)

Here we can rearrange the order of multiplication, so that the calculation can be made easy.

⟹ 8 × ( -125 ) × 53

⟹ 1000 × 53

⟹ 53000

(iii) 15 (-25) * (-4) * (-10)

Here, we can rearrange the order of multiplication, by multiplying (-25) by (-4) first can make the calculations easy.

⟹ 15 × 10 × (-25) × (-4)

⟹ 150 × 100

⟹ 15000

(iv) (41) × 102

Here, we can rewrite 102 as 100 + 2 and then we can use distributive property.

⟹ 41 × ( 100 + 2)

⟹ 41 × 100 + 41 × 2

⟹ 4100 + 82

⟹ 4182

(v) 625 * (-35) + (-625) * 65

by using reverse of distributive property

⟹ 625( 65 - 35 )

⟹ 625( 30 )

⟹ 18750

(vi) 7 x (50 – 2)

By using distributive property

⟹ 7(50) - 7(2)

⟹ 350 - 14

⟹ 336

(vii) (-17) * (-29)

We can rewrite negative -29 as (1 - 30) after that we can use distributive property

⟹ (-17)( 1 - 30 )

⟹ -17( 1 ) -17(-30)

⟹ -17 + 510

⟹ 493

(viii) (-57) × (-19) + 57

By using rivers of distributive property. Note that -57 × -19 is same as 57 × 19

⟹ 57 × 19 + 57 × 1

⟹ 57 ( 19 + 1 )

⟹ 57 ( 20 )

⟹ 1140