Question

Solve the following using suitable properties :
(a) 135 x 201 + 135 x (-1) (b) 125 x 624 x 8 x 10
(c) 455 x 1001 (d) 17 x (-7) + 17 x (-3)

Answer 1

Answer:

(a) 26 × (– 48) + (– 48) × (–36)

(– 48) [ 26 +(–36) ]

(– 48) × [-10]

= 480

(b) 8 × 53 × (–125)

53\times[8\times(-125)]53×[8×(−125)]

53\times\left(-1000\right)53×(−1000)

=\ -53000= −53000

(c) 15 × (–25) × (– 4) × (–10)

15\times\left(-1000\right)\ =-1500015×(−1000) =−15000

(d) (– 41) × 102

-41\times\left[100+2\right]−41×[100+2]

-41\ \times\ 100\ +\left[\left(-41\right)\times2\right]−41 × 100 +[(−41)×2]

-4100+\left(-82\right)\ \ =\ -4182−4100+(−82) = −4182

(e) 625 × (–35) + (– 625) × 65

625\times\left[\left(-35\right)+\left(-65\right)\right]625×[(−35)+(−65)]

625\times\left(-100\right)\ \ =\ -62500625×(−100) = −62500

(f) 7 × (50 – 2)

7\times50-7\times27×50−7×2

350-14\ \ =\ 336350−14 = 336

(g) (–17) × (–29)

(-17)\times\left[(-30)\ +1\right](−17)×[(−30) +1]

\left(-17\right)\times30\ +\ \left(-17\right)\times1\ (−17)×30 + (−17)×1

510\ +\left(-17\right)\ =\ 493510 +(−17) = 493

(h) (–57) × (–19) + 57

\left(-57\right)\times\left(-19\right)+57\times1(−57)×(−19)+57×1

57\times\left(19+1\right)57×(19+1)

57\ \times\ 20\ =114057 × 20 =1140

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Answer 2

Answer:

(a) 26 × (– 48) + (– 48) × (–36)

(– 48) [ 26 +(–36) ]

(– 48) × [-10]

= 480

(b) 8 × 53 × (–125)

53\times[8\times(-125)]53×[8×(−125)]

53\times\left(-1000\right)53×(−1000)

=\ -53000= −53000

(c) 15 × (–25) × (– 4) × (–10)

15\times\left(-1000\right)\ =-1500015×(−1000) =−15000

(d) (– 41) × 102

-41\times\left[100+2\right]−41×[100+2]

-41\ \times\ 100\ +\left[\left(-41\right)\times2\right]−41 × 100 +[(−41)×2]

-4100+\left(-82\right)\ \ =\ -4182−4100+(−82) = −4182

(e) 625 × (–35) + (– 625) × 65

625\times\left[\left(-35\right)+\left(-65\right)\right]625×[(−35)+(−65)]

625\times\left(-100\right)\ \ =\ -62500625×(−100) = −62500

(f) 7 × (50 – 2)

7\times50-7\times27×50−7×2

350-14\ \ =\ 336350−14 = 336

(g) (–17) × (–29)

(-17)\times\left[(-30)\ +1\right](−17)×[(−30) +1]

\left(-17\right)\times30\ +\ \left(-17\right)\times1\ (−17)×30 + (−17)×1

510\ +\left(-17\right)\ =\ 493510 +(−17) = 493

(h) (–57) × (–19) + 57

\left(-57\right)\times\left(-19\right)+57\times1(−57)×(−19)+57×1

57\times\left(19+1\right)57×(19+1)

57\ \times\ 20\ =114057 × 20 =1140