Find using distributive property: (a) 728 × 101 (b) 5437 × 1001 (c) 824 × 25 (d) 4275 × 125 (e) 504 × 35

Question – Find using distributive property:
(a) 728 × 101
(b) 5437 × 1001
(c) 824 × 25    
(d) 4275 × 125
(e) 504 × 35

Solution 

(a) 728 × 101

= 728 × (100 + 1) [∴ 101 = 100 + 1]

= (728 × 100) + (728 × 1) [∴By distributive property i.e., (a+ b)× c = a× c + c× b]

= 72,800 +728

= 73,528

(b) 5437 × 1001

= 5437 × (1000 + 1)  [∴ 1001 = 1000 + 1]

= 5437 × 1000 + 5437 × 1  [∴By distributive property i.e., (a+ b)c = ac + cb]

= 54,37,000 + 5437

= 54,42,437

(c) 824 × 25

= 824 × (20 + 5) [∴25 = 20 + 5]

= 824 × 20 +824 × 5  [∴By distributive property i.e., (a+ b)×c = a× c + c ×b]

= 16,480 + 4,120

= 20,600

(d) 4275 × 125

= 4275 × (100 + 20 + 5)

= 4275 × 100 + 4275 × 20 + 4275 × 5 [∴By distributive property i.e., (a+ b+ c)×d = a× d + b ×d + c ×d]

= 427,500 + 85,500 + 21,375

= 5,34,375

(e) 504 × 35

= 504 × (30 + 5)  [∴ 35 = 30 + 5]

= 504 × 30 + 504 × 5 [∴By distributive property i.e., (a+ b)×c = a ×c + c× b]

= 15,120 + 2,520

= 17,640

Hence, 

(a) 728 × 101 = 73,528

(b) 5437 × 1001 = 54,42,437

(c) 824 × 25 = 20,600   

(d) 4275 × 125 = 5,34,375

(e) 504 × 35 = 17,640

Related Questions – 

• Which of the following will not represent zero (a) 1 + 0  (b) 0 × 0  (c)  0/2  (d) (10-10)/2
• If the product of two whole numbers is zero can we say that one or both of them will be zero ? Justify through examples.
• If the product of two whole numbers is 1, can we say that one or both of them will be 1? Justify through examples.
• Study the pattern: 1 × 8 + 1 = 9, 12 × 8 + 2 = 98, 123 × 8 + 3 = 987, 1234 × 8 + 4 = 9876, 12345 × 8 + 5 = 98765. Write the next two steps. Can you say how the pattern works? (Hint: 12345 = 11111 + 1111 + 111 + 11 + 1).