Question

Q2. Using concepts of Vedic maths show simplification of these mathematical problems. 1) 8655675 x 9999999 2) 352132 x 11 3) 332241334 x 111 4) 65 x 45 5) 533532 x 77​

Answer 1

Answer:

A) 8655675

B) 387352

C) 36878788074

Step-by-step explanation:

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Answer 2

1. 86556741344325
2. 3873452
3. 36878788074
4. 2925
5. 41081964

To Find :- Using concepts of Vedic maths show simplification of these mathematical problems :-

1) 8655675 x 9999999

2) 352132 x 11

3) 332241334 x 111

4) 65 x 45

5) 533532 x 77

Solution :-

1) 8655675 x 9999999

Concept when any number is multiply by 9, 99, 999, 9999 etc :-

• a × 9 = (a - 1)(10 - a)
• ab × 99 = (ab - 1)(100 - ab)
• abc × 999 = (abc - 1)(1000 - abc)
• abcd × 9999 = (abcd - 1)(10000 - abcd)

Example :-

→ 8 × 9 = (8 - 1)(10 - 8) = 72

→ 42 × 99 = (42 - 1)(100 - 42) = 4158

→ 375 × 999 = (375 - 1)(1000 - 375) = 374625

→ 6281 × 9999 = (6281 - 1)(10000 - 6281) = 62803719

using same concept we get,

→ 8655675 x 9999999

→ (abcdefg) × 9999999

→ (abcdefg - 1)(10000000 - abcdefg)

→ (8655675 - 1)(10000000 - 8655675)

→ 86556741344325 (Ans.)

2) 352132 x 11

Concept when any number is multiply by 11 :-

• ab × 11 = a(a + b)b
• abc × 11 = a(a + b)(b + c)c
• abcd × 11 = a(a + b)(b + c)(c + d)d

Example :-

→ 34 × 11 = 3(3 + 4)4 = 374

→ 236 × 11 = 2(2 + 3)(3 + 6)6 = 2596

→ 4875 × 11 = 4(4 + 8)(8 + 7)(7 + 5)5 = 4(12)(15)(12)5 = Starting from left now and taking carry in next we get = 4(12)(15 + 1)25 = 4(12 + 1)625 = (4+1)3625 = 53625

using same concept we get,

→ 352132 x 11

→ 3(3+5)(5+2)(2+1)(1+3)(3+2)2

→ 3873452 (Ans.)

3) 332241334 x 111

Concept when any number is multiply by 11 :-

• abc × 111 = a(a + b)(a + b + c)(b + c)c
• abcd × 111 = a(a + b)(a + b + c)(b + c + d)(c + d)d
• abcde × 111 = a(a + b)(a + b + c)(b + c + d)(c + d + e)(d + e)e

Example :-

→ 365 × 111 = 3(3+6)(3+6+5)(6+5)5 = 39(14)(11)5 = 39(14 + 1)15 = 39(15)15 = 3(9+1)515 = 3(10)515 = (3+1)0515 = 40515

using same concept we get,

→ 332241334 x 111

→ 3(3+3)(3+3+2)(3+2+2)(2+2+4)(2+4+1)(4+1+3)(1+3+3)(3+3+4)(3+4)4

→ 36878787(10)74

→ 3687878(7+1)074

→ 36878788074 (Ans.)

4) 65 × 45

Concept :-

• a5 × b5 = (a × b + 5)25 where (a + b) is equal to 10 .

Example (1) :-

→ 15 × 95

As we can see that 1 + 9 = 10 . So,

→ (1 × 9 + 5)25

→ (9 + 5)25

→ 1425

Example (2) :-

→ 25 × 85

since 2 + 8 = 10,

→ (2 × 8 + 5)25

→ (16 + 5)25

→ 2125

using same concept we get,

→ 65 × 45

since 6 + 4 = 10,

→ (6 × 4 + 5)25

→ (24 + 5)25

→ 2925 (Ans.)

5) 533532 x 77

Concept :-

• abc × 77 = (a × 7){(a + b)×7}{(b + c)×7}(c × 7)

Example :-

→ 123 × 77

→ (1×7){(1 + 2)×7}{(2 + 3)×7}(3 × 7)

→ 7(21)(35)(21)

→ 7(21)(35+2)1

→ 7(21)(37)1

→ 7(21+3)71

→ 7(24)71

→ (7+2)471

→ 9471

using same concept we get,

→ 533532 x 77

→ (5×7){(5+3)×7}{(3+3)×7}{(3+5)×7}{(5+3)×7}{(3+2)×7}(2×7)

→ (35)(56)(42)(56)(56)(35)(14)

starting from left side now and adding carry in next,

→ (35)(56)(42)(56)(56)(35 + 1)4

→ (35)(56)(42)(56)(56)(36)4

→ (35)(56)(42)(56)(56 + 3)64

→ (35)(56)(42)(56)(59)64

→ (35)(56)(42)(56 + 5)964

→ (35)(56)(42)(61)964

→ (35)(56)(42 + 6)1964

→ (35)(56)(48)1964

→ (35)(56 + 4)81964

→ (35)(60)81964

→ (35+6)081964

→ 41081964 (Ans.)

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