The digits of both the two-digit numbers in the first calculation below have been reversed to give the two-digit numbers in the second calculation. The answers to the two calculations are the same. 62 × 13 = 806 26 × 31 = 806 For which one of the calculations below is the same thing true? Please Answer Quickly
Answers
Given : The digits of both the two-digit numbers in the first calculation below have been reversed to give the two-digit numbers in the second calculation. The answers to the two calculations are the same
To find : Rule For which calculations is the true
Solution:
ab * cd
= (10a + b) * (10c + d)
= 100ac + 10(ad + bc) + bd
ba * cd
= (10b + a)(10d + c)
= 100bd + 10(ad + bc) + ac
Equating both
100ac + 10(ad + bc) + bd = 100bd + 10(ad + bc) + ac
=> 99ac = 99bd
=> ac = bd
It will be true for those number which will Satisfy this
Like here a = 2 b = 6 c = 3 d = 1
ac = bd = 6
25 * 36 here 2 * 3 ≠ 5 * 6
34 * 42 here 3 * 4 ≠ 4 * 2
54 * 56 here 5 * 5 ≠ 4 * 6
42 * 48 here 4 * 4 = 2 * 8 ( will Satisfy)
32 * 43 here 3 * 4 ≠ 2 * 3
42 * 48 = 2016
24 * 84 = 2016
=> 42 * 48 = 24 * 84
HOPE IT HELPS YOU!!!
Step-by-step explanation:
Given : The digits of both the two-digit numbers in the first calculation below have been reversed to give the two-digit numbers in the second calculation. The answers to the two calculations are the same
To find : Rule For which calculations is the true
Solution:
ab * cd
= (10a + b) * (10c + d)
= 100ac + 10(ad + bc) + bd
ba * cd
= (10b + a)(10d + c)
= 100bd + 10(ad + bc) + ac
Equating both
100ac + 10(ad + bc) + bd = 100bd + 10(ad + bc) + ac
=> 99ac = 99bd
=> ac = bd
It will be true for those number which will Satisfy this
Like here a = 2 b = 6 c = 3 d = 1
ac = bd = 6
25 * 36 here 2 * 3 ≠ 5 * 6
34 * 42 here 3 * 4 ≠ 4 * 2
54 * 56 here 5 * 5 ≠ 4 * 6
42 * 48 here 4 * 4 = 2 * 8 ( will Satisfy)
32 * 43 here 3 * 4 ≠ 2 * 3
42 * 48 = 2016
24 * 84 = 2016
=> 42 * 48 = 24 * 84
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