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Above shows an incomplete long multiplication. Complete this long multiplication. What is the value of the product obtained?
The answer is 12478.
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3 solutions
Let the single digits blank = X and tens digit blank = Y for the two factors at the top.
7*X = a number ending in 8 (8 in single digit). The only X that satisfies this is X=4. Therefore, the bottom factor is 34.
Because this product is 28, you must carry 2 up.
4*Y + 2 = a number ending in 6 (6 in single digit). Let's call this number A6, where A represents the tens digit and not multiplication with 6.
A6 = 4
Y+2
A4 =4
Y
4 divides A4, because Y and A must be single digit integers. Y = (A4)/4
The only single digit A that satisfies this is A = 6.
This gives you 367 * 34 = 12,478
Moderator note:
Y = (A4)/4
The only single digit A that satisfies this is A = 6.
Why can't we have A = 2 , Y = 4 ?
The only choice for bottom unit is 4 in order to get the 8, so the bottom number is 34. Then, 7x4 = 28, so and we have solve which number times 4 plus 2= [ ]6. Could be 1 or 6, but if it was 1, there is no way to get a 4 in the hundreds, so it must be 6.
Then, 367x34 =12478
Thanks for the solution, Cristian! Very clearly explained.
The only number that when multiplied by 7 gives a digit value of 8 is 4, 4X7 = 28. This means that the bottom factor is 34. Then, there are two choices for the top factor, 316 and 346, which both gives a tens digit value of 6 when multiplied by 34. However, 316 doesn't work because we need the hundredth digit value to be 4, and 316X34 only gives 2. So, the other factor must be 346. Multiplying the two factors gives 346X34 = 12478.