In the multiplication problem
A S
__x__A____
M A N
each letter represents a different one of the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Which one of the ten digits does A represent?
i need help with my homework
85 x 8 = 680
To find out which digit A represents in the multiplication problem, we can start by analyzing the equation step by step.
Let's break down the multiplication problem:
A S
x A _
M A N
Since each letter represents a different digit from 0 to 9, we need to determine what digit A could be.
Let's consider the rightmost column in the multiplication problem, which is the units place. We can see that multiplying A with a single-digit number will give us a digit in the units place. The only single-digit number that results in a single-digit product is 1. Therefore, A must be 1.
By substituting A with 1, we have:
1 S
x 1 _
M 1 N
Now, we can deduce the value of the second digit S. To do this, we multiply the single-digit number A (which is now 1) by the second digit. In this case, the second digit is A itself, which is 1.
Therefore, 1 multiplied by 1 equals 1, giving us:
1 1
x 1 _
M 1 N
Now, let's move on to the next step, which is the multiplication of the tens place. We multiply the second digit S by the number A (which is now known as 1). The product will determine the digit in the tens place.
If we multiply 1 by 1, we get 1. So, the tens place digit S is 1.
Now, our equation becomes:
1 1
x 1 1
M 1 N
Finally, we can determine the value of the third digit N. The result of multiplying two digits (1 and 1) is always a single-digit number. Since each letter represents a different digit, N cannot be 1, as both the second and third digits are 1.
Therefore, the only remaining digit for N is 0.
So, in the multiplication problem:
1 1
x 1 1
M 1 0
A represents the digit 1.