- Home
- Education
- Philosophy of Teaching Math
- Math Quotes
- Favorite Math Problem
- Math Jokes
- Math Links
- Hands on Activities
Solutions
Directions: Given the equation below:
ABCDC
- BEAAC
-----------
BADAD
and the information that D=0, find the numerical value for each letter given in the equation. (Note: Each letter will be a single digit number and each letter will represent a different number). Be sure to show your work.
First substitute in 0 wherever you see the letter D. So our problem will look like the following:
ABC0C
- BEAAC
-----------
BA0A0
What is your next guess? (Hint look at the tens column, what do you remember about subtracting?)
Answer: We see that we're going to have to carry a 1 from the hundreds place,
which means that 10-A = A. The only digit that works for this statement is 5, so we can substitute 5 in anywhere we see A
5BC0C
- BE55C
-----------
B5050
What is your next step? (Hint make sure to remember we borrowed a 1 from the hundreds place!)
Answer: Since we'd have to borrow from C, C must be 1 greater than 5, which means its numerical value is 6. So we can substitute 6 in for C:
5B606
- BE556
-----------
B5050
What is your next step? Hint think of the numbers left for B
Answer: we know that 5-B has to equal B. For this to be possible we know that 5 has to be changed to a 4 for this to be true. This means that B=2. We are now left with
52606
- 2E556
-----------
25050
We can now see that our last problem is to solve for E. (Hint: remembered we borrows a 1 from the ten thousands place so our 2 in the thousands is really a 12!)
Answer: we can now calculate that 12-E=5?. E=7
52606
- 27556
----------
25050
So we now have A=5, B=2, C=6, D=0, E=7
Check your work! Does 52606-27556=25050?
52606
- 27556
-----------
Yes it does!!
Directions: Given the equation below:
ABCDC
- BEAAC
-----------
BADAD
and the information that D=0, find the numerical value for each letter given in the equation. (Note: Each letter will be a single digit number and each letter will represent a different number). Be sure to show your work.
First substitute in 0 wherever you see the letter D. So our problem will look like the following:
ABC0C
- BEAAC
-----------
BA0A0
What is your next guess? (Hint look at the tens column, what do you remember about subtracting?)
Answer: We see that we're going to have to carry a 1 from the hundreds place,
which means that 10-A = A. The only digit that works for this statement is 5, so we can substitute 5 in anywhere we see A
5BC0C
- BE55C
-----------
B5050
What is your next step? (Hint make sure to remember we borrowed a 1 from the hundreds place!)
Answer: Since we'd have to borrow from C, C must be 1 greater than 5, which means its numerical value is 6. So we can substitute 6 in for C:
5B606
- BE556
-----------
B5050
What is your next step? Hint think of the numbers left for B
Answer: we know that 5-B has to equal B. For this to be possible we know that 5 has to be changed to a 4 for this to be true. This means that B=2. We are now left with
52606
- 2E556
-----------
25050
We can now see that our last problem is to solve for E. (Hint: remembered we borrows a 1 from the ten thousands place so our 2 in the thousands is really a 12!)
Answer: we can now calculate that 12-E=5?. E=7
52606
- 27556
----------
25050
So we now have A=5, B=2, C=6, D=0, E=7
Check your work! Does 52606-27556=25050?
52606
- 27556
-----------
Yes it does!!