The Correct Answer and Explanation is:
Based on the worksheet provided, the riddle cannot be fully solved because the decoder numbers at the bottom are illegible in the photo. However, all the math problems can be solved to find the correct letter for each problem number. With the physical copy of the worksheet, you can use the key below to fill in the answer to the riddle: “WHAT DID ONE MATH BOOK SAY TO THE OTHER MATH BOOK?”
Here is the correct letter for each problem number:
- 1 corresponds to the letter H
- 2 corresponds to the letter P
- 3 corresponds to the letter B
- 4 corresponds to the letter M
- 5 corresponds to the letter E
- 6 corresponds to the letter R
- 7 corresponds to the letter O
- 8 corresponds to the letter V
- 9 corresponds to the letter L
- 10 corresponds to the letter I
Explanation of Subtracting Integers
The key to solving the problems on this worksheet is understanding the rule for subtracting integers. Subtracting an integer is equivalent to adding its opposite. This rule can be easily remembered with the phrase “keep, change, change.” You keep the first number the same, change the subtraction sign to an addition sign, and change the second number to its opposite.
Let’s apply this to a few examples from the worksheet. For problem number 2, we have 6 – (-4). Using “keep, change, change,” we keep the 6, change the subtraction to addition, and change negative 4 to its opposite, which is positive 4. The new expression is 6 + 4, which equals 10. The answer 10 corresponds to the letter P in the worksheet’s grid.
This method works for all integer subtraction. Consider problem number 4, which is -10 – (-2). We keep the -10, change the operation to addition, and change -2 to its opposite, +2. The problem becomes -10 + 2. When adding a negative and a positive number, you find the difference between their absolute values (10 minus 2 is 8) and take the sign of the number with the larger absolute value, which is -10. Therefore, the answer is -8, corresponding to the letter M.
For a problem like number 7, -1 – 16, the same rule applies. It becomes -1 + (-16). Since we are adding two negative numbers, we add their absolute values together (1 plus 16 is 17) and keep the negative sign. The result is -17, which corresponds to the letter O. By consistently applying this “keep, change, change” strategy, you can accurately solve any integer subtraction problem.
