use the order of operations and the digit 4 four times to write problems that have the following answers 44 and 12
44 = 44 * 4/4
12 = 4*(4 - 4/4)
To create problems using the digit 4 four times with the desired answers of 44 and 12, we can utilize the order of operations. The order of operations is a set of rules that define the sequence in which mathematical operations should be performed. These rules ensure that the answer is consistent and unbiased. The order of operations is as follows:
1. Parentheses: Perform operations inside parentheses first.
2. Exponents: Evaluate any expressions with exponents.
3. Multiplication and Division: Perform multiplication and division from left to right.
4. Addition and Subtraction: Perform addition and subtraction from left to right.
Let's go ahead and create the problems:
Problem 1 (with the answer of 44):
To achieve the answer of 44, we can use the following expression:
4 * (4 + 4) = 4 * 8 = 32
Now, to obtain the answer of 44, we can add another operation to the equation:
4 * (4 + 4) + 4 = 32 + 4 = 36
Lastly, we need to add another operation to the equation:
4 * (4 + 4) + 4 + 4 = 36 + 4 = 40
And finally, to obtain the answer of 44:
4 * (4 + 4) + 4 + 4 + 4 = 40 + 4 = 44
Problem 2 (with the answer of 12):
To achieve the answer of 12, we can use the following expression:
4 * (4 - 4) = 4 * (0) = 0
Now, let's add some more operations to the equation:
4 * (4 - 4) + 4 = 0 + 4 = 4
To reach the answer of 12, we need to add more operations:
4 * (4 - 4) + 4 + 4 = 4 + 4 = 8
And finally, to obtain the answer of 12:
4 * (4 - 4) + 4 + 4 + 4 = 8 + 4 = 12
Using these order of operations and four 4's, we have created two problems with the desired answers of 44 and 12.