Use absolute value to determine the distance between the two numbers.
-3.5 and 4 1/4
|-3.5- 1 1/4|
|-3.5- 9/4|
|-3.5/1 - 9/4|
|-14/4 - 9/4|
|-23/4|
23/4
5.75
I got 5.75 as my answer. But why does my answer key show 7.75 units?
I'm not sure what I did wrong. I've double checked it multiple times and I keep getting the same answer.
try adding the absolute values of the two numbers
they are on opposite sides of zero
I've tried that. And I either get |-5.75| or I get 5.75 which are the same thing
Oh never mind. I realized my mistake. It was 4 1/4 in the question but I accidentally changed it to 1 1/4. Thank you so much for the help though
To find the distance between two numbers using absolute value, you need to take the difference between the two numbers and ignore the sign. Let's go step by step and clarify your mistake.
You correctly wrote the expression: |-3.5 - 4 1/4|.
Now, let's simplify the expression:
-3.5 - 4 1/4 = -3.5 - 17/4
Remember that when subtracting fractions, you need to have a common denominator:
-3.5 will be expressed as -14/4 (since 3.5 is equal to -3.5/1, and multiplying numerator and denominator by 4 gives -14/4).
So, the expression becomes:
|-14/4 - 17/4|
Now, subtract the numerators and keep the common denominator:
|-14/4 - 17/4| = |-31/4|
Now, here's where you made the error. The value inside the absolute value is -31/4, which represents a negative value. When finding the distance, we always take the absolute value to ignore the sign. Therefore:
|-31/4| = 31/4 = 7.75
So, the correct answer is indeed 7.75 units, not 5.75.
Remember to take the absolute value of the expression inside the absolute value function.