Answer:
Answer as an improper fraction = -15/8
Answer as a mixed number = -1 7/8
I provided both the answer as an improper fraction and a mixed number just in case you preferred or were required to use one over the other
Explanation:
Step 1: Convert -5 3/4 and -3 7/8 from mixed numbers to improper fractions:
- When converting from mixed numbers to improper fractions, we keep the same denominator.
- The numerator is the product of the whole number and the denominator, with the numerator added to it.
Since we have negative numbers, let's leave out the negative sign out and add it back at the end to prevent confusion:
Converting -5 3/4 to an improper fraction:
(5 * 4 + 3) / 4
(20 + 3) / 4
23/4
-23/4
Thus, -5 3/4 as an improper fraction is -23/4.
Converting -3 7/8 to an improper fraction:
(3 * 8 + 7) / 8
(24 + 7) / 8
31/8
-31/8
Thus, -3 7/8 as an improper fraction is -31/8.
Step 2: Find the difference of -23/4 and -31/8:
Note that when subtracting two negative numbers, the number being subtracted becomes positive:
-23/4 - (-31/8)
-23/4 + 31/8
We can rearrange the two fractions to still have a subtraction problem:
31/8 - 23/4
Step 2: Convert -23/4 to a fraction with a denominator of 8:
When two fractions have the same denominator, we're able to add or subtract the numerators and ignore the denominators.
We know that 8 is a multiple of 4, so we can multiply -23/4 by 2/2 to make the fraction have a denominator of 8:
-23/4 * 2/2
-46/8
Now we can subtract the fractions straight across:
31/8 - 46/8
-15/8
Thus, the answer (as an improper fraction) is -15/8.
Optional Step 3: Convert -15/8 from an improper fraction to a mixed number:
Since we started with mixed numbers, we can convert -15/8 to a mixed number for the sake of consistency (if you prefer to use the improper fraction, ignore this optional Step 3:)
- To convert an improper fraction to a mixed number, we must divide the numerator by the denominator.
- The quotient is the whole number part of the mixed number, and the remainder is the numerator of the fractional part.
- In this case, -15 divided by 8 is -1 with a remainder of 7. So, -15/8 can be written as the mixed number -1 7/8.