Subtract the sum of [tex]\(13 \frac{1}{2}\)[/tex] and [tex]\(6 \frac{2}{3}\)[/tex] from the sum of [tex]\(15 \frac{1}{2}\)[/tex] and [tex]\(6 \frac{3}{4}\)[/tex].
To solve this problem, we need to follow a series of steps to handle the mixed fractions and perform the necessary arithmetic operations. Let's break it down step by step.
### Step 1: Convert Mixed Numbers to Improper Fractions or Decimals
It's often easier to work with either improper fractions or decimals. For simplicity, we'll convert the mixed numbers to decimals.
1. Convert [tex]\(13 \frac{1}{2}\)[/tex]: - [tex]\(13 \frac{1}{2} = 13 + \frac{1}{2}\)[/tex] - As a decimal, [tex]\(1/2\)[/tex] is 0.5 - [tex]\(13 + 0.5 = 13.5\)[/tex]
2. Convert [tex]\(6 \frac{2}{3}\)[/tex]: - [tex]\(6 \frac{2}{3} = 6 + \frac{2}{3}\)[/tex] - As a decimal, [tex]\(2/3\)[/tex] is approximately 0.6667 (or [tex]\( \frac{2}{3} = 0.\overline{6}\)[/tex]) - [tex]\(6 + 0.6667 = 6.6667\)[/tex]
Finally, we subtract the sum of the first pair from the sum of the second pair: [tex]\[ 22.25 - 20.1667 = 2.0833 \][/tex]
### Step 5: Summary of Results
Let's list out the numerical results clearly: - The sum of [tex]\(13 \frac{1}{2}\)[/tex] and [tex]\(6 \frac{2}{3}\)[/tex] is [tex]\(20.1667\)[/tex]. - The sum of [tex]\(15 \frac{1}{2}\)[/tex] and [tex]\(6 \frac{3}{4}\)[/tex] is [tex]\(22.25\)[/tex]. - Subtracting these sums gives: [tex]\(22.25 - 20.1667 = 2.0833\)[/tex].
Thus, the result of subtracting the sum of [tex]\(13 \frac{1}{2}\)[/tex] and [tex]\(6 \frac{2}{3}\)[/tex] from the sum of [tex]\(15 \frac{1}{2}\)[/tex] and [tex]\(6 \frac{3}{4}\)[/tex] is [tex]\(2.0833\)[/tex].
