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]
3. Convert [tex]\(15 \frac{1}{2}\)[/tex]:
- [tex]\(15 \frac{1}{2} = 15 + \frac{1}{2}\)[/tex]
- [tex]\(1/2\)[/tex] is 0.5
- [tex]\(15 + 0.5 = 15.5\)[/tex]
4. Convert [tex]\(6 \frac{3}{4}\)[/tex]:
- [tex]\(6 \frac{3}{4} = 6 + \frac{3}{4}\)[/tex]
- As a decimal, [tex]\(3/4\)[/tex] is 0.75
- [tex]\(6 + 0.75 = 6.75\)[/tex]
### Step 2: Add the First Pair of Numbers
Now, we'll add [tex]\(13.5\)[/tex] and [tex]\(6.6667\)[/tex]:
[tex]\[ 13.5 + 6.6667 = 20.1667 \][/tex]
### Step 3: Add the Second Pair of Numbers
Next, we'll add [tex]\(15.5\)[/tex] and [tex]\(6.75\)[/tex]:
[tex]\[ 15.5 + 6.75 = 22.25 \][/tex]
### Step 4: Subtract the Two Sums
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].
