To determine how many yards of paper are left after cutting a certain amount from a roll, we need to follow these steps:
1. Convert the mixed numbers to improper fractions.
- Convert [tex]\(18 \frac{2}{5}\)[/tex] to an improper fraction or a decimal.
- Convert [tex]\(4 \frac{1}{3}\)[/tex] to an improper fraction or a decimal.
2. Subtract the lengths to find the remaining amount of paper.
### Step-by-Step Solution:
#### Step 1: Convert Mixed Numbers to Decimals
1. [tex]\(18 \frac{2}{5}\)[/tex]:
- First, convert the fractional part [tex]\( \frac{2}{5} \)[/tex] to a decimal:
[tex]\[
\frac{2}{5} = 0.4
\][/tex]
- Add this decimal to the whole number part:
[tex]\[
18 + 0.4 = 18.4
\][/tex]
2. [tex]\(4 \frac{1}{3}\)[/tex]:
- First, convert the fractional part [tex]\( \frac{1}{3} \)[/tex] to a decimal:
[tex]\[
\frac{1}{3} \approx 0.333333333333333
\][/tex]
- Add this decimal to the whole number part:
[tex]\[
4 + 0.333333333333333 \approx 4.333333333333333
\][/tex]
So, we have:
- The initial length of the paper roll: [tex]\(18.4\)[/tex] yards.
- The length of the paper cut: [tex]\(4.333333333333333\)[/tex] yards.
#### Step 2: Subtract the Lengths
Subtract the length of the paper cut from the initial length of the roll:
[tex]\[
18.4 - 4.333333333333333 \approx 14.066666666666666
\][/tex]
### Result:
After cutting [tex]\(4 \frac{1}{3}\)[/tex] yards from an [tex]\(18 \frac{2}{5}\)[/tex] yard roll, there are approximately [tex]\(14.066666666666666\)[/tex] yards of paper left.
So, the answer is:
[tex]\[
\boxed{14.066666666666666 \text{ yards}}
\][/tex]
