To determine how much more carpet runner Arliss needs to buy, let's solve this step-by-step:
1. Add the length of the two pieces of carpet runner she currently has:
Arliss has two pieces of carpet runner: one is [tex]\(2 \frac{1}{3}\)[/tex] yards long and the other is [tex]\(3 \frac{1}{3}\)[/tex] yards long.
First, convert these mixed numbers into improper fractions:
[tex]\[
2 \frac{1}{3} = \frac{6}{3} + \frac{1}{3} = \frac{7}{3}
\][/tex]
[tex]\[
3 \frac{1}{3} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3}
\][/tex]
Now, add the two improper fractions:
[tex]\[
\frac{7}{3} + \frac{10}{3} = \frac{17}{3}
\][/tex]
Convert the result back into a mixed number:
[tex]\[
\frac{17}{3} = 5 \frac{2}{3} \text{ (since } 17 \div 3 = 5 \text{ remainder } 2)
\][/tex]
Therefore, the total length of the carpet runner she currently has is [tex]\(5 \frac{2}{3}\)[/tex] yards.
2. Determine how much more carpet runner she needs to buy:
She needs 10 yards of carpet runner in total. We need to find the difference between the total needed and what she currently has.
Subtract the mixed number [tex]\(5 \frac{2}{3}\)[/tex] from 10:
[tex]\[
10 - 5 \frac{2}{3}
\][/tex]
First, convert [tex]\(5 \frac{2}{3}\)[/tex] into an improper fraction:
[tex]\[
5 \frac{2}{3} = \frac{15}{3} + \frac{2}{3} = \frac{17}{3}
\][/tex]
Now, rewrite 10 as a fraction with the same denominator:
[tex]\[
10 = \frac{30}{3}
\][/tex]
Perform the subtraction:
[tex]\[
\frac{30}{3} - \frac{17}{3} = \frac{30 - 17}{3} = \frac{13}{3}
\][/tex]
Convert [tex]\(\frac{13}{3}\)[/tex] back into a mixed number:
[tex]\[
\frac{13}{3} = 4 \frac{1}{3} \text{ (since } 13 \div 3 = 4 \text{ remainder } 1)
\][/tex]
Therefore, Arliss needs to buy an additional [tex]\(4 \frac{1}{3}\)[/tex] yards of carpet runner.
In conclusion:
[tex]\[
10 - 5 \frac{2}{3} = 4 \frac{1}{3} \text{ yards}
\][/tex]
So, Arliss needs to buy [tex]\(4 \frac{1}{3}\)[/tex] yards of carpet runner.
