Question

edgar bought 8 yards of fabric. he used $1\frac{5}{12}$ yards of the fabric to make napkins, $2\frac{5}{12}$ yards to make place mats, and $4\frac{1}{12}$ yards to make a tablecloth. how much fabric does edgar have left over?
\\(\frac{\square}{\square}\\) yards

Explanation:

Step1: Convert 8 to twelfths

To subtract mixed numbers, we first convert 8 to a fraction with denominator 12. So, \( 8=\frac{96}{12} \) (since \( 8\times12 = 96 \)).

Step2: Add the used fabric amounts

Now, add the amounts of fabric used: \( 1\frac{5}{12}+2\frac{5}{12}+4\frac{1}{12} \). First, add the whole numbers: \( 1 + 2+4=7 \). Then add the fractions: \( \frac{5}{12}+\frac{5}{12}+\frac{1}{12}=\frac{5 + 5+1}{12}=\frac{11}{12} \). So the total used fabric is \( 7\frac{11}{12} \), which as an improper fraction is \( \frac{7\times12 + 11}{12}=\frac{84 + 11}{12}=\frac{95}{12} \).

Step3: Subtract used from total

Subtract the used fabric from the total fabric: \( \frac{96}{12}-\frac{95}{12}=\frac{96 - 95}{12}=\frac{1}{12} \).

Answer:

\(\frac{1}{12}\)