Question

19 how many feet are in $6\frac{1}{2}$ yards? describe how you would find the answer.

Explanation:

Step1: Recall the conversion factor

We know that 1 yard is equal to 3 feet. So the conversion factor from yards to feet is 3 feet per yard.

Step2: Convert the mixed number to an improper fraction

The length in yards is \( 6\frac{1}{2} \) yards. To convert this mixed number to an improper fraction, we use the formula \( a\frac{b}{c}=\frac{a\times c + b}{c} \). So \( 6\frac{1}{2}=\frac{6\times2 + 1}{2}=\frac{13}{2} \) yards.

Step3: Multiply by the conversion factor

To find the number of feet, we multiply the number of yards by the conversion factor (3 feet/yard). So we calculate \( \frac{13}{2}\times3 \).

Step4: Perform the multiplication

\( \frac{13}{2}\times3=\frac{13\times3}{2}=\frac{39}{2} = 19.5 \) feet.

Alternatively, we can also calculate it as \( 6\times3+\frac{1}{2}\times3=18 + 1.5=19.5 \) feet.

Answer:

There are 19.5 feet in \( 6\frac{1}{2} \) yards. The way to find the answer is to use the conversion factor (1 yard = 3 feet) and multiply the number of yards (\( 6\frac{1}{2} \)) by 3.