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What would the answer to the following conversion problem be?

[tex]$96 \, \text{ft} \times \frac{1 \, \text{yd}}{3 \, \text{ft}}$[/tex]

A. [tex]$\frac{32 \, \text{ft}}{1 \, \text{yd}}$[/tex]
B. 32 yd
C. 32 ft
D. [tex][tex]$\frac{32 \, \text{yd}}{1 \, \text{ft}}$[/tex][/tex]

Sagot :

GinnyAnswer
To solve the conversion problem, we need to convert 96 feet into yards using the conversion factor [tex]\( \frac{1 \text{ yd }}{3 \text{ ft }} \)[/tex].

Here’s the step-by-step solution:

1. Identify the conversion factor:
- We know that 1 yard (yd) is equal to 3 feet (ft).

2. Set up the conversion:
- We start with 96 feet and multiply it by the conversion factor [tex]\( \frac{1 \text{ yd }}{3 \text{ ft }} \)[/tex].

[tex]\[ 96 \text{ ft} \times \frac{1 \text{ yd}}{3 \text{ ft}} \][/tex]

3. Perform the multiplication:
- Multiply the number of feet by the fraction [tex]\(\frac{1}{3}\)[/tex].

[tex]\[ = \frac{96 \text{ ft} \times 1 \text{ yd}}{3 \text{ ft}} \][/tex]

4. Simplify the expression:
- The units of feet (ft) cancel out, leaving us with:

[tex]\[ = \frac{96}{3} \text{ yd} \][/tex]

5. Divide the remaining values:
- Perform the division:

[tex]\[ = 32 \text{ yd} \][/tex]

So, the answer to the conversion problem is:
B. [tex]\(32 \text{ yd}\)[/tex]
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