Question

1. blake needs a wood board with an area of \\(\frac{7}{15}\\) square yard to complete a project. if the wood board is \\(\frac{1}{2}\\) yard wide, how long must the board be? think: \\(a = l \times w\\), so if you know the area and the width, how can you find the length. how do you undo multiplication? no calculator. must show all work to receive credit.

Explanation:

Step1: Recall area formula

$A = l \times w$

Step2: Rearrange for length

$l = \frac{A}{w}$

Step3: Substitute given values

$l = \frac{\frac{7}{15}}{\frac{1}{2}}$

Step4: Divide by multiplying reciprocal

$l = \frac{7}{15} \times \frac{2}{1}$

Step5: Calculate product

$l = \frac{7 \times 2}{15 \times 1} = \frac{14}{15}$

Answer:

The board must be $\frac{14}{15}$ yard long. To undo multiplication (since $A = l \times w$), you divide the area by the width, which is equivalent to multiplying the area by the reciprocal of the width.