Questions: Select all the expressions that represent the difference of the length to the width of rectangle A. (w+5)/w-(w+1)/(2w) 4/(3w) (w+5)/(w+1)-w/(2w) (w+9)/(2w) (w+11)/(2w)

Transcript text: Select all the expressions that represent the difference of the length-to is the width of rectangle $A$. $\frac{w+5}{w}-\frac{w+1}{2 w}$ $\frac{4}{3 w}$ $\frac{w+5}{w+1}-\frac{w}{2 w}$ $\frac{w+9}{2 w}$ $\frac{w+11}{2 w}$

Solution

Solution Steps

Step 1: Find the length-to-width ratio of rectangle A

The length of rectangle A is $w + 5$, and the width is $w$. The length-to-width ratio of rectangle A is $\frac{w+5}{w}$.

Step 2: Find the length-to-width ratio of rectangle B

The length of rectangle B is $w + 1$, and the width is $2w$. The length-to-width ratio of rectangle B is $\frac{w+1}{2w}$.

Step 3: Find the difference between the length-to-width ratios

The difference between the length-to-width ratios is $\frac{w+5}{w} - \frac{w+1}{2w}$.

Step 4: Simplify the difference

To subtract the two fractions, find a common denominator. In this case, the common denominator is $2w$. Multiply the numerator and denominator of the first fraction by 2: $\frac{2(w+5)}{2w} - \frac{w+1}{2w} = \frac{2w+10}{2w} - \frac{w+1}{2w}$. Now subtract the numerators: $\frac{(2w+10)-(w+1)}{2w} = \frac{2w+10-w-1}{2w} = \frac{w+9}{2w}$.