Question

mindy has a piece of string that is $5\frac{1}{2}$ yd long. she cuts it into pieces that are each $\frac{1}{2}$ yd long. solve the equation $5\frac{1}{2} = \frac{1}{2}x$ to find out how many pieces of string, $x$, she gets. show your work.

Explanation:

Step1: Start with the given equation

The equation is \( 5\frac{1}{2}=\frac{1}{2}x \). First, convert the mixed number \( 5\frac{1}{2} \) to an improper fraction. \( 5\frac{1}{2}=\frac{5\times2 + 1}{2}=\frac{11}{2} \). So the equation becomes \( \frac{11}{2}=\frac{1}{2}x \).

Step2: Solve for x

To solve for \( x \), multiply both sides of the equation by 2 (the reciprocal of \( \frac{1}{2} \)) to isolate \( x \).
\( \frac{11}{2}\times2=\frac{1}{2}x\times2 \)
Simplifying both sides, we get \( 11 = x \).

Answer:

The number of pieces of string Mindy gets is \( \boldsymbol{11} \).