Knitting a scarf

Rebecca is knitting a scarf. She runs out of yarn when the scarf is 1 1/2 feet long, which is ⅔ of the length she wants to make. How long is the scarf when finished? Write a multiplication and division equation to represent this situation.

Correct answer:

x =  2 ¹⁄₄ = 9/4 ft

Step-by-step explanation:

$$\begin{gathered} a=1\frac{1}{2}=1+\frac{1}{2}=\frac{1\cdot 2+1}{2}=\frac{2+1}{2}=\frac{3}{2}=1.5\text{ft} \\ a=\frac{2}{3}\cdot x \\ 1.5=\frac{2}{3}\cdot x \\ 1.5=2/3\cdot x \\ 2x=4.5 \\ x=\frac{4.5}{2}=2.25 \\ x=\frac{9}{4}=2.25=\frac{9}{4}\text{ft}=2\frac{1}{4}\text{ft}=2.25\text{ft} \end{gathered}$$

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