Bookshelf

Bill is cutting boards to build a bookshelf for his apartment. While cutting boards, he accidentally cut 3/16th ft. His board is 3 3/4th. How long should it have been?

Correct answer:

x =  3 ¹⁵⁄₁₆ = 63/16 ft

Step-by-step explanation:

$$\begin{gathered} a=3\frac{3}{4}=3+\frac{3}{4}=\frac{3\cdot 4+3}{4}=\frac{12+3}{4}=\frac{15}{4}=3.75\text{ft} \\ b=\frac{3}{16}=0.1875\text{ft} \\ x=a+b=\frac{15}{4}+\frac{3}{16}=\frac{60}{16}+\frac{3}{16}=\frac{60+3}{16}=\frac{63}{16}=\frac{63}{16}\text{ft}=3\frac{15}{16}\text{ft}=3.9375\text{ft} \end{gathered}$$

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