Mariana

Mariana wants to put 6 3/4 feet of border across the top of a wall. She has 3 6/7 feet of border. What fraction of the project can she complete?

Final Answer:

r =  4/7

Step-by-step explanation:

$$\begin{gathered} a=6\frac{3}{4}=6+\frac{3}{4}=\frac{6\cdot 4+3}{4}=\frac{24+3}{4}=\frac{27}{4}=6\frac{3}{4}=6.75\text{ft} \\ b=3\frac{6}{7}=3+\frac{6}{7}=\frac{3\cdot 7+6}{7}=\frac{21+6}{7}=\frac{27}{7}=3\frac{6}{7}\doteq 3.8571\text{ft} \\ r=b/a=\frac{27}{7}/\frac{27}{4}=\frac{27}{7}:\frac{27}{4}=\frac{27}{7}\cdot \frac{4}{27}=\frac{27\cdot 4}{7\cdot 27}=\frac{108}{189}=\frac{4}{7}=0.5714 \end{gathered}$$

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