Question

A certain plant grows 1 3/4 inches every week. How long will it take the plant to grow 7 3/4 inches?

Answer 1

Firsr, we must convert the mixed fractions to simple fractions in order to solve this question:

$1\text{ }\frac{3}{4}=\frac{4\cdot1+3}{4}=\frac{7}{4}$

and

$7\frac{3}{4}=\frac{4\cdot7+3}{4}=\frac{31}{4}$

Now, we can solve this question by means of the rule of three:

$\begin{gathered} \frac{7}{4}\text{inches ------- 1 we}ek \\ \frac{31}{4}\text{inches ------- x} \end{gathered}$

hence,

$\begin{gathered} x=\frac{\frac{31}{4}\cdot1}{\frac{7}{4}} \\ x=\frac{\frac{31}{4}}{\frac{7}{4}} \end{gathered}$

by applying the Sandwich law, we have

$\begin{gathered} x=\frac{31\cdot4}{7\cdot4} \\ x=\frac{31}{7} \end{gathered}$

In mixed fraction, 31/7 is

$4\frac{3}{7}$

that is, 4 and 3/7 weeks