Question

1. a certain plant grows 1\frac{1}{6} inches every week. how long will it take the plant to grow 6\frac{1}{6} inches?

Explanation:

Step1: Convert mixed - numbers to improper fractions

$1\frac{1}{6}=\frac{6\times1 + 1}{6}=\frac{7}{6}$ and $6\frac{1}{6}=\frac{6\times6+1}{6}=\frac{37}{6}$.

Step2: Use division formula

The time $t$ (in weeks) is found by dividing the total growth by the growth per week. So $t=\frac{\frac{37}{6}}{\frac{7}{6}}$.

Step3: Simplify the division of fractions

When dividing by a fraction, we multiply by its reciprocal. So $t=\frac{37}{6}\times\frac{6}{7}=\frac{37}{7}=5\frac{2}{7}$ weeks.

Answer:

$5\frac{2}{7}$ weeks