Question

a plant has grow one and 1/2 inches in the last year and now it is 8 1/3 inches tall how tall was it a year ago?

Answer 1

To find out how tall the plant was a year ago, subtract the growth from its current height.

The current height of the plant is \( 8 \frac{1}{3} \) inches, and it grew \( 1 \frac{1}{2} \) inches in the last year.

First, convert both mixed numbers to improper fractions:

1. For \( 8 \frac{1}{3} \):
\[
8 \frac{1}{3} = \frac{8 \times 3 + 1}{3} = \frac{24 + 1}{3} = \frac{25}{3}
\]

2. For \( 1 \frac{1}{2} \):
\[
1 \frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2}
\]

Now, subtract the growth from the current height:
\[
\text{Height a year ago} = \frac{25}{3} - \frac{3}{2}
\]

To perform this subtraction, find a common denominator. The least common multiple of 3 and 2 is 6.

Convert both fractions:
\[
\frac{25}{3} = \frac{25 \times 2}{3 \times 2} = \frac{50}{6}
\]
\[
\frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6}
\]

Now, subtract the two fractions:
\[
\frac{50}{6} - \frac{9}{6} = \frac{50 - 9}{6} = \frac{41}{6}
\]

Now, convert \( \frac{41}{6} \) back to a mixed number:
\[
\frac{41}{6} = 6 \frac{5}{6}
\]

So, the height of the plant a year ago was \( 6 \frac{5}{6} \) inches.