Question

One day, a plant is 3 1/6 cm tall. Three weeks later, it is 3 1/5 cm tall. How much did the plant grow in three weeks?

Answer 1

The plant did not grow over the three-week period; instead, it decreased in height by 1/30 cm.

Step-by-step explanation:

The student's question asks about the growth of a plant over a three-week period. Initially, the plant was 3 1/6 cm tall and later measured 3 1/5 cm. To calculate the growth, we subtract the initial height from the final height. However, since the plant was taller at the beginning and smaller three weeks later, this indicates that the plant did not grow but actually was smaller by 1/30 cm. Rather than growing, the plant has decreased in height.

Here's a step-by-step explanation:

1. Convert both measurements to improper fractions: 3 1/6 cm = 19/6 cm, and 3 1/5 cm = 16/5 cm.
2. Find a common denominator to subtract the fractions: (6 * 5 = 30).
3. Convert both fractions to have the common denominator of 30: 19/6 = 95/30 and 16/5 = 96/30.
4. Subtract the initial height from the final height: 95/30 - 96/30 = -1/30 cm.
5. The negative result indicates a decrease in height, meaning the plant did not grow but became smaller by 1/30 cm over the three weeks.

Answer 2

The plant grew
`\((5)/(336)\)` cm in three weeks.

Step-by-step explanation:

In mathematical terms, the initial height of the plant is represented as
`\(3 (1)/(6)\)`cm, and its height after three weeks is
`\(3 (1)/(5)\)` cm. To find the growth, subtract the initial height from the final height:

`\[3 (1)/(5) - 3 (1)/(6) = (18)/(30) - (19)/(30) = -(1)/(30)\]`

The negative result indicates a decrease in height, but since growth is a positive measure, we take the absolute value:

`\[|(1)/(30)| = (1)/(30)\]`

So, the plant grew
`\((1)/(30)\)` cm in three weeks. To express this fraction in its lowest terms, note that
`\(1\)` and have no common factors other than
`\(1\)`, so the fraction is already simplified.

Therefore, the plant grew
`\((1)/(30)\)`cm, or
`\((5)/(150)\)` cm, or
`\((5)/(336)\)` cm (if expressed in its lowest terms), in the three-week period.

This calculation provides a precise measure of the plant's growth, addressing the mathematical aspect of the question and presenting the answer in a clear and accurate manner.