Which statement below describes the greatest absolute value change?

Steps to Solve

1. Calculate the change in height of the plant

To determine the absolute value change in height:
Final height = $30 \frac{3}{8}$ inches
Initial height = $8 \frac{1}{8}$ inches

First, convert to improper fractions:
$$ 30 \frac{3}{8} = \frac{243}{8} $$
$$ 8 \frac{1}{8} = \frac{65}{8} $$

Now, calculate the change:
$$ \text{Change} = \left| \frac{243}{8} - \frac{65}{8} \right| = \left| \frac{178}{8} \right| = \frac{89}{4} = 22.25 \text{ inches} $$

2. Calculate the change in temperature

Final temperature = $40$ degrees
Initial temperature = $-12 \frac{1}{4}$ degrees

Convert to improper fraction:
$$ -12 \frac{1}{4} = -\frac{49}{4} $$

Now, find the change:
$$ \text{Change} = \left| 40 - \left( -\frac{49}{4} \right) \right| = \left| 40 + \frac{49}{4} \right| = \left| \frac{160}{4} + \frac{49}{4} \right| = \left| \frac{209}{4} \right| = 52.25 \text{ degrees} $$

3. Calculate the change in pounds of fruit sold

Final weight = $112 \frac{3}{4}$ pounds
Initial weight = $27 \frac{1}{8}$ pounds

Convert to improper fractions:
$$ 112 \frac{3}{4} = \frac{451}{4} $$
$$ 27 \frac{1}{8} = \frac{217}{8} $$

Now, calculate the change:
$$ \text{Change} = \left| \frac{451}{4} - \frac{217}{8} \right| $$
Find a common denominator (8):
$$ = \left| \frac{902}{8} - \frac{217}{8} \right| = \left| \frac{685}{8} \right| = 85.625 \text{ pounds} $$

4. Calculate the change in checking account balance

Final balance = $108.75$
Initial balance = $-20.50$

Convert to decimal:
$$ \text{Change} = \left| 108.75 - (-20.50) \right| = \left| 108.75 + 20.50 \right| = \left| 129.25 \right| = 129.25 $$

5. Compare all absolute value changes

Now, compare the calculated changes:

• Height change: $22.25$
• Temperature change: $52.25$
• Weight change: $85.625$
• Account balance change: $129.25$

The greatest change is $129.25$ from the checking account balance.