Which statement below describes the greatest absolute value change?
Understand the Problem
The question is asking which of the provided statements describes the greatest absolute value change among several scenarios involving changes in height, temperature, weight, and bank balance. To solve this, we will calculate the absolute values of the changes in each scenario and compare them to identify the largest.
Answer
The greatest absolute value change is from the bank balance: $129.25$.
Answer for screen readers
The statement that describes the greatest absolute value change is the bank balance change from ( -20.50 ) to ( 108.75 ), which is ( 129.25 ).
Steps to Solve
-
Calculate the height change
The height of the plant changes from ( 8 \frac{1}{4} ) inches to ( 30 ) inches.
Convert ( 8 \frac{1}{4} ) to an improper fraction:
$$ 8 \frac{1}{4} = \frac{33}{4} $$
Now calculate the change:
$$ 30 - \frac{33}{4} = \frac{120}{4} - \frac{33}{4} = \frac{87}{4} $$
The absolute value change is ( \left|\frac{87}{4}\right| = \frac{87}{4} = 21.75 ). -
Calculate the temperature change
The temperature changed from ( -12 ) degrees to ( 40 ) degrees.
Calculate the change:
$$ 40 - (-12) = 40 + 12 = 52 $$
The absolute value change is ( |52| = 52 ). -
Calculate the weight change
The number of pounds of fruit sold increased from ( 27 ) to ( 112 ).
Calculate the change:
$$ 112 - 27 = 85 $$
The absolute value change is ( |85| = 85 ). -
Calculate the bank balance change
The balance changed from ( -20.50 ) to ( 108.75 ).
Calculate the change:
$$ 108.75 - (-20.50) = 108.75 + 20.50 = 129.25 $$
The absolute value change is ( |129.25| = 129.25 ). -
Compare the absolute changes
Now, compare the absolute changes:
- Height change: ( 21.75 )
- Temperature change: ( 52 )
- Weight change: ( 85 )
- Bank balance change: ( 129.25 )
The greatest absolute value change is ( 129.25 ).
The statement that describes the greatest absolute value change is the bank balance change from ( -20.50 ) to ( 108.75 ), which is ( 129.25 ).
More Information
Absolute value changes show how much something increases or decreases without considering the direction (positive or negative). In this case, the bank balance had the largest impact.
Tips
- Failing to convert mixed numbers into improper fractions correctly.
- Forgetting to take the absolute value when calculating changes.
- Not checking all options to find the maximum change.
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