Which statement below describes the greatest absolute value change?

Steps to Solve

1. Calculate the Absolute Change in Height The height changes from ( 8\frac{1}{4} ) to ( 30\frac{3}{8} ). Convert mixed numbers to improper fractions: [ 8\frac{1}{4} = \frac{33}{4} \quad \text{and} \quad 30\frac{3}{8} = \frac{243}{8} ] To compare, convert to a common denominator (which is 8): [ \frac{33}{4} = \frac{66}{8} ] Now calculate the absolute change: [ \left| \frac{243}{8} - \frac{66}{8} \right| = \left| \frac{243 - 66}{8} \right| = \left| \frac{177}{8} \right| = 22.125 \text{ inches} ]

2. Calculate the Absolute Change in Temperature The temperature changes from ( -12\frac{1}{2} ) to ( 40\frac{4}{4} ). Convert mixed numbers: [ -12\frac{1}{2} = -\frac{25}{2} \quad \text{and} \quad 40\frac{4}{4} = 40 ] Convert 40 to a fraction: [ 40 = \frac{80}{2} ] Now calculate the absolute change: [ \left| \frac{80}{2} - \left(-\frac{25}{2}\right) \right| = \left| \frac{80 + 25}{2} \right| = \left| \frac{105}{2} \right| = 52.5 \text{ degrees} ]

3. Calculate the Absolute Change in Weight The weight changes from ( 27\frac{1}{8} ) to ( 112\frac{3}{4} ). Convert mixed numbers: [ 27\frac{1}{8} = \frac{217}{8} \quad \text{and} \quad 112\frac{3}{4} = \frac{451}{4} ] Convert to a common denominator (which is 8): [ \frac{451}{4} = \frac{902}{8} ] Now calculate the absolute change: [ \left| \frac{902}{8} - \frac{217}{8} \right| = \left| \frac{902 - 217}{8} \right| = \left| \frac{685}{8} \right| = 85.625 \text{ pounds} ]

4. Calculate the Absolute Change in Bank Balance The balance changes from (-20.50) to (108.75). Convert to fractions: [ -20.50 = -\frac{41}{2} \quad \text{and} \quad 108.75 = \frac{435}{4} ] Convert to a common denominator (which is 4): [ -\frac{41}{2} = -\frac{82}{4} ] Now calculate the absolute change: [ \left| \frac{435}{4} - \left(-\frac{82}{4}\right) \right| = \left| \frac{435 + 82}{4} \right| = \left| \frac{517}{4} \right| = 129.25 \text{ dollars} ]

5. Compare the Absolute Changes The absolute changes calculated are:

• Height: ( 22.125 ) inches
• Temperature: ( 52.5 ) degrees
• Weight: ( 85.625 ) pounds
• Bank Balance: ( 129.25 ) dollars

The greatest absolute change is in the bank balance.