Question

for problems 10–15, use >, <, or = to compare the rational numbers.

1. $-2\frac{1}{2}$ ______ $-1.5$
2. $-1.2$ ______ $-1.25$
3. $0$ ______ $-3.5$
4. $-6.2$ ______ $-1.5$
5. $-4.6$ ______ $-4.06$
6. $-\frac{1}{2}$ ______ $-\frac{1}{4}$
7. the elevation of a new york bank vault is $-50$ feet. the elevation of the city of heber, california, is $-10$ feet. which location is at a lower elevation? explain. draw a number line to support your answer.

Explanation:

Step1: Convert to decimal

$-2\frac{1}{2} = -2.5$

Step2: Compare values

$-2.5 < -1.5$

Step1: Compare decimals

$-1.2 > -1.25$ (closer to 0)

Step1: Compare with zero

$0 > -3.5$ (zero > negatives)

Step1: Compare decimals

$-6.2 < -1.5$ (farther from 0)

Step1: Compare decimals

$-4.6 < -4.06$ (farther from 0)

Step1: Convert to decimals

$-\frac{1}{2} = -0.5$, $-\frac{1}{4} = -0.25$; $-0.5 < -0.25$

Step1: Compare elevations

$-50 < -10$ (farther below sea level)

Answer:

1. <
2. >
3. >
4. <
5. <
6. <
7. The New York bank vault (elevation -50 feet) is at a lower elevation. On the number line, -50 is to the left of -10, meaning it is farther below sea level.