Question

select all of the true statements.
□ 2.25 > 2
□ 2.25 < 2
□ -2.25 > -2
□ -2.25 < -2
□ 2.25 > -2

Explanation:

Step1: Analyze \( 2.25 > 2 \)

Compare the decimal \( 2.25 \) and the integer \( 2 \). Since \( 2.25 - 2 = 0.25>0 \), so \( 2.25 > 2 \) is true.

Step2: Analyze \( 2.25 < 2 \)

From Step 1, we know \( 2.25>2 \), so \( 2.25 < 2 \) is false.

Step3: Analyze \( -2.25 > -2 \)

For negative numbers, the larger the absolute value, the smaller the number. \( | - 2.25|=2.25 \), \( | - 2| = 2 \), and \( 2.25>2 \), so \( - 2.25<-2 \), thus \( -2.25 > -2 \) is false.

Step4: Analyze \( -2.25 < -2 \)

As in Step 3, since \( | - 2.25|=2.25>|-2| = 2 \), negative numbers with larger absolute values are smaller, so \( -2.25 < -2 \) is true.

Step5: Analyze \( 2.25 > -2 \)

Positive numbers are always greater than negative numbers, so \( 2.25 > -2 \) is true.

Answer:

The true statements are:

• \( 2.25 > 2 \)
• \( -2.25 < -2 \)
• \( 2.25 > -2 \)