Question

evaluate -2.5 + 5 - (-4\frac{1}{4})
a. complete the number line to evaluate the expression.
number line from -10 to 10 with -2.5 marked
the answer is ______.
b. complete the rule to add the first two numbers of the expression.
____ the absolute values and take the sign of the one with the ____ absolute value.
c. explain how the number line supports the rule used in part b.
d. write the rule to subtract (-4\frac{1}{4}) from your answer to part b. show the work to use the rule to find the answer.
e. explain how the number line supports the rule used in part d.
f. in previous lessons, the rules were used with integers. now they are being used with mixed numbers and decimals. explain how the rules for adding and subtracting integers apply to rational numbers.

Explanation:

Step1: Evaluate -2.5 + 5

To add -2.5 and 5, we use the rule for adding a negative and a positive number. The absolute value of -2.5 is 2.5, and the absolute value of 5 is 5. Since 5 > 2.5, we subtract the smaller absolute value from the larger one: \(5 - 2.5 = 2.5\). The result takes the sign of the number with the larger absolute value, which is positive, so \(-2.5 + 5 = 2.5\).

Step2: Subtract \(-4\frac{1}{4}\) from 2.5

First, convert \(4\frac{1}{4}\) to a decimal. \(4\frac{1}{4}=4 + \frac{1}{4}=4 + 0.25 = 4.25\), so \(-4\frac{1}{4}=-4.25\). The rule for subtracting a number is to add its opposite. So, \(2.5 - (-4.25)=2.5 + 4.25\). Now, add these two positive numbers: \(2.5 + 4.25 = 6.75\).

Answer:

The final result of \(-2.5 + 5 - (-4\frac{1}{4})\) is \(6.75\) (or \(6\frac{3}{4}\)).