Question

for problems 1 and 2, evaluate each expression. explain how you evaluated the expression.

1. $-3\left(2\frac{1}{4}\

ight)$

1. $-\frac{5}{2} - (-5) - 6 + 2\frac{1}{2}$

Explanation:

Problem 1:

Step1: Convert mixed number to improper fraction

The mixed number \( 2\frac{1}{4} \) can be converted to an improper fraction. We know that \( 2\frac{1}{4}=\frac{2\times4 + 1}{4}=\frac{9}{4} \). So the expression becomes \( - 3\times\frac{9}{4} \).

Step2: Multiply the integers and the fraction

We multiply \( -3 \) and \( \frac{9}{4} \). Using the rule of multiplying a negative number with a positive number (the result is negative), we have \( -3\times\frac{9}{4}=-\frac{27}{4}=- 6\frac{3}{4} \).

Step1: Simplify the subtraction of a negative number

Recall that subtracting a negative number is the same as adding its positive counterpart. So \( -\frac{5}{2}-(-5)-6 + 2\frac{1}{2}=-\frac{5}{2}+5 - 6+2\frac{1}{2} \).

Step2: Combine the fractional terms and the integer terms separately

First, combine the fractional terms: \( -\frac{5}{2}+2\frac{1}{2} \). Convert \( 2\frac{1}{2} \) to an improper fraction: \( 2\frac{1}{2}=\frac{5}{2} \). Then \( -\frac{5}{2}+\frac{5}{2}=0 \).
Next, combine the integer terms: \( 5-6=-1 \).

Step3: Add the results of the two combinations

Now, add the result of the fractional combination and the integer combination: \( 0+(-1)=-1 \).

Answer:

\( -6\frac{3}{4} \) (or \( -\frac{27}{4} \))

Problem 2: