Solved on Mar 07, 2024

Simplify the expression $3.5+2.25 \div 0.75-6 \cdot \frac{1}{8}$ and select the correct answer.

STEP 1

Assumptions
1. We will follow the order of operations, also known as PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division from left to right, Addition and Subtraction from left to right).
2. Division and multiplication have the same precedence and are performed from left to right.
3. Addition and subtraction also have the same precedence and are performed from left to right.

STEP 2

First, we need to perform the division operation.
$3.5 + \frac{2.25}{0.75} - 6 \cdot \frac{1}{8}$

STEP 3

Calculate the division.
$\frac{2.25}{0.75} = 3$

STEP 4

Replace the division with its result in the original expression.
$3.5 + 3 - 6 \cdot \frac{1}{8}$

STEP 5

Next, we perform the multiplication operation.
$6 \cdot \frac{1}{8} = \frac{6}{8}$

STEP 6

Simplify the fraction.
$\frac{6}{8} = \frac{3}{4}$

STEP 7

Convert the fraction to a decimal.
$\frac{3}{4} = 0.75$

STEP 8

Replace the multiplication with its result in the original expression.
$3.5 + 3 - 0.75$

STEP 9

Now, we perform the addition and subtraction from left to right.
$3.5 + 3 = 6.5$

STEP 10

Subtract the last term from the result of the addition.
$6.5 - 0.75 = 5.75$
The simplified result of the expression $3.5+2.25 \div 0.75-6 \cdot \frac{1}{8}$ is $5.75$ .
Therefore, the correct answer is B. 5.75.

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Simplify the expression $3.5+2.25 \div 0.75-6 \cdot \frac{1}{8}$ and select the correct answer.

STEP 1

STEP 2

First, we need to perform the division operation.
$3.5 + \frac{2.25}{0.75} - 6 \cdot \frac{1}{8}$

STEP 3

Calculate the division.
$\frac{2.25}{0.75} = 3$

STEP 4

Replace the division with its result in the original expression.
$3.5 + 3 - 6 \cdot \frac{1}{8}$

STEP 5

Next, we perform the multiplication operation.
$6 \cdot \frac{1}{8} = \frac{6}{8}$

STEP 6

Simplify the fraction.
$\frac{6}{8} = \frac{3}{4}$

STEP 7

Convert the fraction to a decimal.
$\frac{3}{4} = 0.75$

STEP 8

Replace the multiplication with its result in the original expression.
$3.5 + 3 - 0.75$

STEP 9

Now, we perform the addition and subtraction from left to right.
$3.5 + 3 = 6.5$

STEP 10

Subtract the last term from the result of the addition.
$6.5 - 0.75 = 5.75$
The simplified result of the expression $3.5+2.25 \div 0.75-6 \cdot \frac{1}{8}$ is $5.75$ .
Therefore, the correct answer is B. 5.75.

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Simplify the expression 3.5+2.25÷0.75−6⋅183.5+2.25 \div 0.75-6 \cdot \frac{1}{8}3.5+2.25÷0.75−6⋅81​ and select the correct answer.

STEP 1

STEP 2

First, we need to perform the division operation.3.5+2.250.75−6⋅183.5 + \frac{2.25}{0.75} - 6 \cdot \frac{1}{8}3.5+0.752.25​−6⋅81​

STEP 3

Calculate the division.2.250.75=3\frac{2.25}{0.75} = 30.752.25​=3

STEP 4

Replace the division with its result in the original expression.3.5+3−6⋅183.5 + 3 - 6 \cdot \frac{1}{8}3.5+3−6⋅81​

STEP 5

Next, we perform the multiplication operation.6⋅18=686 \cdot \frac{1}{8} = \frac{6}{8}6⋅81​=86​

STEP 6

Simplify the fraction.68=34\frac{6}{8} = \frac{3}{4}86​=43​

STEP 7

Convert the fraction to a decimal.34=0.75\frac{3}{4} = 0.7543​=0.75

STEP 8

Replace the multiplication with its result in the original expression.3.5+3−0.753.5 + 3 - 0.753.5+3−0.75

STEP 9

Now, we perform the addition and subtraction from left to right.3.5+3=6.53.5 + 3 = 6.53.5+3=6.5

STEP 10

Subtract the last term from the result of the addition.6.5−0.75=5.756.5 - 0.75 = 5.756.5−0.75=5.75The simplified result of the expression 3.5+2.25÷0.75−6⋅183.5+2.25 \div 0.75-6 \cdot \frac{1}{8}3.5+2.25÷0.75−6⋅81​ is 5.755.755.75.Therefore, the correct answer is B. 5.75.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Simplify the expression $3.5+2.25 \div 0.75-6 \cdot \frac{1}{8}$ and select the correct answer.

First, we need to perform the division operation.
$3.5 + \frac{2.25}{0.75} - 6 \cdot \frac{1}{8}$

Calculate the division.
$\frac{2.25}{0.75} = 3$

Replace the division with its result in the original expression.
$3.5 + 3 - 6 \cdot \frac{1}{8}$

Next, we perform the multiplication operation.
$6 \cdot \frac{1}{8} = \frac{6}{8}$

Simplify the fraction.
$\frac{6}{8} = \frac{3}{4}$

Convert the fraction to a decimal.
$\frac{3}{4} = 0.75$

Replace the multiplication with its result in the original expression.
$3.5 + 3 - 0.75$

Now, we perform the addition and subtraction from left to right.
$3.5 + 3 = 6.5$

Subtract the last term from the result of the addition.
$6.5 - 0.75 = 5.75$
The simplified result of the expression $3.5+2.25 \div 0.75-6 \cdot \frac{1}{8}$ is $5.75$ .
Therefore, the correct answer is B. 5.75.