QuestionCalculate the expression: $\frac{1}{2}-3\left(\frac{1}{2}+1\right)^{2}$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\frac{1}{}-3\left(\frac{1}{}+1\right)^{}$ . . We will follow the order of operations, also known as BIDMAS or PEMAS, which stands for Brackets, Indices (or Exponents), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

STEP 2

First, we need to simplify the expression inside the brackets.
$\frac{1}{2}+1 =1.5$

STEP 3

Now, we substitute the value we just calculated back into the original expression.
$\frac{1}{2}-3\left(1.5\right)^{2}$

STEP 4

Next, we need to calculate the square of1., which is the operation indicated by the exponent of2.
$(1.)^{2} =2.25$

STEP 5

Substitute the value we just calculated back into the expression.
$\frac{1}{2}-3 \cdot2.25$

STEP 6

Now, we need to multiply3 by2.25.
$3 \cdot2.25 =6.75$

STEP 7

Substitute the value we just calculated back into the expression.
$\frac{1}{2}-6.75$

STEP 8

Finally, subtract6.75 from0.5.
$0.5 -6.75 = -6.25$ The solution to the expression $\frac{1}{2}-3\left(\frac{1}{2}+1\right)^{2}$ is -6.25.

Was this helpful?

QuestionCalculate the expression: $\frac{1}{2}-3\left(\frac{1}{2}+1\right)^{2}$ .

Studdy Solution

STEP 1

STEP 2

First, we need to simplify the expression inside the brackets.
$\frac{1}{2}+1 =1.5$

STEP 3

Now, we substitute the value we just calculated back into the original expression.
$\frac{1}{2}-3\left(1.5\right)^{2}$

STEP 4

Next, we need to calculate the square of1., which is the operation indicated by the exponent of2.
$(1.)^{2} =2.25$

STEP 5

Substitute the value we just calculated back into the expression.
$\frac{1}{2}-3 \cdot2.25$

STEP 6

Now, we need to multiply3 by2.25.
$3 \cdot2.25 =6.75$

STEP 7

Substitute the value we just calculated back into the expression.
$\frac{1}{2}-6.75$

STEP 8

Finally, subtract6.75 from0.5.
$0.5 -6.75 = -6.25$ The solution to the expression $\frac{1}{2}-3\left(\frac{1}{2}+1\right)^{2}$ is -6.25.

Get Studdy

Studdy solves anything!

Start learning now

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

QuestionCalculate the expression: 12−3(12+1)2\frac{1}{2}-3\left(\frac{1}{2}+1\right)^{2}21​−3(21​+1)2.

Studdy Solution

STEP 1

STEP 2

First, we need to simplify the expression inside the brackets.12+1=1.5\frac{1}{2}+1 =1.521​+1=1.5

STEP 3

Now, we substitute the value we just calculated back into the original expression.12−3(1.5)2\frac{1}{2}-3\left(1.5\right)^{2}21​−3(1.5)2

STEP 4

Next, we need to calculate the square of1., which is the operation indicated by the exponent of2.(1.)2=2.25(1.)^{2} =2.25(1.)2=2.25

STEP 5

Substitute the value we just calculated back into the expression.12−3⋅2.25\frac{1}{2}-3 \cdot2.2521​−3⋅2.25

STEP 6

Now, we need to multiply3 by2.25.3⋅2.25=6.753 \cdot2.25 =6.753⋅2.25=6.75

STEP 7

Substitute the value we just calculated back into the expression.12−6.75\frac{1}{2}-6.7521​−6.75

STEP 8

Finally, subtract6.75 from0.5.0.5−6.75=−6.250.5 -6.75 = -6.250.5−6.75=−6.25The solution to the expression 12−3(12+1)2\frac{1}{2}-3\left(\frac{1}{2}+1\right)^{2}21​−3(21​+1)2 is -6.25.

Get Studdy

Studdy solves anything!

Start learning now

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

QuestionCalculate the expression: $\frac{1}{2}-3\left(\frac{1}{2}+1\right)^{2}$ .

First, we need to simplify the expression inside the brackets.
$\frac{1}{2}+1 =1.5$

Now, we substitute the value we just calculated back into the original expression.
$\frac{1}{2}-3\left(1.5\right)^{2}$

Next, we need to calculate the square of1., which is the operation indicated by the exponent of2.
$(1.)^{2} =2.25$

Substitute the value we just calculated back into the expression.
$\frac{1}{2}-3 \cdot2.25$

Now, we need to multiply3 by2.25.
$3 \cdot2.25 =6.75$

Substitute the value we just calculated back into the expression.
$\frac{1}{2}-6.75$

Finally, subtract6.75 from0.5.
$0.5 -6.75 = -6.25$ The solution to the expression $\frac{1}{2}-3\left(\frac{1}{2}+1\right)^{2}$ is -6.25.