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Principles of Algebra - Simplify Expression











































Perform the indicated operation and, if possible, simplify. Please show all of your work.

-5/12*(-9)*(-3/20)

Comments for Principles of Algebra - Simplify Expression

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Sep 26, 2011
Simplify Expression
by: Staff

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Part II


Step 4: DIVISION


PEMDAS order of evaluation: parentheses, exponents, multiplication, DIVISION, addition, subtraction

There is one division operation

-9 / 16

= -0.5625


Step 5: evaluate ADDITION & SUBTRACTION

PEMDAS order of evaluation: parentheses, exponents, multiplication, division, ADDITION, SUBTRACTION

There is no addition or subtraction in the expression.



The final answer is: - 9 / 16, or - 0.5625



The entire simplification process looks like this:


-5 / 12 * (-9) * (-3 / 20)

= (-5 / 12) * (-9) * (-3 / 20)

= (-5 / 12) * (-9 / 1) * (-3 / 20)

= {[(-5)*(-9)] / (12*1) } * (-3 / 20)

= (45 / 12 ) * (-3 / 20)

= [(45)*(-3)] / (12*20)

= -135 / 240

= -(3 * 3 * 3 * 5) / (2 * 2 * 2 * 2 * 3 * 5)

= -(3 / 3) * (5 / 5) * (9 / 16)

= -(1) * (1) * (9 / 16)

= -9 / 16

= -0.5625




This problem also illustrates how important it is to include parentheses to clarify the order of operations.



To ensure every reader understands the expression, it should have been written

(-5/12) * (-9) * (-3/20)

Instead of

-5/12*(-9)*(-3/20)


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A final note:

You can CHECK YOUR WORK with a CALCULATOR.

. . . but, not an ordinary (basic) calculator.


To compute -5 / 12 * (-9) * (-3 / 20), you should use a “SMART” CALCULATOR.

A "Smart" Calculator (Formula Calculator) automatically takes into account PEMDAS order. The person using the calculator does not need to be concerned about which numbers to evaluate 1st, 2nd, 3rd, etc.

This is not what most people use. Most people use a basic calculator.

Basic calculators are inexpensive (as low as $1) and plentiful (you can buy one at any drugstore or supermarket).

I call basic calculators “dumb calculators” because they rely on the person using the calculator to input the numbers in PEMDAS order.

If the person using the calculator inputs the numbers incorrectly, a basic calculator will give an incorrect answer.

You can download a FREE SMART CALCULATOR at:

http://www.zoesoft.com/console-calculator/


If you decide to check the work for your problem using a smart calculator, input the entire expression exactly as you submitted it to me:

-5 / 12 * (-9) * (-3 / 20)

You will see that a smart calculator it will automatically calculate the proper answer using the correct PEMDAS order.

You still need to know and understand how PEMDAS works because you will use variables (instead of numbers) in your classes. However, a smart calculator will help you check your work when you evaluate numerical expressions.



Thanks for writing.

Staff
www.solving-math-problems.com



Sep 26, 2011
Simplify Expression
by: Staff


Part I

The question:

Perform the indicated operation and, if possible, simplify. Please show all of your work.

-5/12*(-9)*(-3/20)


The answer:

To simplify this expression:

1. IMPORTANT – This is the key: Read the expression from LEFT to RIGHT

-5 / 12 * (-9) * (-3 / 20)

2. Use the PEMDAS order of operations.

PEMDAS order tells you what to do first, second, . . . etc.

PEMDAS stands for: parentheses, exponents, multiplication, division, addition, subtraction


Step 1: evaluate PARENTHESES

PEMDAS order of evaluation: PARENTHESES, exponents, multiplication, division, addition, subtraction

There are no expressions enclosed in parentheses


Step 2: evaluate EXPONENTS


PEMDAS order of evaluation: parentheses, EXPONENTS, multiplication, division, addition, subtraction

There are no exponents to evaluate.


Step 3: MULTIPLICATION


PEMDAS order of evaluation: parentheses, exponents, MULTIPLICATION, division, addition, subtraction

-5 / 12 * (-9) * (-3 / 20)

There are two places where multiplication must be completed:



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*****REMEMBER TO READ FROM LEFT TO RIGHT*****

Why?

Why should you read from left to right?

You have two choices of how to evaluate the expression -5 / 12 * (-9). When you read from left to right, you automatically select the correct choice.

The choices are:

1) Leave the fraction -5/12 as it is (or divide -5 by 12 to get the decimal value), and then multiply by -9

or

2) Multiply 12 by -9 first, and then divide -5 by the product of 12 and -9.


The first choice is the correct choice: leave the fraction -5/12 as it is (or divide -5 by 12 to get the decimal value), and then multiply by -9

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1st multiplication

-5 / 12 * (-9)

= (-5 / 12) * (-9)

= (-5 / 12) * (-9 / 1)


When multiplying two fractions, remember to multiply the numerators together, and multiply the denominators together.

= (-5 / 12) * (-9 / 1)

= [(-5)*(-9)] / (12*1)

= 45 / 12


After multiplying -5 / 12 * (-9), the partially simplified expression looks like this:

-5 / 12 * (-9) * (-3 / 20)

= (45 / 12 ) * (-3 / 20)


2nd multiplication

(45 / 12 ) * (-3 / 20)


= [(45)*(-3)] / (12*20)

= -135 / 240


After completing the multiplication, the partially simplified expression looks like this:

-5 / 12 * (-9) * (-3 / 20)

= (-5 / 12) * (-9) * (-3 / 20)

= (-5 / 12) * (-9 / 1) * (-3 / 20)

= {[(-5)*(-9)] / (12*1) } * (-3 / 20)

= (45 / 12 ) * (-3 / 20)

= [(45)*(-3)] / (12*20)

= -135 / 240


Reduce the fraction -135 / 240 to its lowest possible terms:

-135 / 240

= -(3 * 3 * 3 * 5) / (2 * 2 * 2 * 2 * 3 * 5)

= -(3 / 3) * (5 / 5) * (9 / 16)

= -(1) * (1) * (9 / 16)

= -9 / 16





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