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Need Correct Solution - Arithmetic Expression

by Carol
(Kerrville, TX)











































Evaluate Arithmetic Expression

7+7 divided by 7+7×7-7

I can't find the division symbol on my keyboard. I believe the answer is 0.
7+7 is 14, divided by 7+7 (14) = 1 × 7-7 (0) = 0
or 7+7 (14) divided by 7 = 2 + 7×7 (49)= 51- 7 = 44

Comments for Need Correct Solution - Arithmetic Expression

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May 23, 2013
Evaluate Expression
by: Staff


Answer

Part I

The answer:


There are two keys to understanding how to evaluate this expression:

- Use the PEMDAS order of operations.

PEMDAS tells you exactly what parts of the expression to evaluate first, second, . . and so on.

PEMDAS order stands for evaluating this expression in the following order: parentheses, exponents, multiplication, division, addition, subtraction

Following PEMDAS order works exactly the same way following a set of directions to a friend's house works.

When you do not know your friend's home address you must follow the directions you have - exactly. Without following the directions to the letter you will not arrive at the correct destination. No deviations are allowed. You cannot challenge the directions. You cannot make up your own directions.

This is similar to trying to solve the expression 7+7 divided by 7+7×7-7. Since you do not know the answer in advance, you must follow the only directions you have: PEMDAS.

Follow the PEMDAS directions as if you are a robot with no thought of your own, blindly following a computer algorithm.



- If parts of the expression are unclear after applying PEMDAS order, read from left to right.



Applying PEMDAS order to your expression:

7 + 7 divided by 7 + 7 × 7 - 7





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May 23, 2013
Evaluate Expression
by: Staff


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Part II


Step 1: evaluate the expression inside PARENTHESES first (always first)

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


There are no expressions enclosed within parentheses.


7 + 7 divided by 7 + 7 × 7 - 7 using PEMDAS - no parentheses



Step 2: evaluate all EXPONENTS second (always second)

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

There are no exponents to evaluate.

7 + 7 divided by 7 + 7 × 7 - 7 using PEMDAS - no exponents







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May 23, 2013
Evaluate Expression
by: Staff


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Part III


Step 3: MULTIPLICATION (note that multiplication must be completed before addition or subtraction)

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

7 + 7 / 7 + 7 × 7 - 7


DON'T try to DO SOMETHING ELSE FIRST, such as 7 - 7.

Remember, you are following the PEMDAS rules like a robot, blindly following the tasks in order.

You may disagree with PEMDAS.

You may have rules that make more sense to you. However, you are wrong. Your rules do not matter.

You must follow the PEMDAS directions exactly to arrive at the correct answer.

7 + 7 / 7 + 7 × 7 - 7


After completing the multiplication, the expression looks like this:


7 + 7 / 7 + 49 - 7


7 + 7 divided by 7 + 7 × 7 - 7 using PEMDAS - multiplication





Step 4: DIVISION


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

7 + 7 / 7 + 49 - 7

After completing the division, the expression looks like this:

7 + 1 + 49 - 7

7 + 7 divided by 7 + 7 × 7 - 7 using PEMDAS - division







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May 23, 2013
Evaluate Expression
by: Staff


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Part IV


Step 5: evaluate ADDITION & SUBTRACTION

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

7 + 1 + 49 - 7

7 + 7 divided by 7 + 7 × 7 - 7 using PEMDAS - addition and subtraction





The final answer is: 50


7 + 7 divided by 7 + 7 × 7 - 7 using PEMDAS - final answer





This problem 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

7 + (7 / 7) + (7 × 7) - 7

Instead of

7+7/7+7×7-7

The entire simplification process is illustrated below:


7 + 7 / 7 + 7 × 7 - 7

= 7 + 7 / 7 + 49 - 7

= 7 + 1 + 49 - 7

= 50


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You can CHECK YOUR WORK with a SMART CALCULATOR (formula 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.




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May 23, 2013
Evaluate Expression
by: Staff


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Part V


Click the following link to download a Free Smart Calculator:

FREE SMART CALCULATOR (automatically takes PEMDAS into account)

Input the entire expression "exactly" as you submitted it to me:

7+7/7+7×7-7

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.


For example, simplify the expression: x + y²[3 + (22x - 40)] – 15x/3

A step-by-step simplification looks like this:

x + y²[3 + (22x - 40)] - 15x/3

= x + y²[3 + 22x - 40] - 15x/3

= x + y²[22x + 3 - 40] - 15x/3

= x + y²[22x - 37] - 15x/3

= x + y²*22x - y²*37 - 15x/3

= x + 22xy² - 37y² - 15x/3

= x - 15x/3 + 22ay² - 37y²

= x - 5x + 22xy² - 37y²

= -4x + 22xy² - 37y²


x + y²[3 + (22x - 40)] - 15x/3 = -4x + 22xy² - 37y²

In this case you can CHECK YOUR WORK with an ALGEBRA CALCULATOR.


Click either one of the following links to download a FREE ALGEBRA CALCULATOR from Microsoft. This calculator will automatically take PEMDAS into account for an algebraic expression:


FREE ALGEBRA CALCULATOR


OR

FREE ALGEBRA CALCULATOR





Thanks for writing.

Staff
www.solving-math-problems.com


Sep 30, 2015
Need Correct Solution
by: Anonymous


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Alex

Nov 02, 2015
Arithmetic Expression
by: Anonymous


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Addison

Oct 09, 2016
your method for PEMDAS is wrong NEW
by: Anonymous

First you do Parenthesis then you do Exponent. You
said that correctly.But, it is Multiplication or
Division whichever comes first. Same thing for Addition and Subtraction.

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