MATH QUESTION

[Edward]

I saw this equation on facebook in which they stated that 73% of people failed to answer this correctly? 4 x 4 + 4 x 4 + 4 - 4 x 4 = ?. The many answers were 320, 20, 480 and 128. Could you show your computation and break down?

[taxxcpa]

If you enter each number on a calculator enter and the X or + exactly as it is written, including the minus sign in front of the penultimate "4", you will get 320 as the answer

If you were to treat it as (4X4) + (4X4) + (4-4) X 4, you get a whole 'nother answer which would be incorrect for the problem as presented.

[Gail in Virginia]

But I think that the ordering rules mean that even though no parentheses are shown, the correct way to view this equation is to do all of the multiplication first, which gives you:

(4x4)+(4x4)+4-(4x4) which equals 16+16+4-16 which equals 20. Math class was a long time ago, so I am willing to be corrected.

[Jack from Ohio]

Rules of calculation:

1. All calculations inside parantheses

2. All multiplication and division.

3. All add and subtract.

4 x 4 + 4 x 4 + 4 - 4 x 4 =

(4 x 4) + (4 x 4) + 4 - (4 x 4) =

16 + 16 + 4 - 16= The correct answer is 20.

Math, Algebra, Geometry, Trigonometry and Calculus major in High School.

[mcb39]

I came up with 20 (16 plus 16 plus 4 minus 16)

[ILLMAS]

Using Order of Operation gives you 20, I also seen this on facebook, and I will say a high number of people have responded with 320

[Edward]

For taxxcpa: It appears that the previous posters believe the correct answer is 20 - I tried it twice and came up with 256 or 64 short of 320. Could you show us a copy of your calculator tape to see how you arrived at 320?

[JohnH]

I don't have the tape handy, but here's the result on my calculator display:

[Lion EA]

lol. Jack showed his work as did a couple more posters above him.

[Jack from Ohio]

lol. Jack showed his work as did a couple more posters above him.

My math teachers would count a problem wrong if the work was not shown.

On a separate issue of those trying to use calculators.... There will be different answers from a calculator compared to an adding machine. One is literal, the other is accounting. If that confuses you.... Hmmmmmmmm

[Edward]

So JohnH uses a soroban or japanese abucus in his tax work - well, I don't believe that there are many tax preparers that also use such and I'm certain the calculator is the most preferred instrument. I'm certain 320 is the correct answer so we'll just wait till taxxcpa responds.

[Jack from Ohio]

I know, beyond any reasonable doubt, the correct answer is 20. Would someone contact an algebra or advanced math teacher and let them verify for me.

[AnnieR]

I didn't use a calculator or adding machine...paper & pen...4x4=16+4=20x4=80+4=84-4=80x4=320.

AnnieR

[ILLMAS]

PEMDAS This stands for Parenthesis (are none), Exponents (are none), Multiplication (yes), Division (none), Addition, and Subtraction (yes)

[michaelmars]

I am on board with $20

[cred65]

I computed it using Excel and got 20.

[JohnH]

http://www.mathgoodi...operations.html

The answer is 20 using the order of operations rules.

(The order of operations rules essentially tell you where the parentheses should be)

4 x 4 + 4 x 4 + 4 - 4 x 4

is the same as (4x4) + (4x4) + (4) - (4x4)

is the same as (16) + (16) + (4) - (16)

is the same as (32) + (4) - (16)

is the same as (36) - (16)

You could also get the same result by canceling out the 16's (after the multiplication is done) or by any of several other routes.

My abacus also yielded the same result

[Edward]

AnnieR has the corrrect answer. Case closed.

[Jack from Ohio]

AnnieR has the corrrect answer. Case closed.

Are you a math teacher or major? Ask an advanced math teacher.

[Don in Upstate NY]

Our basic arithmetic notational system has the property that expressions containing multiple components may be evaluated differently depending on the order that the components are evaluated. To eliminate this undesirable property, ordering rules have been defined. Using these conventional ordering rules, the "answer" is 20.

The advent of calculators and computers complicated things by introducing different notations and default ordering rules. For example, I have three calculators on my desk. If I enter the same keystrokes " 3 X 4 + 5 = " on all three, they all give the correct answer of 17. However, if I enter " 3 + 4 X 5 = ", two of them give the incorrect answer of 35 while one gives the correct answer of 23. In general, four function and business calculators ignore ordering rules and evaluate in the order the data are presented, while scientific calculators wait until the "=" key is pressed before evaluating.

It is not unusual for two calculator models from the same vendor to give different results. And no engineer of the 70'scan ever forget that one of the earliest hand held calculators (the hp-35 and sucessors) used a totally different notation (RPN - Reverse Polish Notation) " 4 5 X 3 + "

If you want to delve further into this area, you can google 'math ordering rules' or start with Wikipedia http://en.wikipedia....r_of_operations

[Catherine]

The mathematically correct answer is 20, for reasons shown and displayed above.

There is a reason for the ordering of mathematical operations -- and this "test" is a prime example of why they exist. Do the problem in other orders if it pleases you, but you must NOT then claim that your answer is the only "correct" one. After all, you have started by tossing centuries-old conventions to the wind. You may not then claim that your method is the new convention, giving the only correct answer.

[RitaB]

The correct answer is 20. I was an algebra teacher for eight years. Unless there are grouping symbols, you perform multiplication and division, from left to right, before addition and subtraction. Do one operation per step. JohnH showed all the steps. He was one of my best students back in the day. Wait til you see him on the slide rule.

http://www.math.com/...s/S2U1L2GL.html

[JohnH]

Yes, I remember that class well. At 12 years of age Rita was the youngest person to ever teach at my middle school. And thanks to her excellent teaching skills, I made it into high school just after my 21st birthday.

BTW, I can still use a slide rule. Best way in the world to visualize a log table.

[taxxcpa]

If you just enter the figures in a calculator without using any parentheses you will get 320. Broken down it comes to:

4x4=16

16x4=20

20x4=80

80+4= 84

84-4=80

80x4=320

If the rules of math stipulate that parentheses are to be assumed as mentioned, then the answer would be 16.

I've always worked with parentheses that are shown, not assumed.

[Kea]

I kept my Dad's and uncle's slide rules, but have never learned how to use them. My dad tried to teach me a couple of times, but it never stuck. I came along at the advent of the calculator. When I was in elementary school, Dad (an algebra teacher for many years) bought an early Sears 4 function calculator. I was allowed to use it to check my math answers - but not to calculate them in the first place. In junior high, I used the printed log tables and by high school my calculator had a "log" button.

And, yes, the answer is 20. Parentheses were not "assumed." They are based on following My Dear Aunt Sal order of operations (M = multiplication, D = Division / A = Addition / S = Subtraction).