Math CentralQuandaries & Queries


Question from Adrian:

50+9-13 multiplied by 2=

Hi Adrian,

What you have is

\[50 + 9 - 13 \times 2\]

where $\times$ is multiplication.

I expect the question is do you read from left to write to get

\[50 + 9 - 13 \times 2 = 46 \times 2 = 92\]

or do you apply the multiplication first to get

\[50 + 9 - 13 \times 2 = 50 + 9 - 26 = 33?\]

This is a legitimate question so to eliminate this confusion mathematicians have agreed to always perform multiplication before addition or subtraction. Hence the correct answer is 33. If you want to write this so that the answer is 92 write the expression as

\[(50 + 9 - 13) \times 2.\]

The added punctuation, the parentheses, tell you to perform what is inside the parentheses first to get

\[(50 + 9 - 13) \times 2 = 46 \times 2 = 92.\]


Adrian replied

I previously sent you a question that is posted for your response but when wording is added to the question as indicated should not you apply the words direction as saying Multiplied notice not Multiply so should not the response to my question really be 92. To follow from left to right response and then wording to multiply by 2. The question was 50+9-13 multiplied by 2 A teacher had told me the response was because words are used that you would do the equation and then the wording of multiply the response by 2

Hi Again Adrian,

I purposly rewrote your question as

\[50 + 9 - 13 \times 2\]

because I thought you had a mathematical expression to evaluate. The wording you sent "50+9-13 multiplied by 2=" is somewhat unusual because it mixes a mathematical expression with words as if it were an English sentence. If the question is to be understood as an English sentance "Fifty plus nine minus thirteen multiplied by two is what?" then I agree that you read the sentence from left to right obtaining an answer is ninty-two. If, as I expected, this question was to illustrate to students the importance of order of operations then the expression should be seen as

\[50 + 9 - 13 \times 2\]

and the mathematical conventions of order of operations used to obtain the answer 33.


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