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Posted November 3, 2016 By Presh Talwalkar. Read about me, or email me.
Here we go again, another order of operations problem. This equation has been shared on Twitter and Facebook and many people are confused about the correct answer.
7 + 7 ÷ 7 + 7 × 7 – 7 =
In the following video I explain the answer and present two different ways to simplify the expression.
What Is 7 + 7 ÷ 7 + 7 × 7 + 7 Equal To? The Correct Answer Explained
Or keep reading for a text explanation. "All will be well if you use your mind for your decisions, and mind only your decisions." Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon.
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The Correct Answer
The correct answer is 50.
One way to see this is to translate the expression 7 + 7 ÷ 7 + 7 × 7 – 7 = into a situation about money.
The expression begins with 7, so you start out with $7.
The next part is “+ 7 ÷ 7.” This means you get a 1/7 share of $7. Since a 1/7 share of $7 is $1, that means you get $1. At this point you have $7 + $1 = $8.
The next part is “+ 7 × 7.” This means you get $7 more, repeated 7 times. Since a $7 times 7 is $49, that means you get $49 in total. At this point you have $8 + $49 = $57.
The last part is “- 7.” That means $7 is taken away from you. You subtract $7, so you end up with $57 – $7 = $50.
The correct answer is therefore 50.
The expression can also be simplified by the order of operations, often remembered by the acronyms PEMDAS/BODMAS.
First evaluate Parentheses/Brackets, then evaluate Exponents/Orders, then evaluate Multiplication-Division, and finally evaluate Addition-Subtraction.
The expression 7 + 7 ÷ 7 + 7 × 7 – 7 has no parentheses or exponents, so we evaluate multiplication and division.
7 ÷ 7 = 1
7 × 7 = 49
This means
7 + 7 ÷ 7 + 7 × 7 – 7
= 7 + 1 + 49 – 7
Now we can evaluate the addition and the subtraction from left to right.
= 8 + 49 – 7
= 57 – 7
= 50
The correct answer is 50.
Published by
PRESH TALWALKAR
I run the MindYourDecisions channel on YouTube, which has over 1 million subscribers and 200 million views. I am also the author of The Joy of Game Theory: An Introduction to Strategic Thinking, and several other books which are available on Amazon.
(As you might expect, the links for my books go to their listings on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay.)
By way of history, I started the Mind Your Decisions blog back in 2007 to share a bit of math, personal finance, personal thoughts, and game theory. It's been quite a journey! I thank everyone that has shared my work, and I am very grateful for coverage in the press, including the Shorty Awards, The Telegraph, Freakonomics, and many other popular outlets.
I studied Economics and Mathematics at Stanford University.
People often ask how I make the videos. Like many YouTubers I use popular software to prepare my videos. You can search for animation software tutorials on YouTube to learn how to make videos. Be prepared--animation is time consuming and software can be expensive!
Feel free to send me an email [emailprotected]. I get so many emails that I may not reply, but I save all suggestions for puzzles/video topics.
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