To grasp arithmetic, it’s sometimes necessary to be clued-in on certain tips, tricks, and principles, as this subject isn’t always totally straightforward. To that end, we’ve got the perfect challenge for you.
Take a look at this simple-seeming math problem below. At first glance, you may think the answer is obvious, but getting it right relies on more than meets the eye. Can you solve it?
You’ll need to draw upon your math lessons from years ago if you want to solve this one. If you whiled away the majority of your junior high math lessons doodling in your notebook when you should have been studying, it might prove impossible.
Spend a few moments trying to solve it on your own. When you think you have the answer, or if you’re totally stumped, scroll down for the final answer.
Do you think you have the right answer?
One way that some people might have approached this would be to simply solve it from left to right, the same way you might punch in the numbers on a calculator … sometimes, however, calculators can get you into trouble! And that’s where remembering junior high math class comes in.
Solved from left to right, you get a final answer of 1, but that is not the correct answer.
In fact, the correct answer is 30!
Undoubtedly, some will have retained enough math class to arrive at this answer; should you be one of those who fell by the wayside and became calculator-dependent, here’s an explanation of how we got this answer.
The Order of Operations
The reason that 1 is not the correct solution alludes to the use of a decades-old mathematical convention known as the “order of operations.”
The order of operations dictates the order in which we are to solve an equation, as this can affect what the final answer is. Luckily, there is a useful acronym for remembering this rule: PEMDAS, which you may recall from junior high math class.
PEMDAS tells us that the problem should be solved in the following order: Parentheses first, Exponents next, then Multiplication and Division (which are of equal priority), and finally Addition and Subtraction (which are also of equal priority).
Functions of equal priority should be solved in order from left to right.
So, let’s revisit our original equation and solve it using the order of operations:
1 + 1 + 1 + 1 + 11 + 1 + 1 + 1 + 11 + 1 × 0 + 1 = ?
There are no Parentheses or Exponents, but there is a pesky multiplication hiding toward the end of the equation. Eagle-eyed math whizzes may already have noticed that tackling this function first, then proceeding to work through the additions from left to right, radically alters the outcome of the puzzle. We must solve the multiplication part first. Thus:
1 + 1 + 1 + 1 + 11 + 1 + 1 + 1 + 11 + (1 × 0) + 1
= 29 + 0 + 1
Did you get it right? If so, give yourself a hearty pat on the back in congratulation for recalling an age-old math trick that makes all the difference between right and wrong!
Mathematicians reached consensus over the order of operations many years ago, says The Math Forum, as a way to universalize the way that people approach math problems. By employing the order of operations, each and every person is able to arrive at the same solution to any given equation.
If this mini mental arithmetic challenge provided some respite for you and your family during the lockdown, then consider sharing it online to offer the same light relief to your loved ones. It’ll be a chance to discover how many math whizzes you have in your social circle!