At first glance, this simple math expression may seem easy to solve. However, many people make a common mistake when calculating it because they forget one important rule in mathematics: the order of operations.
Take a moment to solve the expression below before looking at the explanation. Can you get the correct answer without falling for the trick?
The Math Challenge
5 + 5 + 5 ÷ 5
What is your answer? Is it 3, 11, or 15? Think carefully before choosing, because the order in which you perform the calculations makes all the difference.
The secret to solving this puzzle lies in one fundamental mathematical rule. Let's break it down step by step to discover the correct answer. ---Step 1: Remember the Order of Operations
When solving mathematical expressions, you must follow the correct order of operations. Division and multiplication are performed before addition and subtraction, unless parentheses indicate otherwise.
In this expression:
5 + 5 + 5 ÷ 5
You must perform the division first, even though it appears after the addition signs.
Start with:
5 ÷ 5 = 1
Now replace the division part with its result. The original expression becomes:
5 + 5 + 1
With the division completed, you can move on to the remaining addition.
Step 2: Complete the Addition
Now that the division is finished, the expression is much easier to solve:
5 + 5 + 1
First, add the two fives:
5 + 5 = 10
Then add the remaining 1:
10 + 1 = 11
Therefore, the correct answer is 11.
But why do so many people get a different answer? The mistake usually happens when they ignore the division sign and rush straight into the addition. ---Why Is 15 the Wrong Answer?
A common mistake is to calculate the expression from left to right without considering the order of operations.
Someone might begin by adding the three fives:
5 + 5 + 5 = 15
Then they might divide the result by 5:
15 ÷ 5 = 3
However, this changes the original expression. The division sign applies only to the final 5, not to the entire sum of the three fives.
To divide the entire sum by 5, the expression would need parentheses, like this:
(5 + 5 + 5) ÷ 5 = 3
Without those parentheses, the original expression must be evaluated according to the standard order of operations.
The Final Answer
Let's review the original expression one last time:
5 + 5 + 5 ÷ 5
Perform the division first:
5 ÷ 5 = 1
Then complete the addition:
5 + 5 + 1 = 11
Final answer: 11
The lesson is simple: never rush through a math puzzle just because it looks easy. Paying attention to the order of operations can help you avoid common mistakes and solve similar challenges with confidence.
