At first glance, this equation looks almost too easy to be worth discussing.
There are only a few numbers.
There are no parentheses.
There are no fractions stacked on top of each other.
And every operation is something most people learned in elementary school.
Yet put the expression 5×5+5÷5−5 in front of a group of people, and you may suddenly get several completely different answers.
Some people will confidently say 1.
Others will argue for 25.
A few may even insist that the answer depends on how you read the equation.
But mathematics has a standard set of rules for expressions like this—and once you follow those rules, the answer becomes much easier to see.
So before you look at the answer, take a moment.
Can you solve it without using a calculator?
The Equation That Looks Easier Than It Is
Here is the full puzzle:
5 × 5 + 5 ÷ 5 − 5 = ?
Try solving it in your head.
Don't rush.
A common instinct is to simply start at the left side and work toward the right:
5 × 5 = 25
Then add 5:
25 + 5 = 30
Then divide by 5:
30 ÷ 5 = 6
Then subtract 5:
6 − 5 = 1
It seems perfectly logical if you're treating the equation like a sequence of instructions.
But there is a problem.
That's not how standard mathematical expressions are evaluated.
The Rule That Changes Everything
The key is the order of operations.
You may have learned it as PEMDAS:
P — Parentheses
E — Exponents
M — Multiplication
D — Division
A — Addition
S — Subtraction
This tells us that multiplication and division must be handled before addition and subtraction.
There is one important detail, though.
Multiplication does not always come before division. They have the same priority and are evaluated from left to right.
The same principle applies to addition and subtraction.
That's the detail that makes this puzzle so interesting.
Let's Solve It Step By Step
Start with the original equation:
5 × 5 + 5 ÷ 5 − 5
First, identify the multiplication and division.
There are two:
5 × 5
and
5 ÷ 5
Calculate those first.
Step One: Multiplication
5 × 5 = 25
Step Two: Division
5 ÷ 5 = 1
Now replace those results in the original expression.
Instead of:
5 × 5 + 5 ÷ 5 − 5
we now have:
25 + 1 − 5
The multiplication and division are finished.
Now we move on to addition and subtraction.
Step Three: Addition
25 + 1 = 26
The equation becomes:
26 − 5
Step Four: Subtraction
26 − 5 = 21
And there it is.
The Answer Is 21
5 × 5 + 5 ÷ 5 − 5 = 21
No calculator is required.
The entire puzzle comes down to understanding the order in which mathematical operations are performed.
But there's another reason this equation causes so many arguments online.
Why Do So Many People Answer 1?
The answer 1 comes from performing every operation strictly from left to right.
That method would look like this:
5 × 5 = 25
25 + 5 = 30
30 ÷ 5 = 6
6 − 5 = 1
The arithmetic itself isn't wrong.
The problem is when the operations are being performed.
The addition in the middle should not happen before the division.
The expression tells us that multiplication and division have priority over addition and subtraction.
So the mistake isn't necessarily a failure to calculate.
It's a failure to apply the correct rule.
What About People Who Say 25?
Another common answer floating around is 25.
That usually comes from interpreting the expression incorrectly or mentally grouping some of the numbers in a way that isn't actually written.
For example, someone might focus heavily on the repeated 5s and assume that some terms cancel or combine.
But mathematical notation has to be followed exactly as written.
There are no hidden parentheses.
There are no implied groupings.
There is simply:
5 × 5 + 5 ÷ 5 − 5
And standard order of operations gives us 21.
The Interesting Part: Multiplication and Division
There's a small detail here that is worth remembering because it causes confusion in many other problems.
People sometimes memorize PEMDAS as though multiplication must always be completed before division.
That's not quite right.
Multiplication and division have equal priority.
If an equation contains both, you work through them from left to right.
For example:
20 ÷ 5 × 2
You would first calculate:
20 ÷ 5 = 4
Then:
4 × 2 = 8
You wouldn't multiply 5 × 2 first simply because multiplication is listed before division in the acronym.
The same principle applies to addition and subtraction.
They share the same level of priority and are evaluated from left to right.
Why These Puzzles Are So Addictive
There is something satisfying about a math puzzle that looks obvious but contains a hidden trap.
Your brain wants to recognize a pattern immediately.
You see five 5s and several familiar symbols, and your mind starts calculating before you've consciously decided which operation should come first.
That's why these puzzles work so well on social media.
People don't necessarily get them wrong because they're bad at math.
They get them wrong because they're moving too quickly.
The first answer that appears in your head can feel so obvious that you don't stop to question it.
And once someone posts an answer confidently, other people often follow along.
Before long, a simple equation turns into a debate.
The Best Way To Avoid The Trap
Whenever you see a mathematical expression containing several different operations, don't immediately start calculating.
Instead, pause for a second.
Ask yourself:
Are there parentheses?
If yes, handle those first.
Then look for exponents.
After that, handle multiplication and division from left to right.
Finally, handle addition and subtraction from left to right.
This tiny pause can prevent a surprisingly large number of mistakes.
Try These Before You Look At The Answers
Now that you've solved the original puzzle, see whether you can handle a few similar ones.
Puzzle One
8 + 4 × 2 = ?
Don't add 8 + 4 first.
Multiplication comes first.
4 × 2 = 8
Then:
8 + 8 = 16
Puzzle Two
20 − 12 ÷ 3 = ?
Division comes first.
12 ÷ 3 = 4
Then:
20 − 4 = 16
Puzzle Three
6 × 3 − 8 ÷ 2 = ?
Handle multiplication and division first.
6 × 3 = 18
8 ÷ 2 = 4
Then:
18 − 4 = 14
Once you understand the pattern, these become much easier.
What If There Are Parentheses?
Parentheses can completely change an answer.
Compare these two expressions:
5 × 5 + 5 ÷ 5 − 5
and:
(5 × 5 + 5) ÷ 5 − 5
They may contain the same numbers and symbols, but the parentheses tell you to group certain operations together.
That's why punctuation in mathematics matters so much.
A pair of parentheses can completely change the structure of an equation.
Don't Let A Viral Puzzle Fool You
The internet is full of mathematical riddles designed to create arguments.
Some are genuinely challenging.
Others are deliberately simple but use unusual formatting to encourage people to make mistakes.
The best response isn't to guess based on what other people are saying.
Write the expression down.
Apply the rules.
Work through it one operation at a time.
That's much more reliable than trusting the first answer that pops into your head.
So, Did You Get It?
Let's return to the original puzzle one final time:
5 × 5 + 5 ÷ 5 − 5
Multiplication:
5 × 5 = 25
Division:
5 ÷ 5 = 1
Then:
25 + 1 − 5
25 + 1 = 26
26 − 5 = 21
So the final answer is:
21
If you answered 21, you followed the standard order of operations correctly.
If you answered 1, don't worry—you simply used the tempting left-to-right approach without applying operation priority.
And that's exactly what makes this little equation such an effective brain teaser.
It isn't really testing whether you know how to multiply, divide, add, or subtract.
It's testing whether you can slow down, recognize the rules, and resist the first answer your brain gives you.
So now comes the real question:
Did you get 21 immediately, or did your brain say 1 before you stopped and checked the order of operations?
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