Math shouldn't be a source of blood pressure spikes. Yet, here we are. You've probably seen it on your feed—that one equation that starts a thousand-comment war between people who haven't opened a textbook since 2005. It looks innocent. It's just 9 divided 3 4, usually written as $9 \div 3(4)$ or maybe even $9/3(4)$. It looks like elementary school homework. It feels like something a calculator should solve in a millisecond. But it isn't just about the numbers; it’s about how we interpret the very language of mathematics.
Honestly, the internet loves a good fight. This specific expression is the perfect bait because it exploits a tiny, dusty corner of our memory where the "Order of Operations" lives.
Why 9 divided 3 4 isn't as simple as it looks
Depending on who you ask, the answer is either 1 or 12. That’s a massive gap for such a small set of numbers. If you take $9 \div 3(4)$ and follow modern PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), you’ll likely land on 12. But wait. If you were taught math a few decades ago, or if you’re a fan of "implied multiplication," you’re screaming at your screen that the answer is 1.
It's about the syntax.
Mathematics is a language, and just like English, it has rules of grammar. In the math world, we call this the Order of Operations. Most of us learned the acronym PEMDAS or BODMAS. But the problem is that these acronyms are often taught poorly. They make it look like multiplication always comes before division because the 'M' is before the 'D.' That's a lie. It’s a flat-out myth that causes half the confusion with 9 divided 3 4.
In reality, multiplication and division are equals. They have the same priority. You solve them from left to right, like you're reading a sentence.
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The case for 12: Modern conventions
Let's break down the logic that leads to 12. It's the "calculator way." If you punch this into a modern Google search bar or a high-end Texas Instruments graphing calculator, you're going to see 12.
First, you look at the parentheses. Inside the parentheses is just the number 4. There’s no operation to perform inside of it, so the parentheses just signify multiplication. Now the expression looks like $9 \div 3 \times 4$.
Following the left-to-right rule:
- $9 \div 3 = 3$
- $3 \times 4 = 12$
Simple. Clean. Done. This is how most modern math curricula in the United States and the UK teach students to handle the problem. If you follow the strict hierarchical rules of modern algebra, 12 is the only logical destination. It’s the standard used in computer science and most engineering fields today.
The case for 1: The "Implicit" argument
Now, let's look at why your smart friend—the one who’s an engineer or a physicist—might insist the answer is 1. They aren't "bad at math." They're using a different convention called multiplication by juxtaposition.
This is the idea that numbers tucked right next to a parenthesis have a stronger bond than a standard division sign. In this view, $3(4)$ is a single term. It’s treated as if it were $(3 \times 4)$.
If you treat it that way:
- $3 \times 4 = 12$
- $9 \div 12 = 0.75$
Wait, that's not 1. To get 1, the problem usually appears as $9 / 3(1+2)$ or something similar. In our specific case of 9 divided 3 4, if the person assumes the 3 and 4 are "stuck" together, they do that multiplication first. If the original problem was actually intended to be written as a fraction with 9 on top and $3(4)$ on the bottom, then $9/12$ or $0.75$ is the result.
But why do some people get 1? Usually, it's because they are misremembering the numbers from a similar viral problem ($9 \div 3(1+2)$). In that version, the $1+2$ equals 3, and then $3 \times 3$ is 9. $9 \div 9 = 1$.
The nuance here is that "implied multiplication" is actually common in high-level physics and chemistry journals. If you see $1/2b$ in a textbook, most scientists assume it means $1 / (2 \times b)$, not $(1/2) \times b$. This is why the 9 divided 3 4 debate never truly dies. It's a conflict between "school math" and "professional shorthand."
The ambiguity of the obelus
The division symbol ($\div$), known as the obelus, is actually part of the problem. You rarely see it in high-level mathematics. Once you get past middle school, everything is written as fractions. Fractions are great because they have a clear "top" and "bottom." There is no ambiguity.
If you write 9 over 3, and then put the 4 next to it, it’s 12.
If you write 9 over the product of 3 and 4, it’s 0.75.
The obelus is a clunky, historical relic that creates these "gotcha" moments. It's why math professors generally hate these viral memes. They aren't testing your math skills; they're testing your ability to guess what the person who wrote the poorly formatted question was thinking.
How to actually solve these in the real world
If you’re ever in a situation where you need to program this into a spreadsheet or write code, you can’t afford to be ambiguous. Excel doesn't care about your feelings or how you were taught in 1994.
To ensure accuracy:
- Use nested parentheses. If you want the multiplication to happen first, write $9 / (3 \times 4)$.
- Follow the software logic. Most coding languages (Python, C++, Java) will treat 9 divided 3 4 by doing the division first.
- Avoid the obelus. Use the forward slash (/) or, better yet, clear fractional notation.
Mathematics is supposed to be the universal language, but the way we write it can be surprisingly messy. The 9 divided 3 4 problem is a reminder that even in a world of absolute truths, communication matters. If the person reading your work can interpret it in two different ways, the fault isn't with their math—it's with your "grammar."
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Next time you see this on Facebook, don't get into a fight. Just realize that both sides are usually following a specific set of rules; they're just playing from different rulebooks. If you want to be strictly correct by modern academic standards, 12 is your winner. If you're looking at it through the lens of historical "implied" multiplication, you'll see why people get stuck.
To stay sharp, always prioritize operations inside brackets first, then handle multiplication and division strictly from left to right. This keeps your calculations consistent with modern computing and standardized testing. If you're building a spreadsheet, double-wrap your denominators in parentheses to prevent the software from splitting your terms. Accuracy in math is 50% calculation and 50% clear formatting.