It's funny how a simple mathematical phrase can sometimes feel like a riddle, isn't it? "12 divided by 2/3." On the surface, it looks straightforward, but the way we interpret "divided by" is key to unlocking the answer. Think of it like a friendly conversation about numbers. When we say "A divided by B," we're essentially saying "A is being split up by B." In mathematical terms, this translates directly to A ÷ B.
So, when we encounter "12 divided by 2/3," the "12" is our dividend – the number being divided. And "2/3" is our divisor – the number doing the dividing. This means the expression is equivalent to 12 ÷ (2/3).
Now, dividing by a fraction might seem a bit tricky at first. But there's a neat trick to it: dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 2/3 is simply 3/2 (you just flip the numerator and denominator).
So, our problem transforms from 12 ÷ (2/3) into 12 × (3/2).
Let's break that down. We can think of 12 as 12/1. So, we have (12/1) × (3/2). To multiply fractions, we multiply the numerators together and the denominators together: (12 × 3) / (1 × 2) = 36 / 2.
And 36 divided by 2? That gives us a nice, clean 18.
It's a good reminder that even in the world of numbers, understanding the language we use is crucial. Just like in any conversation, clarity in expression prevents misunderstandings. Whether it's a simple "divided by" or a more complex fraction, knowing the roles each number plays helps us navigate the calculation smoothly. It’s a little bit of math, a little bit of language, all working together.
