Let's talk about a common point of confusion in math: dividing by a fraction. Specifically, we're looking at the problem: 3 divided by 2/3.
When you see a division problem like this, especially with fractions, it's easy to feel a bit lost. But there's a neat trick that makes it much simpler. Remember that dividing by a number is the same as multiplying by its reciprocal. The reciprocal of a fraction is just that fraction flipped upside down.
So, for our problem, 3 divided by 2/3, we first need to find the reciprocal of 2/3. Flip it over, and you get 3/2.
Now, we can rewrite the original problem as a multiplication problem: 3 multiplied by 3/2.
To multiply a whole number by a fraction, you can think of the whole number as a fraction too. So, 3 becomes 3/1.
Now we have (3/1) * (3/2). To multiply fractions, you simply multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together.
3 * 3 = 9 1 * 2 = 2
So, the result is 9/2.
This fraction, 9/2, is an improper fraction because the numerator is larger than the denominator. You can leave it as is, or you can convert it to a mixed number. To do that, you divide 9 by 2. It goes in 4 times with a remainder of 1. So, as a mixed number, it's 4 and 1/2.
It's fascinating how a seemingly complex division problem can be simplified with a fundamental rule of fractions. It’s a bit like finding a hidden shortcut on a familiar path, isn't it? This principle applies to all sorts of fraction division, making those problems much more approachable.
