It's easy to get a little turned around when you see fractions and multiplication mixed together. The query "4/3 times 2" might look a bit like a puzzle at first glance, especially if you've recently been diving into more complex math concepts like multiples and factors, as some of the reference materials suggest. But let's break it down, shall we?
At its heart, this is a straightforward multiplication problem. We have a fraction, 4/3, and we're being asked to multiply it by a whole number, 2. Think of it like having four-thirds of something, and then wanting to double that amount. How do we do that?
When multiplying a fraction by a whole number, the simplest way to approach it is to treat the whole number as a fraction itself. So, 2 can be written as 2/1. Now our problem looks like this: (4/3) * (2/1).
Multiplying fractions is pretty intuitive: you multiply the numerators (the top numbers) together, and you multiply the denominators (the bottom numbers) together. So, in our case:
Numerator: 4 * 2 = 8 Denominator: 3 * 1 = 3
Putting it all together, we get 8/3.
Now, 8/3 is a perfectly correct answer. It's an improper fraction because the numerator is larger than the denominator. Sometimes, depending on the context or what's being asked, you might want to convert this into a mixed number. To do that, you'd ask yourself, 'How many times does 3 go into 8?' It goes in 2 times (because 3 * 2 = 6), with a remainder of 2 (8 - 6 = 2). So, 8/3 is the same as 2 and 2/3.
It's interesting how sometimes the simplest questions can lead us to think about related concepts. For instance, the reference materials touch upon multiples and factors. If we were looking at multiples of 4, we'd list numbers like 4, 8, 12, 16, and so on. Factors of 36, on the other hand, are numbers that divide evenly into 36, like 1, 2, 3, 4, 6, 9, 12, 18, and 36. While these are important mathematical ideas, they don't directly apply to solving '4/3 times 2'. That problem is purely about fraction multiplication.
Another reference shows a series of calculations, including mixed operations like (15+35) * 6 or 32 + 17 * 3. These highlight the order of operations (PEMDAS/BODMAS), where multiplication and division are done before addition and subtraction, and parentheses are handled first. Our problem, '4/3 times 2', is simpler as it only involves one type of operation: multiplication. There are no parentheses or mixed operations to worry about.
So, to circle back to the original query, '4/3 times 2' is simply 8/3, or 2 and 2/3. It's a good reminder that even in mathematics, sometimes the most direct path is the clearest, and a little bit of step-by-step thinking can make any calculation feel manageable.
