You've got a question that pops up quite a bit in math, especially when you're first getting the hang of fractions: 'What's 2/3 times 15?' It sounds straightforward, and thankfully, it really is.
Think of it like this: you have a whole, and you're taking a portion of that whole. In this case, the whole is 15, and the portion you're interested in is two-thirds of it. The "times" symbol here is really just a way of saying "of". So, we're looking for "two-thirds of 15".
Reference Material 1 gives us a perfect example with apples. Imagine a box of apples weighing 15 kilograms. If you eat 2/3 of them, how much did you eat? The calculation is simple multiplication: $\frac{2}{3} \times 15$.
To solve this, you can think of 15 as $\frac{15}{1}$. So, the problem becomes $\frac{2}{3} \times \frac{15}{1}$. When you multiply fractions, you multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together.
That gives us $\frac{2 \times 15}{3 \times 1} = \frac{30}{3}$.
And $\frac{30}{3}$ simplifies beautifully to 10. So, if you ate 2/3 of the 15 kilograms of apples, you ate 10 kilograms.
What about what's left? Well, if you started with 15 kilograms and ate 10, you'd have $15 - 10 = 5$ kilograms remaining. Alternatively, if you ate 2/3, then $1 - \frac{2}{3} = \frac{1}{3}$ of the apples are left. And $\frac{1}{3}$ of 15 is $\frac{1}{3} \times 15 = \frac{15}{3} = 5$ kilograms.
So, to recap: 2/3 times 15 equals 10. It's a fundamental concept that opens the door to understanding proportions and parts of a whole, whether you're dealing with apples, ingredients in a recipe, or even statistics in a sports event like the FIBA World Cup mentioned in Reference Material 2 (though that's a different kind of calculation entirely!). The core idea remains: multiplying a fraction by a whole number is about finding a specific portion of that number.
