Find the value of one over 𝑥𝑦𝑧 given 𝑥 equals four-thirds, 𝑦 equals three- halves, or three over two, and 𝑧 equals negative five.
The first thing to do is look at our expression. We’ve got one over 𝑥𝑦𝑧, but what does that one over 𝑥𝑦𝑧 mean? Well it means one divided by 𝑥𝑦𝑧, and 𝑥𝑦𝑧 means 𝑥 multiplied by 𝑦 multiplied by 𝑧. Okay, so now we know what that means, we want to actually substitute in our values for 𝑥, 𝑦, and 𝑧.
So when we actually substitute in our values, we’re gonna have one divided by, and I’ve written it this way rather than one over because actually it gets bit untidy when we’ve got one over and then fractions, and then four over three multiplied by three over two and then multiplied by negative five over one because it’s just negative five, but we can write negative five as negative five over one just so we’ve actually got three fractions here.
And just to remind us of one of our rules of operations of fractions, which is going to help us here, if we multiply two fractions together, then all we do is multiply the numerators and denominators. And this works the same if we have three together. So for instance, if we had 𝑎 over 𝑏 multiplied by 𝑐 over 𝑑, it would be equal to 𝑎𝑐 over 𝑏𝑑.
So therefore, we’re gonna have one divided by, then we’re gonna have the numerators multiplied together, so four multiplied by three multiplied by negative five, and then the denominators multiplied together, three multiplied by two multiplied by one.
So then we’re gonna have one divided by negative 60 over six. So therefore, what we can do is actually divide negative 60 and six by six because it actually goes into both negative 60 and six. And when we do that, we’ll have one divided by negative 10. So therefore, we can say that the value of one over 𝑥𝑦𝑧 given that 𝑥 is equal to four-thirds, 𝑦 equals three-halves, and 𝑧 equals negative five is going to be equal to negative one over 10 or negative one-tenth.
And that’s cause we had one divided by negative 10. Well one divided by 10 is one-tenth, and it’s negative, so we get negative one-tenth.