Helping grandson

Question

If 1/6 is 1/2 of 3/4 of a certain number what is that number

Answer 1

These questions are usually a lot easier to answer once we've "translated" them from words into a math expression or equation!

Some "translations" that can be used are things like "is" meaning "=", or "of" meaning "×" or "•" (multiplication), and usually when the question asks about "a certain number" they're asking you to consider that like a variable -- we can use "K", for your name :)

So let's look at the word problem:

1/6 is 1/2 of 3/4 of a certain number

and let's go ahead and replace those English words with the translations I mentioned above:

1/6 = 1/2 × 3/4 × K

First, let's simplify. Our right-hand side has only multiplication operations, so we don't have to worry about order of operations; we can just do them in order. The first multiplication is 1/2 × 3/4. If your grandson is allowed to use a calculator, he might come up with the answer 0.375, or if he chooses to multiply and simplify the fractions he might get 3/8. I'm going to stick with 3/8, as I think that's what most teachers would want for this problem. So, we can rewrite our equation with the new right-hand side:

1/6 = 3/8 × K

Now, to get K by itself (because we want to know, what does K = ? Or, what = K ?), we have to "peel off" that 3/8 from that side. We divide both sides by 3/8 (if you're confused here, let me know! I'm skipping over some of the "why" so you don't have a lot to read) and that gives us the new form:

(1/6) ÷ 3/8 = (3/8 × K) ÷ 3/8

And we know our right-hand side is going to simplify to just K, because that's the whole reason we divided by 3/8 in the first place, so now:

1/6 ÷ 3/8 = K

Alright, so K = 1/6 ÷ 3/8. Again, if your grandson is allowed to use a calculator, and knows how to enter this expression in so that Order of Operations is followed, then he'll get 0.4444 repeating. Or, if he needs to manually find the answer, he can divide the fractions out by hand. If you have trouble with this part, or any part of this explanation, let me know and I'll be happy to go into more detail!