A machine produces 105 parts in five minutes. At this rate, how many parts can it produce in 17 minutes?
The machine produces 105 parts in five minutes. We can set up a proportion like this: 105 parts in five minutes. We know that the machine is going to keep the same rate. One thing that we could do to solve this problem is find out how many parts are made every minute. If 105 parts are made in five minutes, then how many parts are made in one minute?
If we divide a denominator by five, we have to divide the numerator by five. 105 divided by five equals 21. We now know that our machine makes 21 parts every minute. At this rate, how many parts would be made in 17 minutes? We could multiply the denominator by 17. And that means we would need to multiply the numerator by 17. Multiplying 21 by 17, seven times one equals seven. Seven times two equals 14. Now, one times one equals one. And one times two equals two.
We take our two partial products and add them together. Seven plus zero equals seven. Four plus one equals five. One plus two equals three. 21 times 17 equals 357. And that tells us that 357 parts can be made in 17 minutes.