# Video: Solving Problems Involving Percentage

Estimate seventy-eight percent of thirty.

02:23

### Video Transcript

Estimate 78 percent of 30.

So we want to estimate 78 percent of 30. Well, 100 percent of 30 would be the whole thing, so it will be equal to 30. 50 percent of 30 will be exactly half of that, and half of 30 is 15.

Now 75 percent of 30 would be somewhere in the middle because 75 percent is exactly halfway between 50 percent and 100 percent. So what number is halfway between 15 and 30? Well, exactly halfway would be 22.5, so close to 23.

So if we were asked to find 78 percent of 30, let’s see where 78 percent would lie between 100 percent, 75 percent, and 50 percent. 78 percent would be just above 75 percent. So we would want to estimate the number that’s close to 22.5, but it’s above it, so possibly 24, because 78 is very close to 75 and it’s pretty far away from 100 percent. So we want the number to be pretty close to 22.5, yet kind of far away from 30.

Another way that we could estimate this number: 78 percent is really close to 80 percent. And 80 percent of 30 we can actually find because the word “of” in mathematics means to multiply. And 80 percent we can change to a decimal. We drop the percent sign, and then we’ll move the decimal place two places to the left.

Now we can either do that here or do it in our answer. So if we would multiply 80 times 30, well, eight times three is 24, and then we have two zeros. So it’s equal to 2400. Now like we said though, since 80 was a percent and we needed to move the decimal point two places to the left, we have to do that in our answer if we didn’t do it with the 80. So we have our decimal point, and we move it one, two. So now we have 24.0, which is what we’d estimated before. So after estimating 78 percent of 30, we get an answer of 24.