Video: Estimating the Result of Multiplying Fractions by Whole Numbers

Estimate 4/5 of 9. [A] 2 [B] 12 [C] 8 [D] 3 [E] 4


Video Transcript

Estimate four-fifths of nine. And we’ve got five possible answers to choose from: two, 12, eight, three, and four.

This question is asking us to estimate the value of four-fifths of nine. Why isn’t it asking us to calculate the value of four-fifths of nine? Well, normally, if we’re being asked to find four-fifths of a number, we start by dividing that number by five. This will give us the value of one-fifth. And if we know what one-fifth is worth, we then multiply it by four to find the value of four-fifths. But the trouble is nine isn’t a multiple of five. And so, if we tried to do the first step and divide nine by five we’re not going to get a whole number as an answer. And so, this is why the question is asking us to estimate the value of four-fifths of nine.

There are two ways we can estimate the answer. The first way is to use a little bit of number sense. We know already and we can see from the bar model that four-fifths is nearly one whole. We can ask ourselves which of the five numbers is very nearly nine. Well, straightaway, we can see one number that it definitely isn’t. It’s impossible for four-fifths of a number to be a number greater than that number. So the answer can’t be 12. And out of the remaining numbers, it looks like the number eight might be the number we’re looking for. It’s very close to nine. But it’s not quite one whole.

Another method we could use to estimate four-fifths of nine is to round nine to a number that’s easier to deal with. Nine is very close to 10. Let’s see what happens if we try to find four-fifths of 10. It should give us an answer fairly close to four-fifths of nine. Remember how we described we’re going to find the answer? First, we divide the number by five. And we said the reason we were going to do this was to help us to find one-fifth of the number. 10 divided by five equals two. So one-fifth of 10 is two. We now need to multiply this by the number of fifths we need, which is four. And this will give us the value of four-fifths.

Two multiplied by four or four multiplied by two equals eight. And so, four-fifths of 10 is eight. We’d expect four-fifths of nine to be less than eight, probably between seven and eight. But that’s not one of the choices that we have. So out of our list of five numbers, the best number to estimate is the number eight.

We used two methods to find the answer. The first method we used was to use some number sense. We knew that four-fifths was very nearly one whole. And so, we look for a number that was very near to one whole if we were thinking about the number nine. The number eight was very close to nine. Our second method which we used to check our estimate with was to find four-fifths of a number that was easier to work with. Nine is very close to 10. And so, we calculated four-fifths of 10, which we found was eight.

Out of the numbers we’re given, our best estimate for four-fifths of nine is eight.

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