Video: Solving Word Problems by Multiplying Fractions by Whole Numbers

If you exercise every day for 2/3 of an hour, how many hours would you spend exercising every week?

02:29

Video Transcript

If you exercise everyday for two thirds of an hour, how many hours would you spend exercising every week?

We know that a week is made up of seven days, although if we exercise for two-thirds of an hour in a whole week, we’ll have exercised seven lots of two-thirds. This is what we need to do to find the answer, work out seven multiplied by two-thirds. Here is one lot of two-thirds. But how many thirds will we have if we have seven lots of two-thirds instead. To work out the answer, we keep the denominator the same. We’re still talking about thirds. And then we multiply the numerator by the number seven. So seven lots of two-thirds equals fourteen-thirds.

This is an improper fraction. It’s more than a whole because the numerator is larger than the denominator. We could give the answer fourteen-thirds of an hour. But it might be best if we convert this into a mixed number. We know three-thirds make a whole. And if we divide 14 by three, we get four because four threes are 12. And then two left over. So we got a remainder of two. This is the same as four in two-thirds hours. We can also show the answer using a diagram. One times two-thirds, two times two-thirds, three lots of two-thirds, four, five, six lots of two-thirds, and seven lots of two-thirds. This is the same as four whole hours and two-thirds of an hour.

So the answer is four and two-thirds of an hour. And so if we exercise everyday for two-thirds of an hour, we need to multiply this by seven to find out the number of hours we’ll spend exercising every week. We found the answer was fourteen-thirds of an hour. And so we used our knowledge of fractions to change this improper fraction into a mixed number. The number of hours that we’ll spend exercising every week is four and two-thirds of an hour.

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