Video: Interpreting and Computing Partitive Division of a Fraction by a Fraction of Different Denominator

Jacob practices his trumpet for 20 minutes per day. His trumpet teacher said it is only two-thirds of the daily practice required at his level. How long should he practice every day?

02:17

Video Transcript

Jacob practices his trumpet for 20 minutes per day. His trumpet teacher said it is only two-thirds of the daily practice required at his level. How long should he practice each day?

The first piece of information that we’re told in this problem is that Jacob practices his trumpet for 20 minutes every day. Let’s draw a bar to represent this fact. There we are, and we’ll label it 20 minutes. This represents the length of time that Jacob spends every day practicing his trumpet. But the problem tells us that Jacob isn’t practicing as much as he should be. According to his trumpet teacher, Jacob is only practicing two-thirds of the daily practice that’s required at his level. He’s not practicing enough.

The question asks us to find how long Jacob should be practicing each day. So, as we’ve just discussed, Jacob is practicing two-thirds of the amount that he should be practicing every day. To find the full amount that Jacob needs to be practicing, we need to calculate three-thirds. And to do this, we can use what we know to find what one-third of the daily amount is.

If two-thirds of the daily amount is 20 minutes, then dividing 20 by two or finding half of 20 will be a way to find what one-third of the daily practice should be. 20 divided by two equals 10. So, we can say that one-third of the amount that Jacob needs to practice every day is 10 minutes. Now that we know what one-third of this amount is, we can calculate the whole amount. Three times 10 equals 30.

Because we know that Jacob’s practice of 20 minutes every day is two-thirds of the daily practice that he needs to do, we worked out that one-third of the amount he needs to do is 10 minutes every day. And then, we used this fact to find out the total amount that he needs to do every day. Jacob needs to be practicing his trumpet for another 10 minutes. The amount of time that Jacob should be practicing every day is 30 minutes.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.