One day, a flock of birds flew for two and three-quarter hours. The next day, they flew for three and four-fifths hours. How many hours did the birds fly for in total?
To find the total number of hours that the birds flew for, we need to add together two and three-quarter hours and three and four-fifths hours. At the moment, these fractions both have different denominators. We have an amount of quarters and an amount of fifths. Before we can add these two numbers together, we need to make sure that the denominators are the same. We need to find a number which we can divide by four and by five. 20 can be divided by four and five. To get from four to 20, we need to multiply by five. We need to do the same to the number on top, the numerator. What is three multiplied by five? 15.
We don’t need to do anything to the whole number, number two. Two and three-quarters is equal to two and fifteen twentieths. Similarly, we don’t need to do anything to the three, the whole number. We can just add the whole numbers together, two and three. To get from five to 20, we had to multiply by four. And so, we need to do the same to the numerator. Four multiplied by four gives us sixteen twentieths. Oh, now we can add our two numbers together because the denominators in our fractions are the same.
First, we can add the whole numbers. Two plus three equals five. And now, we need to add the twentieths. We have fifteen twentieths and sixteen twentieths. How many twentieths do we have altogether? 16 plus 15 equals 31. Thirty-one twentieths is an improper fraction. It’s top heavy; the number on the top, the numerator, is heavier or larger than the number on the bottom. 31 is more than 20. This means, our fraction is worth more than one. So, we can exchange twenty twentieths for one whole, which means now we have six. And because we exchanged 20 of our twentieths, we no longer have thirty-one twentieths. We have 11. 31 subtract 20 is 11.
If a flock of birds flew for two and three-quarter hours on one day and on the next day flew for three and four-fifths hours, the total number of hours the birds flew is six and eleven twentieths hours. We added together our two fractions. Because the denominators were different, we had to change the fractions to make the denominators the same. Then, we were able to add the two fractions together, which gave us a total of five and thirty-one twentieths. But this is an improper fraction. So, we simplified it to six and eleven twentieths. The total number of hours the birds flew is six and eleven twentieths hours.