Express the following ratio as a unit rate: 136 dollars for eight books.
Working out the unit rate means that we need to work out the cost of one item, in this case the cost of one book. As eight books cost 136 dollars, we need to divide 136 by eight. One way of calculating this is using the bus stop method. We put 136 underneath the bus stop and eight outside. Eight does not divide into one. So we put a zero above the bus stop and carry the one.
13 divided by eight is equal to one remainder five. So we put one above the bus stop and carry the five. Finally, 56 divided by eight is equal to seven. This means that the answer to 136 divided by eight is equal to 17. We can therefore say that the unit rate is 17 dollars per book.
We will also show an alternative method for calculating the unit rate. We know from the question that eight books cost 136 dollars. One-half of eight is four. Therefore, we can calculate the cost of four books by dividing by two. 136 divided by two or a half of 136 is equal to 68. Therefore, four books would cost 68 dollars.
We can halve this again to calculate the cost of two books. One-half of four is equal to two. And a half of 68 dollars is equal to 34 dollars. Therefore, two books would cost 34 dollars. We can halve this one more time to find the cost of one book. One-half of 34 or 34 divided by two is equal to 17.
We have once again proved that the unit rate for one book was equal to 17 dollars.