The ratio of yellow to green buttons in a bag is 4 : 7. (a) What fraction of the buttons in the bag are green? Circle your answer. 4/7, 7/4, 4/11, 7/11. (b) A second bag contains exactly 50 buttons. 60% of the buttons are blue. Calculate how many blue buttons are in the bag.
Let’s go back to part a. We have a bag full of buttons, that is, four parts yellow for every seven part green, for a total of 11 parts. If we draw four parts yellow, but remember each yellow dot just represents one part. We don’t actually know how many buttons are in this bag. The same thing goes for the green parts. Each green button represents one part green. Four parts yellow, seven parts green are total of 11 parts.
Now we need to decide for what our question is asking us to do. It wants to know what fraction of the buttons are green. We know that there seven parts green. In this statement, “of the buttons” means that we will consider how many are green out of the total parts. There are seven green parts out of a total of 11 parts. And that means our fraction will be seven over 11.
We can consider the other three choices. The first fraction, four-sevenths, represent the parts of yellow over the parts of green. Seven-fourths represents the green parts to the yellow parts. Four over 11 show the yellow parts out of the total. And again, seven over 11 represents the green parts out of the total, which is what we’re looking for.
Now let’s look at part b. A second bag contains exactly 50 buttons. 60 percent of the buttons are blue. Calculate how many blue buttons there are in the bag. In our second bag, there are 50 buttons. And 60 percent of the 50 buttons are blue. We need to calculate what 60 percent of 50 is equal to.
10 percent of 50 is something we could easily calculate. We remember that the word “of” means multiply. 10 percent of 50 is 10 percent times 50, and that equals five. We can also multiply 10 percent by six to give a 60 percent. And five times six equals 30, which tells us that 60 percent of 50 must equal 30. And that means 30 of the buttons are blue. In our bag of 50 buttons, 30 are blue and 20 are another color.
Let’s look at one other way to solve this problem. Instead of leaving 60 percent in percent form, we could write it as a fraction, 60 over 100. We would still need to multiply this fraction, 60 over 100, by 50. If we did that, we could say that 60 over 100 simplifies to six over 10. Now we have six over 10 times 50. But 50 divided by 10 equals five. We now have six times five equals 30. 60 over 100 times 50 equals 30. This is another way to show and confirm that there were 30 blue buttons in the second bag.