In Mr. Smith's class, what is the ratio of the number of boy

rajatbanik, this is an idiom that many people struggle with. The first quantity named will always be the larger one. So if I say "There are three times as many girls as boys," then there are more girls. If I say "there are twice as many apples as bananas," then there are more apples.

To turn this into an equation, put the quantities on either side of the equal sign before deciding where to attach numbers:

g = b a = b

If you go in the stated order, the first quantity will be larger. So, to make the two equations equal, you need to multiply the smaller quantity by the stated amount.

g = 3b a = 2b

Now the equations fit the statements. There are three times as many girls as boys, so we need to triple the boys to make the quantities equal. There are twice as many apples as bananas, so we need to double the bananas to make them equal.

Notice that the sides get flipped if we use a fraction less than 1. For instance, the statement "There are 1/3 as many cars as bicycles" means that there are fewer cars. Now the first quantity in our equation is smaller:

c = b

To make the two sides equal, we need to attach 1/3 to the larger quantity

c = 1/3 b

There are 1/3 as many cars as bicycles, so only 1/3 of the bicycles would equal the number of cars.

I hope this helped. Let me know if I can clarify.