**Singapore Workbook 6A Help Needed!**

Hi Amy,Amy C. wrote:I need help on a problem from the Singapore 6A WB, please.

My 8th grader (not the one doing the Singapore 6A but who did Singapore up through 6th grade and is now doing Saxon) figured out how to do #23 using fractions. Very smart of him actually. Good to know that he is learning something! It is times like these that make all the hard work (and sometimes tears) worth it! Makes a mama proud!

- Review 3 Problem # 23: The ratio of the number of boys to the number of girls in a hall was 3:2 at first. After 30 boys left the hall, the ratio became 2:3. How many boys were there in the hall at first?

If anyone has a different way of doing this problem (like using bar diagrams) and would like to share, please do. I can't help but think there's not a different "Singapore" way of doing it that we are just not seeing.

Gotta love Singapore. It really makes us think! Sometimes it takes the whole family!

Amy C.

It's fun for me to keep my math sharp, so I took a peek in my son's old 6A workbook.

- The ratio of the number of boys to the number of girls in a hall was 3:2 at first. After 30 boys left the hall, the ratio became 2:3. How many boys were there in the hall at first?

3:2

2:3

And all we know is that we lost 30 boys

And I guess it's good to notice again that the ratios are "boys:girls," so the 30 are lost from the left side

To compare ratios, it would help to have one side the same in both cases. Sort-of a common denominator. So that would probably be 6. We want to put the common "six" on the right, because the girls never change. If we make the left sides the same, then it will be strange and not helpful, because it will "appear" like the boys stayed the same.

So, 3:2 can be 9:6, because that's the same ratio as 3:2, right?

And 2:3 can be 4:6, because that's also the same as 2:3.

Now, we have these 2:

9:6

4:6

And what else do we know? The difference is 30 boys left the first group. So the "5" that's missing from the second ratio is equal to 30 boys.

If that's so, then "1" in the ratio would be equal to 6 boys, right? (We could draw this out with bars, if it helps.)

So the original amount was 9 (x6) and 6 (x6), does that make sense?

And before we do all that hard math (LOL), let's see "exactly" what we need...

(we only want to do the calculations we really need!)

We just need to know how many boys in the first group.

So the math is 9x6 (answer 54).

Does my thinking make any sense at all? All my son wrote in his workbook was "9:6 4:6 54" so he either did it a faster way or did it in his head (which he often does - he doesn't like pencils ).

Julie