A little math help please

[newlifemom]

Okay, the problem in dd Saxon 6/5 book states:

 

Draw a circle. Shade all but 1/6 of it. What percent of the circle is shaded?

 

 

Now I can see in her book where she has learned this, but only when the denominator can be turned into 100. We have the answer, and I could get it myself. (It would be ugly and I wouldn't be able to explain it mind you. :tongue_smilie:) So bearing in mind the level of math she is doing. What are the steps she is supposed to be taking? Please be kind and use small words so I am sure to understand. :D

 

TIA!

[Julie in Austin]

We use Horizons, not Saxon, but are in the 6th grade book and did cross-multiplying today, so here's how we'd do that problem:

 

If you shade "all but 1/6," then you have shaded 5/6. Set up the fractions so you can cross-multiply:

 

5 N

--- = ---

6 100

 

(The reason we put 100 in the second denominator is so we'll be able to convert it easily to a percentage.)

 

Then we cross-multiply and say:

 

5 times 100 equals 6 times N

 

or

 

500 = 6 x N

 

So we divide each side by 6 and we get

 

83 and 1/3 equals N.

 

So the answer is 83.3%

 

ETA: OK, so my formatting didn't work. I was trying to show "5 over 6 is equal to N over 100."

[Ellie]

We use Horizons, not Saxon, but are in the 6th grade book and did cross-multiplying today, so here's how we'd do that problem:

 

If you shade "all but 1/6," then you have shaded 5/6. Set up the fractions so you can cross-multiply:

 

5 N

--- = ---

6 100

 

(The reason we put 100 in the second denominator is so we'll be able to convert it easily to a percentage.)

 

Then we cross-multiply and say:

 

5 times 100 equals 6 times N

 

or

 

500 = 6 x N

 

So we divide each side by 6 and we get

 

83 and 1/3 equals N.

 

So the answer is 83.3%

 

ETA: OK, so my formatting didn't work. I was trying to show "5 over 6 is equal to N over 100."

Julie! You made my head spin!! Why not just divide 5 by 6?? Wouldn't that just be simpler??

[Marylou]

Julie! You made my head spin!! Why not just divide 5 by 6?? Wouldn't that just be simpler??

 

 

Very, very funny :sneaky2:

[Carol in Cal.]

Very, very funny :sneaky2:

 

5 divided by 6 gives you the decimal fraction, and then you multiply by 100 to get the percent.

 

Cross multiplying is also correct, but takes a longer.

[newlifemom]

Julie! You made my head spin!! Why not just divide 5 by 6?? Wouldn't that just be simpler??

 

 

Exactly, but they haven't taught that yet. This is the reason why I could not do it. I can hack my way through, but remember, Saxon is a spiral approach, for better or worse.:D Thanks for the help.

[Nestof3]

Do you have the Saxon version that sends you to the math lesson? There should be a lesson # next to the problem. Usually, Saxon will not expect a student to do this in a problem set unless the lesson has been taught.

 

And, yes, you just divide 5 by 6 and multiply by 100 because it's "per cent" or "per 100." But, it seems this would have been talked about in the lesson.

[usetoschool]

We are using the same book and just did those the other day and I was a little confused about how they wanted her to solve it. The (very brief) explanation is on pg. 178 of our edition of the book. They just have you divide 100% by the denominator of the fraction to figure the percent. Two pages later the sample problem involves 7ths which creates a big long decimal...and makes things confusing - at what point do you stop dividing because it never mentions that in the book. You have to assume it is after the three places needed to create the percent and the fraction.

 

I am assuming the point of the lesson is to become familiar with converting fractions to percents because it refers you back to two lessons about picturing fractions, so I just took the opportunity to explain that a fraction is really just a division problem. 5/6ths is 5 divided by 6 which is less than one obviously, and the answer is .833333... (which creates another thing to explain, that continuing decimal - I wish they had picked easier examples to start with like 1/2 - it is easy to see that it is 50%!). .833 is 833/100ths, percents (cent = hundred) is just the amount per hundred so it is 83 1/3 percent.

 

The concept is simple but the explanation in the book isn't very good in my opinion. It just says, here do this...divide 100 by 3 without much explanation of why. Some fraction/percent relationships are easy to picture like 1/2 and 50%, 1/4 and 25%. Maybe it will help her is you use some simpler examples and think about it in terms of money - 25 cents is .25 is 1/4 of a dollor is 25% (25 out of 100 cents).

 

More confused now? :001_huh:

[newlifemom]

Do you have the Saxon version that sends you to the math lesson? There should be a lesson # next to the problem. Usually, Saxon will not expect a student to do this in a problem set unless the lesson has been taught.

 

And, yes, you just divide 5 by 6 and multiply by 100 because it's "per cent" or "per 100." But, it seems this would have been talked about in the lesson.

 

Yes, it sent me back to the first lesson(almost 80 lessons prior) However, those were 'pretty' problems that made the switch to 100 easily. This one did not and I have looked long and hard and cannot find where this component was taught. However, it seems that I was looking incorrectly and now maybe I could find that lesson. I do want to make sure dd understanding understands this fully. Thanks for all the help.

[Catwoman]

Okay, the problem in dd Saxon 6/5 book states:

 

Draw a circle. Shade all but 1/6 of it. What percent of the circle is shaded?

 

Are you sure they want your dd to get complicated about this? I would think that in an elementary level math book, you're supposed to think something along the lines of, "If all but 1/6 is shaded, how many sixths are there in total? Ok, there would be 6 sixths. So... 6/6 - 1/6 = 5/6, so 5/6 of the circle is shaded."

 

OTOH, there's probably some frighteningly complex way to solve the same problem in a quick and easy 19 steps... ;)

 

Cat

Edited May 12, 2009 by Catwoman
Some day I will type an entire post without a typo... but not today! ;)