Help needed with a math problem, please

[runamuk]

We're using MUS Epsilon and we're on Chapter 10 - Dividing fractions. Fractions were never my strong point, but until now the video and the TM have made teaching them quite easy. But now I'm stuck.

 

The problem is stated as:

 

Nathan did 1/5 of the job, but only 2/3 of what he did was done correctly. What part of the job was done correctly?

 

I think I would divide the 1/5 of the job he did by 2/3, to find the portion of the 1/5 done correctly. I want to find out what fraction of 1/5, correct? Wouldn't I need to divide that 1/5 into thirds to find out what portion he did correctly?

 

The book answers shows 1/5 being multiplied by 2/3.

 

I would like to know why the problem is multiplied and not divided. There are several other problems in this chapter that we're having trouble with as well. I'd like to be able to explain to my daughter how to determine when to multiply and when to divide.

[Ali in OR]

Quick insufficient answer:

 

"of" usually means multiplication in a word problem. "1/2 of 10" means 1/2 x 10 which is 5. So 1/5 of 2/3 is 1/5 x 2/3.

[LauraGB]

You would multiply because the mathmatical sign for the word "of" is "x", or the multiplication sign. So, you would say he did 2/3 of 1/5, or 2/3 x 1/5.

[joannqn]

Try using the manipulatives or drawing it out so you can see it, too.

 

If you draw a square to represent the job, then divide it into five parts vertically, and color in one part to represent the part he did. Then divide it into three parts horizontally, which divides the job into 15 parts. The part he did correctly is two of the three horizontal sections. Now, you'll see that the colored parts done correctly is 2/15.

[AndyJoy]

I just wanted to add that you are correct that you are dividing 1/5 into thirds, then taking 2 of them. Multiplying by 2/3 is just the one-step way to do this.

 

When you split something into thirds, you divide by 3 or multiply by 1/3, right? This gives you 1/15, which is 1/3 of 1/5 (1/15+1/15+1/15=1/5). Then, since you want to know what 2/3 of 1/5 is, you would need to take two 1/3 portions of 1/5 and add them together or multiply by two. (1/15 + 1/15= 2/15 or 1/15 X 2 = 2/15). Multiplying by 2/3 just simplifies multiplying by 2 and dividing by 3 into one step.

Edited January 8, 2010 by AndyJoy
typo

[Parrothead]

I would like to know why the problem is multiplied and not divided. There are several other problems in this chapter that we're having trouble with as well. I'd like to be able to explain to my daughter how to determine when to multiply and when to divide.

What the others said about of=multiply.

 

You aren't alone in the dividing fractions. This is the first time dd has been totally confused by Mr. Demme's teaching. It got to the point with the dividing the fractions, I told her to just do what he said not to do. It has become common to hear the words "flip that sucker and multiply" around here during math.

 

Dd is just finishing chapter16.

[Tap]

dividing would tell you 'how many 2/3 are in 1/5" you don't want to know that.

 

multiplying would tell you "what is 2/3 of 1/5". Or if you break 1/5 into 3 pieces, what fraction is 2 of those pieces worth.

 

If you still want to divide you could divide 1/5 into 3 pieces, and then multiply that answer by 2. But if you keep it as fraction in the first place, you can skip this step and just multiply (the fraction bar takes place of the division step).

[runamuk]

Thank you for all of the replies! The different explanations really helped me to see the "why" of the problem. I'm printing this out and taping it to the front of my TM.