Solving Water Problems: Fraction Questions Explained in Simple Steps

[Natasha1]

Sarah notices her glass is 6/7 full. She pours 4/5 of its content into an empty jug.

1) What fraction of her glass is then full?

I got 6/35 but cannot remember how. Could someone please explain, i did this ages ago and forgot...

2) Arjun pours the contents of the jug into his glass, which is 4/3 times bigger then Sarah's glass. What fraction of Arjun's glass is then full?

Again I got 18/35 but forgot how I got to that answer...

Any help would be much appreciated.

Many thanks,

Natasha

 

[thelema418]

Probably you should make a visual model of the situation. The hard thing with this type of problem is the concept of a "changing whole." 6/7 is relative to the glass volume as a unit, whereas 4/5 is relative to the amount of water.

 

[Mentallic]

Sarah notices her glass is 6/7 full. She pours 4/5 of its content into an empty jug.

1) What fraction of her glass is then full?

I got 6/35 but cannot remember how. Could someone please explain, i did this ages ago and forgot...

If I have a pie and take away 4/5's of the pie, I'm left with 1/5 of the pie, right? Well what's 1/5 of any value x? That's just x/5 or (1/5)*x which looks like

$$\frac{1}{5}\times x$$

And since in your problem, the value of x=6/7, we then have

$$\frac{1}{5}\times\frac{6}{7}$$

water left in the cup.

2) Arjun pours the contents of the jug into his glass, which is 4/3 times bigger then Sarah's glass. What fraction of Arjun's glass is then full?

Again I got 18/35 but forgot how I got to that answer...

Any help would be much appreciated.

Many thanks,

Natasha

You can figure out how much water is in the jug given the same ideas above, but before we go any further with this problem, can you answer this? If Sarah has a full glass and pours it into Arjun's glass with is 4/3 larger than hers, what fraction of his cup is water?

 

[Natasha1]

Would it be if her glass were to be 7/7 full and pours it in Arjun's glass which is 4/3 times bigger. Would that mean his glass would be now 3/4 full of water?

 

[Natasha1]

Which would mean that 4/5 times 6/7 is 24/35 of water in the glass. But how did I get to 18/35 :(

 

[thelema418]

Which would mean that 4/5 times 6/7 is 24/35 of water in the glass.

No. Again, the whole changes: An amount of water equal to 24/35 of the glass's volume is what you get from that calculation. This is why I think it is important that you draw a picture. Literally divide a piece of paper or something into 7ths. Shade in a portion that represents 6 of those 1/7 units. Then divide that portion into 5ths, etc. Label where everything is going. What pieces of the image answer the original question?

My follow-up question based on your finding of 24/35 is, "How does that relate to your original answer: 6/35 (is the fraction of the glass that is full)?" Again, this is why I think you need to make a picture.

 

[Mentallic]

Would it be if her glass were to be 7/7 full and pours it in Arjun's glass which is 4/3 times bigger. Would that mean his glass would be now 3/4 full of water?

Yes, right! What was the calculation you did to figure that out though? Remember that anything you do will probably need to be understood in a general case because you'll have harder questions to deal with.
If Arjun's glass is x times bigger (x being greater than 1), how full would it be if Sarah's full glass was poured into it? What about Sarah's glass that is a fraction m/n full?

Which would mean that 4/5 times 6/7 is 24/35 of water in the glass. But how did I get to 18/35 :(

That is how much water is in the jug, but now we have to pour that much water into Arjun's glass.

Keep in mind that these values are all in relation to the size of Sarah's cup. 24/35 of water in the jug means 24/35 of Sarah's full glass is in the jug.

 

[thelema418]

Keep in mind that these values are all in relation to the size of Sarah's cup. 18/35 of water in the jug means 18/35 of Sarah's full glass is in the jug.

You mean 24/35 instead of 18/35.

 

[Mentallic]

You mean 24/35 instead of 18/35.

Right, I started copying the wrong value. I edited my previous post.