# Question: Fraction with Many Operations

## Comment on Fraction with Many Operations

### I don't get it. When you

I don't get it. When you subtract 59/124-8/15 and 8/15-59/124,can't we just cancel them out? Giving us an answer of D?I'm a bit confused.

### Be careful. 59/124 - 8/15 is

Be careful. 59/124 - 8/15 is not equal to 8/15 - 59/124

If this were a sum, then it WOULD be true that 59/124 - 8/15 = 8/15 - 59/124

However, in the question we are dealing with subtraction.

Here's a different example: 5 - 1 does not equal 1 - 5

Does that help?

Cheers,
Brent

### do i have the calculator

do i have the calculator always in the quant sections?

Yes, you will have access to an onscreen calculator on the test. It's pretty clunky though. Here's the video on how it works: https://www.greenlighttestprep.com/module/general-gre-info-and-strategie...

### after subtract 411/811, I

After we subtract 411/811, we can rewrite quantity B as -1(59/124 -8/15)
Then, if we divide both quantities by (59/124 - 8/15) we get quantity A = 1 and Quantity B = -1
So, quantity A should be greater than B?

### When you divide both

That's a great idea!

However, when you divide both quantities by (59/124 - 8/15), you are breaking a fundamental rule when it comes to the Matching Operations strategy (covered here: https://www.greenlighttestprep.com/module/gre-quantitative-comparison/vi...)

IMPORTANT: (59/124 - 8/15) is NEGATIVE
So, when you divide both quantities by (59/124 - 8/15), you are dividing both sides by a NEGATIVE value, which is not allowed.

Cheers,
Brent

### How is 8/15 greater than 1/2

How is 8/15 greater than 1/2

### There are a few ways to show

There are a few ways to show that 8/15 is greater than 1/2

APPROACH #1 - number sense
7.5/15 = 1/2, so 8/15 must be greater than 1/2

APPROACH #2 - Use long division to convert each fraction to a decimal
1/2 = 0.5
8/15 = 0.53333.....
Since 0.53333 is greater than 0.5, we know that 8/15 is greater than 1/2.

APPROACH #2 - find common denominators
1/2 = 15/30
8/15 = 16/30
Since 16/30 is greater than 15/30, we know that 8/15 is greater than 1/2.

Cheers,
Brent

### I did not think to simplify

I did not think to simplify the 5/15 until the end. I calculated until I got 2 fractions.

My first step was to cancel out the 411/811 from QA and QB. I was left with
QA: [(59/124)-(8/15)]/1/3 and QB: [(8/15)-(59/124)]/5/15.

From there, I got
QA: [(59-8)/1860]/1/3 and QB: [(8-59)/1860]/5/15.

From there, I got QA: (51/1860)/1/3 and QB: (-51/1860)/5/15.

Lastly, QA: 51/1860 x 3/1 = 153/1860 and QB: -51/1860 x 3/1 = -153/1860.

Answer: QA is greater, QB is negative. Where did I go wrong besides simplifying the 5/15 to 1/3?

### When dealing with 59/124 - 8

When dealing with 59/124 - 8/15, you were correct to rewrite each with the common denominator of 1860.
However, in doing so, you never changed the numerators (in order to create equivalent fractions).

Take: 59/124 - 8/15
Rewrite the fractions with common denominators: 885/1860 - 992/1860
Combine the fractions to get: (885 - 992)/1860
Simplify to get: -107/1860

You made the same error with all fractions.

Does that help?

Cheers,
Brent
For more on adding and subtracting fractions, watch: https://www.greenlighttestprep.com/module/gre-arithmetic/video/1069

### I thought you'd have to

I thought you'd have to multiply the denominator by its reciprocal

### You COULD go that route, but

You COULD go that route, but it will take a while :-)

### After canceling obvious

After canceling obvious values, I converted everthing to decimals using a calculator. I only go 2 decimals places and round if necessary. Do you see any potential problems this way. I know the calculator is discouraged, but what are your thoughts? I ended up with the correct answer nevertheless

### I think that's a totally

I think that's a totally legitimate solution, since it wouldn't take long to perform those calculations on the calculator.