Question: Fraction with Many Operations

Comment on Fraction with Many Operations

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.
greenlight-admin's picture

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?


do i have the calculator always in the quant sections?
greenlight-admin's picture

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:

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?
greenlight-admin's picture

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:

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.


How is 8/15 greater than 1/2
greenlight-admin's picture

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.


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?
greenlight-admin's picture

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?

For more on adding and subtracting fractions, watch:

I thought you'd have to multiply the denominator by its reciprocal
greenlight-admin's picture

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

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
greenlight-admin's picture

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

Hey what i get confused is that when i saw 59/124 i did 60/120 which is 1/2 but real value will be 1/2 a littles less as in orgnial Denominator rises and Numenator decreases

and in 8/15 i did 8/16 so 8 by 15 will be greater as Denominator decreases so am i rigth in this appraoch....i learned it from u.....can u give me some tip/tips to be a bit sure for next time
greenlight-admin's picture

Here's the key property to keep in mind in the future: If the 4 smaller fractions in one quantity are exactly the same as the 4 smaller fractions in the other quantity, there's no need for approximation. Instead you can try eliminating identical fractions.
For example, if you multiply both quantities by 1/3, you can eliminate 1/3 and 5/15 from both denominators.

My man Thank you~!!!

QC Strategies

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