SAT Mathematics : Divisibility & Number Fluency

Study concepts, example questions & explanations for SAT Mathematics

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Example Questions

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Example Question #10 : Simplifying Fractions

Which of the following fractions has the greatest value?

Possible Answers:

Correct answer:

Explanation:

To best compare these fractions, it is helpful to reduce them to their simplest form.  is already as reduced as it can be.

 

 

For , you can factor out a 2 from the numerator and denominator to get to . Note that you could again divide by 2 to get , but here you can also be creative: if you were comparing to  and  as two options, you should see that  is a hair less than , which would reduce directly to .  So you can eliminate  by that comparison.

 

7007 and 6006 are each divisible by 1001 (something that should be somewhat evident by the similar way the numbers look). If you then factor out the 1001 you have  and the 1001s cancel, leaving .  Since you cannot have two correct answers, then  and  are a "tie" and both are incorrect. And when you see that  is just a bit larger than , a number that would also equal , you can see that  is correct.

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