GRE Math : How to subtract fractions

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Example Question #1 : How To Subtract Fractions

Solve for :

$\frac{x}{4}=\frac{3x}{8}-12$

Possible Answers:

Correct answer:

Explanation:

Begin by isolating the factors:

$\frac{x}{4}-\frac{3x}{8}=-12$

Now, the common denominator of these two fractions is . Therefore, multiply $\frac{x}{4}$ by $\frac{2}{2}$ :

$\frac{2}{2}*\frac{x}{4}-\frac{3x}{8}=-12$

$\frac{2x}{8}-\frac{3x}{8}=-12$

Now, you can subtract the left values:

$-\frac{x}{8}=-12$

Now, multiply both sides by :

x=96

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Example Question #1 : How To Subtract Fractions

Simplify:

$\frac{15}{12}-\frac{2}{9}$

Possible Answers:

$\frac{21}{22}$

$\frac{13}{3}$

$\frac{5}{9}$

$\frac{13}{21}$

$\frac{37}{36}$

Correct answer:

$\frac{37}{36}$

Explanation:

Just like adding fractions, when you subtract fractions, you need to find a common denominator. For and , the least common denominator is . In order to do your subtraction, you need to multiply appropriately to give your fractions this denominator:

$\frac{15}{12}-\frac{2}{9}=\frac{15}{12}*\frac{3}{3}-\frac{2}{9}*\frac{4}{4}$

Which is the same as...

$\frac{45}{36}-\frac{8}{36}$

Now, you can subtract the numerators and retain the denominator:

$\frac{37}{36}$

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Example Question #1 : How To Subtract Fractions

Which of the following is true?

Quantity A: $\frac{12}{7}-\frac{3}{5}$

Quantity B: $\frac{11}{6}-\frac{7}{8}$

Possible Answers:

The relationship between the quantities cannot be determined.

Quantity B is larger.

The two quantities are equal.

Quantity A is larger.

Correct answer:

Quantity A is larger.

Explanation:

First, consider each quantity separately.

Quantity A

$\frac{12}{7}-\frac{3}{5}$

These two fractions do not have a common factor. Their common denominator is . Thus, we multiply the fractions as follows to give them a common denominator:

$\frac{12}{7}*\frac{5}{5}-\frac{3}{5}*\frac{7}{7}$

This is the same as:

$\frac{60}{35}-\frac{21}{35}=\frac{39}{35}$

Quantity B

$\frac{11}{6}-\frac{7}{8}$

The common denominator of these two values is . Therefore, you multiply the fractions as follows to give them a common denominator:

$\frac{11}{6}*\frac{4}{4}-\frac{7}{8}*\frac{3}{3}$

This is the same as:

$\frac{44}{24}-\frac{21}{24}=\frac{23}{24}$

Since Quantity A is larger than and Quantity B is a positive fraction less than , we know that Quantity A is larger without even using a calculator.

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GRE Math : How to subtract fractions

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : How To Subtract Fractions

Example Question #1 : How To Subtract Fractions

Example Question #1 : How To Subtract Fractions

All GRE Math Resources

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