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SAT Math : How to subtract complex fractions

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Example Question #82 : Fractions

Solve:

$76-\frac{75}{6}=$ $\displaystyle 76-\frac{75}{6}=$

Possible Answers:

$\frac{7}{6}$ $\displaystyle \frac{7}{6}$

$\displaystyle 75$

$\frac{1}{6}$ $\displaystyle \frac{1}{6}$

$\displaystyle 74$

$\frac{127}{2}$ $\displaystyle \frac{127}{2}$

Correct answer:

$\frac{127}{2}$ $\displaystyle \frac{127}{2}$

Explanation:

First reduce the fraction. We can divide both the numerator and the denominator by 3.

$\frac{75\div 3}{6\div 3}=\frac{25}{2}$ $\displaystyle \frac{75\div 3}{6\div 3}=\frac{25}{2}$

Now our expression looks like this:

$76-\frac{25}{2}$ $\displaystyle 76-\frac{25}{2}$

When you add or subtract fractions, you need to have the same denominator. The lowest common deonminator here is 2. So we need to multiply and solve:

$\left ( \frac{2}{2}\right)\cdot76-\frac{25}{2}=\frac{152}{2}-\frac{25}{2}=\frac{127}{2}$ $\displaystyle \left ( \frac{2}{2}\right)\cdot76-\frac{25}{2}=\frac{152}{2}-\frac{25}{2}=\frac{127}{2}$

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SAT Math : How to subtract complex fractions

Study concepts, example questions & explanations for SAT Math

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Example Question #82 : Fractions

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