# SAT Math: Simplifying Complex Fractions

Complex fractions are made up of one or more other fractions. For instance, a complex fraction could have ½ as its numerator or ¾ as its denominator—or both!

You probably haven’t thought much about complex fractions since elementary or primary school. After all, the further you get in your education, the more you get to lean on your calculator for basic math. But when the SAT hits you with a complex fraction full of variables, your calculator won’t help. You’ll have to get back to basics and simplify that fraction.

Compare these two groups of complex fractions. They’re the same except that one group has variables where the other one doesn’t.

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15n4x8 a3b4

Although your calculator can crush complex fractions made of numbers, it can’t break down ones that have variables. But you can.

First, take the bar that separates the complex fraction’s numerator from its denominator and make that bar a division operator. Then find the reciprocal of the denominator-turned-divisor and multiply rather than divide.

• 15n   ⇒   15 ÷ n1   ⇒   15 × 1n   ⇒   15n
• 4x8   ⇒   41 ÷ x8   ⇒   41 × 8x   ⇒   32x
• a3b4   ⇒   a3 ÷ b4   ⇒   a3 × 4b   ⇒   4a3b

These basic moves will simplify any complex fraction, variables or no variables. A fraction bar implies division, and when the numerator or denominator of a fraction is itself a fraction, the division is replaced with multiplication by the denominator’s reciprocal.

Want more tips like these? Check out this post: SAT Math: Squares Inscribed in Circles.

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