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Archive | *GMAT Algebra

Manipulating Algebraic Equations and Expressions with Fractions: Systems of Equations

A student writes, Sometimes the answer explanation suggests that I clear fractions by multiplying an entire equation by a common denominator. Sometimes the answer explanation suggests that I manipulate just one side of an equation. How do I know which is better? This is a surprisingly subtle question. It turns out that the answer is […]

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Manipulating Algebraic Equations and Expressions with Fractions: A Word Problem

A student writes, Sometimes the answer explanation suggests that I clear fractions by multiplying an entire equation by a common denominator. Sometimes the answer explanation suggests that I manipulate just one side of an equation. How do I know which is better? This is a surprisingly subtle question. It turns out that the answer is […]

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Manipulating Algebraic Equations and Expressions with Fractions: Equations

A student writes, Sometimes the answer explanation suggests that I clear fractions by multiplying an entire equation by a common denominator. Sometimes the answer explanation suggests that I manipulate just one side of an equation. How do I know which is better? This is a surprisingly subtle question. It turns out that the answer is […]

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Manipulating Algebraic Equations and Expressions with Fractions: Another Example

A student writes, Sometimes the answer explanation suggests that I clear fractions by multiplying an entire equation by a common denominator. Sometimes the answer explanation suggests that I manipulate just one side of an equation. How do I know which is better? This is a surprisingly subtle question. It turns out that the answer is […]

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Manipulating Algebraic Equations and Expressions with Fractions: Expressions

A student writes, Sometimes the answer explanation suggests that I clear fractions by multiplying an entire equation by a common denominator. Sometimes the answer explanation suggests that I manipulate just one side of an equation. How do I know which is better? This is a surprisingly subtle question. It turns out that the answer is […]

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Manipulating Algebraic Equations and Expressions with Fractions: A Quick Quiz

A student writes, Sometimes the answer explanation suggests that I clear fractions by multiplying an entire equation by a common denominator. Sometimes the answer explanation suggests that I manipulate just one side of an equation. How do I know which is better? This is a surprisingly subtle question. It turns out that the answer is […]

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Algebraic Fractions on the GMAT

More formally, these are called “rational expressions” in mathematics — “rational” in the sense of “having do with a ratio”, as the word is used in the phrase “rational numbers“.   These rational expression appear in some of the most challenging Quant problems on the GMAT.   Here are a few practice questions. (A) –2 (B) –1 […]

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