GMAT Quant: Arithmetic – Fractions

Arithmetic: Fractions

Fractions, a topic that we had learned in our basic schooling and would still be present in some corner of our head. But with time and no practice on this topic could have rusted the concept. This article is to renew those concepts for the GMAT exam and make you ready to solve any problem related to fractions in minimal time.

What are Fractions?

Any number that cannot be expressed in form of whole number is a fraction.

What makes it Difficult?

The working on fractions is much different then that of whole numbers and so it can create confusion.

Rules of Fractions

Addition and Subtraction

\(\frac{x}{y} + \frac{w}{v} \neq \frac{x + w}{y + v}\) \(\frac{x}{y} – \frac{w}{v} \neq \frac{x – w}{y – v}\)

Multiplication

\(\frac{x}{y} \times \frac{w}{v} = \frac{xw}{yv}\)

Division

\(\frac{x}{y} \div \frac{w}{v} = \frac{xv}{yw}\)

Proportions

If, \(\frac{x}{y} = \frac{w}{v}\)

Then, \(\frac{x}{1} = \frac{yw}{v}\)

Let’s solve some questions and understand fractions in a greater depth

\(\frac{1}{160} + \frac{1}{40} + \frac{1}{1600} + \frac{1}{80}\)

Solution:

\(= \frac{1}{40} + \left ( \frac{1}{40} + 1 + \frac{1}{40} + \frac{1}{2} \right )\) \(= \frac{1}{40} + \left ( \frac{10}{40} + \frac{40}{40} + \frac{1}{40} + \frac{20}{40} \right )\) \(= \frac{1}{40} \left ( \frac{10 + 40 + 1 + 20}{40} \right )\) \(= \frac{1}{40} \times \frac{71}{40}\) \(= \frac{71}{1600}\)

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