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Chapter 5: Chapter 5

Problem 42

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Simplify the following expression: \(1-[1 /(2-1 / 3)]\)

Short Answer

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The simplified expression is: \(\dfrac{-2}{3}\).
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Simplify the Inner Fraction

We first deal with the inner fraction which is \(\dfrac{1}{3}\). Since we need to find \(1 \div \dfrac{1}{3}\), we can rewrite it as \(1 \times \dfrac{3}{1}\) because division is the same as multiplying by the reciprocal of the fraction. The expression becomes: \(1 - \left[1 \div \left(2 - \dfrac{1}{3}\right)\right] = 1 - \left[1 \times \dfrac{3}{1}\right]\).

Step 2: Simplify the Expression Inside the Bracket

Now we have to deal with the expression inside the bracket: \(2 - \dfrac{1}{3}\). To do this, we first find a common denominator for the two fractions. In this case, the common denominator is 3, so we rewrite the expression as: \(\dfrac{6}{3} - \dfrac{1}{3}\). Subtract the fractions to get: \(\dfrac{5}{3}\). The expression becomes: \(1 - \left[\dfrac{5}{3}\right]\).

Step 3: Simplify the Entire Expression

Now we need to simplify the entire expression. We can rewrite it as a single fraction with a common denominator. In this case, the common denominator is 3, so the expression becomes: \(\dfrac{3}{3} - \dfrac{5}{3}\). Subtract the fractions to get: \(\dfrac{-2}{3}\). The simplified expression is: \(\dfrac{-2}{3}\).

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