Chapter 1: Q. 227 (page 54)

Simplify $(\frac{5}{9} + \frac{1}{6}) \div (\frac{2}{3} - \frac{1}{2})$

Short Answer

Expert verified

The result of simplifying the expression is

$(\frac{5}{9} + \frac{1}{6}) \div (\frac{2}{3} - \frac{1}{2}) = \frac{13}{3}$

Step by step solution

Step 1. Given information

$\begin{array}{l} Thegivenexpressionis \\ (\frac{5}{9} + \frac{1}{6}) \div (\frac{2}{3} - \frac{1}{2}) \\ Wehavetosimplifythegivenexpression. \end{array}$

Step 2. Solve the bracket

$\begin{array}{l} \Rightarrow (\frac{5}{9} + \frac{1}{6}) \div (\frac{2}{3} - \frac{1}{2}) = (\frac{5 \times 2 + 1 \times 3}{18}) \div (\frac{2 \times 2 - 1 \times 3}{6}) [TaketheLCMofdenominatorinbrackets] \\ \Rightarrow (\frac{5}{9} + \frac{1}{6}) \div (\frac{2}{3} - \frac{1}{2}) = (\frac{10 + 3}{18}) \div (\frac{4 - 3}{6}) \\ \Rightarrow (\frac{5}{9} + \frac{1}{6}) \div (\frac{2}{3} - \frac{1}{2}) = (\frac{13}{18}) \div (\frac{1}{6}) \end{array}$

Step 3. Divide the fractions

$\begin{array}{l} \Rightarrow (\frac{5}{9} + \frac{1}{6}) \div (\frac{2}{3} - \frac{1}{2}) = (\frac{13}{18}) \div (\frac{1}{6}) \\ Todivide,multiplythefirstfractionbythereciprocalofthesecond \\ \Rightarrow (\frac{5}{9} + \frac{1}{6}) \div (\frac{2}{3} - \frac{1}{2}) = (\frac{13}{18}) \times (\frac{6}{1}) \\ \Rightarrow (\frac{5}{9} + \frac{1}{6}) \div (\frac{2}{3} - \frac{1}{2}) = \frac{13}{3 \times 6} \times \frac{6}{1} \\ \Rightarrow (\frac{5}{9} + \frac{1}{6}) \div (\frac{2}{3} - \frac{1}{2}) = \frac{13}{3} \end{array}$

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Simplify $(\frac{5}{9} + \frac{1}{6}) \div (\frac{2}{3} - \frac{1}{2})$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve the bracket

Step 3. Divide the fractions

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Simplify59+16÷23-12

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve the bracket

Step 3. Divide the fractions

One App. One Place for Learning.

Most popular questions from this chapter

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Simplify $(\frac{5}{9} + \frac{1}{6}) \div (\frac{2}{3} - \frac{1}{2})$