Chapter 5: Problem 11

Remove the brackets from the given expression: \(\frac{3}{4}\left(\frac{1}{2} x+7\right)\)

Short Answer

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Question: Remove the brackets from the given expression: \(\frac{3}{4}\left(\frac{1}{2}x+7\right)\). Answer: \(\frac{3}{8}x + \frac{21}{4}\).

Step by step solution

Identify the terms inside the bracket

The terms inside the bracket are: \(\frac{1}{2}x\) and \(7\).

Multiply first term inside the bracket by the outside fraction

Multiply the first term \(\frac{1}{2}x\) by the outside fractional coefficient \(\frac{3}{4}\). This is done according to the rule \(\frac{a}{b}*\frac{c}{d}=\frac{ac}{bd}\). The resulting fraction is: \(\frac{3}{4}*\frac{1}{2}x = \frac{3*1}{4*2}x = \frac{3}{8}x\).

Multiply second term inside the bracket by the outside fraction

Multiply the second term \(7\) by the outside fractional coefficient \(\frac{3}{4}\). The resulting fraction is: \(\frac{3}{4}*7 = \frac{3*7}{4*1} = \frac{21}{4}\).

Combine the simplified terms

Combine the simplified terms from Steps 2 and 3 to form the final expression without the brackets: \(\frac{3}{4}\left(\frac{1}{2}x+7\right) = \frac{3}{8}x + \frac{21}{4}\).

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Remove the brackets from the given expression: \(\frac{3}{4}\left(\frac{1}{2} x+7\right)\)

Short Answer

Step by step solution

Identify the terms inside the bracket

Multiply first term inside the bracket by the outside fraction

Multiply second term inside the bracket by the outside fraction

Combine the simplified terms

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