Using Brackets

Using brackets


Brackets are used to simplify an expression with more than one mathematical operation.

For removing brackets solve the operation given inside the brackets and change everything into a single number.

  • \left( {6{\rm{ }} + {\rm{ }}8} \right){\rm{ }} \times {\rm{ }}10{\rm{ }} = {\rm{ }}14{\rm{ }} \times {\rm{ }}10{\rm{ }} = {\rm{ }}140
  • \left( {8{\rm{ }} + {\rm{ }}3} \right){\rm{ }}\left( {9{\rm{ }} - {\rm{ }}4} \right){\rm{ }} = {\rm{ }}11{\rm{ }} \times {\rm{ }}5{\rm{ }} = {\rm{ }}55

Expanding brackets


The use of brackets allows us to follow a certain procedure to open the brackets systematically.

e.g.,1)

\begin{array}{l}8{\rm{ }} \times {\rm{ }}109{\rm{ }}\\ = {\rm{ }}8{\rm{ }} \times {\rm{ }}\left( {100{\rm{ }} + {\rm{ }}9} \right){\rm{ }}\\ = {\rm{ }}8{\rm{ }} \times {\rm{ }}100{\rm{ }} + {\rm{ }}8{\rm{ }} \times {\rm{ }}9{\rm{ }}\\ = {\rm{ }}800{\rm{ }} + {\rm{ }}72{\rm{ }} = {\rm{ }}872\end{array}

2)

105{\rm{ }} \times {\rm{ }}108{\rm{ }} = {\rm{ }}\left( {100{\rm{ }} + {\rm{ }}5} \right){\rm{ }} \times {\rm{ }}\left( {100{\rm{ }} + {\rm{ }}8} \right)  = \;{\rm{ }}\left( {100{\rm{ }} + {\rm{ }}5} \right){\rm{ }} \times {\rm{ }}100{\rm{ }} + {\rm{ }}\left( {100{\rm{ }} + {\rm{ }}5} \right){\rm{ }} \times {\rm{ }}8
 = {\rm{ }}\left( {100{\rm{ }} \times 100} \right){\rm{ }} + {\rm{ }}\left( {5{\rm{ }} \times 100} \right){\rm{ }} + {\rm{ }}\left( {100 \times 8} \right){\rm{ }} + {\rm{ }}\left( {5 \times 8} \right)
 = {\rm{ }}10000{\rm{ }} + {\rm{ }}500{\rm{ }} + {\rm{ }}800{\rm{ }} + {\rm{ }}40 = 11340

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