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146 lines
6.4 KiB
HTML
146 lines
6.4 KiB
HTML
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<title>Brackets (Parentheses)</title>
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<h1 align="center">Brackets (Parentheses)</h1>
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<p align="center"><i>Brackets are symbols used in pairs to group things together. </i></p>
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<table border="0" align="center">
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<tr>
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<td><img src="images/brackets.svg" alt="brackets" /></td>
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<td valign="top"><p>Types of brackets include: </p>
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<ul>
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<div class="bigul">
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<li>parentheses or "round brackets" ( ) </li>
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<li>"square brackets" or "box brackets" [ ] </li>
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<li>braces or "curly brackets" { } </li>
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<li>"angle brackets" < ></li>
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</div>
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</ul>
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(Note: Angle brackets can be confusing as they<br>
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look like the "less than" and "greater than" signs)</td>
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</tr>
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</table>
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<p>When we see things inside brackets we do them first (as explained in <a href="../operation-order-pemdas.html">Order of Operations</a>).</p>
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<div class="example">
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<h3>Example: <span class="large">(3 + 2) × (6 − 4)</span></h3>
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<p>The parentheses group 3 and 2 together, and 6 and 4 together, so they get done first:</p>
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<table border="0" align="center">
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<tr>
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<td align="center"><span class="large">(3 + 2) × (6 − 4)</span></td>
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</tr>
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<tr>
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<td align="center"><span class="large">= (5) × (2)</span></td>
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</tr>
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<tr>
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<td align="center"><span class="large">= 5×2</span></td>
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</tr>
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<tr>
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<td align="center"><span class="large">= 10</span></td>
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</tr>
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</table>
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<p align="center" class="large"> </p>
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<p>Without the parentheses the multiplication is done first:</p>
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<p align="center"><span class="large">3 + 2 × 6 − 4 <br>
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= 3 + 12 − 4 <br>
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= 11</span> (not 10)</p>
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</div>
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<p>With more complicated grouping it is good to use <b>different types of brackets</b>:</p>
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<div class="example">
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<h3>Example: <span class="large">[(3 + 2) × (6 - 4) + 2] × 4</span></h3>
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<p>The parentheses group 3 and 2 together, and 6 and 4 together, and the square brackets tell us to do all the calculations inside them before multiplying by 4:</p>
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<table border="0" align="center">
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<tr>
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<td align="center"><span class="large">[(3 + 2) × (6 − 4) + 2] × 4</span></td>
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</tr>
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<tr>
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<td align="center"><span class="large">= [(5) × (2) + 2] × 4</span></td>
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</tr>
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<tr>
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<td align="center"><span class="large">= [10 + 2] × 4</span></td>
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</tr>
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<tr>
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<td align="center"><span class="large">= 12 × 4</span></td>
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</tr>
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<tr>
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<td align="center"><span class="large">= 48</span></td>
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</tr>
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</table>
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</div>
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<h2>Curly Brackets</h2>
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<p>Curly brackets {} are used in <a href="../sets/sets-introduction.html">Sets</a>:</p>
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<div class="example">
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<h3>Example: <span class="large">{2, 4, 6, 8}</span></h3>
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<p>Is the set of even numbers from 2 to 8</p>
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</div>
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<p> </p>
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<div class="questions">
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<script type="text/javascript">getQ(1673, 1674, 1675, 1676);</script>
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</div>
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<div class="related"> <a href="../operation-order-pemdas.html">Order of Operations - PEMDAS (US)</a> <a href="../operation-order-bodmas.html">Order of Operations - BODMAS (UK)</a></div>
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Copyright © 2017 MathsIsFun.com
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