https://peda.net/id/237a8a452cf 2022-09-05T12:42:41+03:00 https://peda.net/:static/535/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div> https://peda.net/id/237b0a982cf 2020-11-25T12:51:25+02:00 <div class="eoppi-summary"> <h3><b>Percentage changes</b></h3> <span><span>When calculating the percentage by which something has changed (i.e. increased or decreased):</span></span> <ul> <li>the <b>magnitude</b> of the change is calculated first.</li> <li>the <b>percentage change</b> from the original value is then calculated.</li> </ul> </div> <h3><b>Example 1</b></h3> <p class="p1">The price of a film ticket was increased from [[$ 5 $]]​ € to [[$ 6,5 $]]​ €. By what percentage did the price increase?</p> <p>The price increase in €:</p> <p class="p1">[[$ 6,5 \: \text {€} \: - 5 \: \text {€} = 1,5 \: \text {€} $]]​</p> <p>The price increase as a percentage:<br/> <br/> <br/> </p> <p class="p1"><br/> <a href="https://peda.net/qis/2022-2023/mathematics/maths-grade-9/1mjvsp/mjvsp/8_13_e1v2-jpg#top" title="13_example1.png"><img src="https://peda.net/qis/2022-2023/mathematics/maths-grade-9/1mjvsp/mjvsp/8_13_e1v2-jpg:file/photo/df2086da8e2ca18c23b3f1a0a1e31b6721abb716/13_example1.png" alt="" title="example 1" class="inline" loading="lazy"/></a><br/> <br/> <b>Answer:</b> The price of a movie ticket increased by [[$ 30 \: \% $]]​.</p> <div class="eoppi-summary"> <h3><b>Comparison percentage</b></h3> When calculating what percentage of a number is greater or smaller than another number:<br/> <ul> <li>the <b>difference</b> between the two numbers is calculated first.</li> <li>the difference of the numbers is <b>compared</b> to the number that follows the word &quot;than&quot;.</li> </ul> </div> <br/> <h3><b>Example 2</b></h3> <p class="p1">Evelina is [[$ 156 $]]​ cm tall, whereas Tony is [[$ 182 $]]​ cm tall.</p> <p>a) By what percentage is Tony taller than Evelina?<br/> <br/> The height difference in centimeters:</p> <p class="p1">[[$ 182 \: \text {cm} \: – 156 \: \text {cm} = 26 \: \text {cm} $]]​.</p> <p class="p1">The percentage difference:</p> <a href="https://peda.net/qis/2022-2023/mathematics/maths-grade-9/1mjvsp/mjvsp/8_13_e2a-jpg#top" title="13_example2a.png"><img src="https://peda.net/qis/2022-2023/mathematics/maths-grade-9/1mjvsp/mjvsp/8_13_e2a-jpg:file/photo/c4be08027a1e42c7110db33c0be83bfcd24befad/13_example2a.png" alt="" title="example 2a" class="inline" loading="lazy"/></a><br/> <p class="p1">b) By what percentage is Evelina shorter than Tony?<br/> <br/> <a href="https://peda.net/qis/2022-2023/mathematics/maths-grade-9/1mjvsp/mjvsp/8_13_e2b-jpg#top" title="13_example2b.png"><img src="https://peda.net/qis/2022-2023/mathematics/maths-grade-9/1mjvsp/mjvsp/8_13_e2b-jpg:file/photo/9f6a47bcc241a7c3505d824df0b945a2ed660e34/13_example2b.png" alt="" title="example 2b" class="inline" loading="lazy"/></a></p> <p class="p1"><b>Answer:</b> a) Tony is [[$ 17 \: \% $]]​ taller than Evelina and b) Evelina is[[$ 14 \: \% $]] shorter than Tony.</p> <p class="p1"><b>NB! </b>Comparison percentages are calculated in the same way as percentage changes. The difference between the two concepts is that percentage changes are always compared to a specific original value, whereas comparison percentages can be compared to all of the values that are examined. </p> <div class="eoppi-summary"> <h3><b>Percentage point</b></h3> The <em>percentage point</em> is different from the percentage. The change in percentage points is obtained by calculating the difference between two percentages.<br/> <br/> </div> <h3><b>Example 3</b></h3> <p class="p1">Popular support for nuclear power fell from [[$ 47 $]]​ percent to [[$ 34 $]]​ percent.</p> <p class="p1">a) By how many percentage points did the support decrease? </p> <p class="p1">[[$ 47 \: - 34 = 13 $]]​</p> <p class="p1">b) By what percentage did the support decrease? <br/> <br/> <a href="https://peda.net/qis/2022-2023/mathematics/maths-grade-9/1mjvsp/mjvsp/8_13_e3-jpg#top" title="13_example3.png"><img src="https://peda.net/qis/2022-2023/mathematics/maths-grade-9/1mjvsp/mjvsp/8_13_e3-jpg:file/photo/1b36571d985a864868160ac34a94155bca863256/13_example3.png" alt="" title="example 3" class="inline" loading="lazy"/></a></p> <p class="p1"><b>Answer:</b> The support decresed by a) by [[$ 13 $]]​ percentage points and b) by [[$ 28 \: \% $]]​.</p> 2022-09-05T12:42:41+03:00 https://peda.net/id/23803ea72cf 2020-06-04T13:10:07+03:00 <a href="https://peda.net/id/2380baf42cf" rel="noopener" target="_blank">Basic exercises<br/> </a><a href="https://peda.net/id/238654582cf" rel="noopener" target="_blank">Applied exercises<br/> </a><a href="https://peda.net/id/238ae6252cf" rel="noopener" target="_blank">Challenging exercises<br/> </a> 2022-09-05T12:42:41+03:00