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317 lines
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HTML
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<h1 class="center">Ratios</h1>
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<h3 align="center">A ratio <b>compares</b> <b>values</b>.</h3>
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<p>A ratio says how much of one thing there is compared to another thing.</p>
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<p class="center"><img src="images/ratio-3-1.svg" alt="ratio 3:1" height="154" width="316"><br>
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<span class="larger">There are 3 blue squares to 1 yellow square</span></p>
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<p>Ratios can be shown in different ways:</p>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td style="text-align:right;"><span class="large">Use the ":" to separate the values:</span></td>
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<td style="width:20px;"> </td>
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<td style="text-align:center;"><span class="larger">3 : 1</span></td>
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</tr>
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<tr>
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<td style="text-align:right;"> </td>
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<td> </td>
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<td style="text-align:center;"> </td>
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</tr>
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<tr>
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<td style="text-align:right;"><span class="large">Or we can use the word "to":</span></td>
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<td> </td>
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<td style="text-align:center;"><span class="larger">3 to 1</span></td>
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</tr>
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<tr>
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<td style="text-align:right;"> </td>
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<td> </td>
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<td style="text-align:center;"> </td>
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</tr>
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<tr>
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<td align="right" height="23"><span class="large">Or write it like a fraction:</span></td>
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<td> </td>
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<td style="text-align:center;"><span class="intbl larger"><em>3</em><strong>1</strong></span></td>
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</tr>
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</tbody></table>
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<p>A ratio can be scaled up:</p>
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<p class="center larger"><img src="images/ratio-3-1b.svg" alt="ratio 3:1 is also 6:2" height="234" width="316"><br>
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Here the ratio is also <span class="larger"> 3 blue squares to 1 yellow square,<br>
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even though there are more squares. </span></p>
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<h3>Try it Yourself</h3>
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<div class="script" style="height: 260px;">images/ratio-slider.js</div>
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<h2>Using Ratios</h2>
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<p>The trick with ratios is to always multiply or divide the numbers <b>by the same value</b>.</p>
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<div class="example">
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<h3>Example:</h3>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td>
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<p><b>4 : 5</b> is the same as<b> 4</b>×2<b> : 5</b>×2<b> = 8 : 10</b></p></td>
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<td style="width:30px;"> </td>
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<td><img src="images/ratio-times-2.svg" alt="ratio 4:5 times 2 is 8:10" height="91" width="80"></td>
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</tr>
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</tbody></table>
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</div>
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<h3>Recipes</h3>
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<div class="example">
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<h3>Example: A Recipe for pancakes uses 3 cups of flour and 2 cups of milk.</h3>
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<p class="center">So the ratio of flour to milk is <b>3 : 2</b></p>
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<p>To make pancakes for a LOT of people we might need 4 times the quantity, so we multiply the numbers by 4:</p>
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<p class="center"><b>3</b>×4<b> : 2</b>×4<b> = 12 : 8</b></p>
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<p><b>In other words, 12 cups of flour and 8 cups of milk</b>.</p>
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<p>The ratio is still the same, so the pancakes should be just as yummy.</p>
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</div>
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<h2>"Part-to-Part" and "Part-to-Whole" Ratios</h2>
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<p>The examples so far have been "part-to-part" (comparing one part to another part).</p>
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<p>But a ratio can also show a part compared to the <b>whole lot</b>.</p>
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<div class="example">
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<h3>Example: There are 5 pups, 2 are boys, and 3 are girls</h3>
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<p class="center"><img src="../images/art/sage-five-pups.svg" alt="five pups" height="171" width="235"></p>
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<p class="larger">Part-to-Part:</p>
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<p class="center">The ratio of boys to girls is <span class="larger">2:3</span> or <span class="frac-large"><sup>2</sup>/<sub>3</sub></span></p>
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<p class="center">The ratio of girls to boys is <span class="larger">3:2</span> or <span class="frac-large"><sup>3</sup>/<sub>2</sub></span></p>
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<p class="larger">Part-to-Whole:</p>
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<p class="center">The ratio of boys to <b>all</b> pups is <span class="larger">2:5</span> or <span class="frac-large"><sup>2</sup>/<sub>5</sub></span></p>
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<p class="center">The ratio of girls to <b>all</b> pups is <span class="larger">3:5</span> or <span class="frac-large"><sup>3</sup>/<sub>5</sub></span></p>
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<p> </p>
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</div>
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<h2>Try It Yourself</h2>
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<div class="script" style="height: 300px;">
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images/ratio.js
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</div>
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<h2>Scaling</h2>
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<p>We can use ratios to scale drawings up or down (by multiplying or dividing).</p>
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<div class="beach">
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td style="text-align:right;">
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<p>The height to width ratio of the Indian Flag is <b>2:3</b></p>
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<p>So for every <b>2</b> (inches, meters, whatever) of height<br>
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there should be <b>3</b> of width.</p></td>
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<td><img src="images/indian-flag.jpg" alt="indian flag" height="77" width="116"></td>
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</tr>
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<tr>
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<td colspan="2" align="right">
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<p class="center">If we made the flag 20 inches high, it should be 30 inches wide.</p>
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<p class="center">If we made the flag 40 cm high, it should be 60 cm wide
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(which is still in the ratio 2:3)</p></td>
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</tr>
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</tbody></table>
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</div>
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<p> </p>
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<div class="example">
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<h3>Example: To draw a horse at 1/10th normal size, <b>multiply all sizes by 1/10th</b></h3>
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<p class="center"><img src="images/scale-horse.svg" alt="scale horse" height="199" width="391"></p>
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<div style="clear:both"></div>
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<p>This horse in real life is 1500 mm high and 2000 mm long, so the ratio of its <b>height to length</b> is</p>
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<p class="center large">1500 : 2000</p>
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<p><b>What is that ratio when <span class="center">we</span> draw it at 1/10th normal size?</b></p>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td><span class="larger">1500 : 2000</span></td>
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<td> </td>
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<td><span class="larger">= 1500<b>×1/10</b> : 2000<b>×1/10</b></span></td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td><span class="larger">= <b>150 : 200</b></span></td>
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</tr>
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</tbody></table>
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</div>
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<div class="simple"></div>
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<p><span class="center">We</span> can make any reduction/enlargement <span class="center">we</span> want that way.</p>
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<h2>Big Foot?</h2>
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<table style="border: 0;">
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<tbody>
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<tr>
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<td><img src="images/allie-foot.jpg" alt="Foot" height="124" width="220"></td>
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<td>Allie measured her foot and it was 21cm long, and then she measured her Mother's foot, and it was 24cm long.</td>
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</tr>
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</tbody></table>
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<p class="center"><i>"I must have big feet, my foot is nearly as long as my Mom's!"</i></p>
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<p>But then she thought to measure heights, and found she is 133cm tall, and her Mom is 152cm tall.</p>
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<p>In a table this is:</p>
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<div class="simple">
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr style="text-align:center;">
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<td style="text-align:right; width:120px;"> </td>
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<td style="width:70px;">Allie</td>
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<td style="width:70px;">Mom</td>
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</tr>
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<tr>
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<td style="text-align:right;">Length of Foot:</td>
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<td style="text-align:right; width:70px;">21cm</td>
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<td style="text-align:right; width:70px;">24cm</td>
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</tr>
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<tr>
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<td style="text-align:right;">Height:</td>
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<td style="text-align:right; width:70px;">133cm</td>
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<td style="text-align:right; width:70px;">152cm</td>
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</tr>
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</tbody></table>
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</div>
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<p>The "foot-to-height" ratio in fraction style is:</p>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td height="23"><span class="larger">Allie:</span></td>
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<td style="text-align:center;"><span class="intbl large"><em>21</em><strong>133</strong></span></td>
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<td style="text-align:center; width:30px;"> </td>
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<td class="larger" align="center">Mom:</td>
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<td style="text-align:center;"><span class="intbl large"><em>24</em><strong>152</strong></span></td>
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</tr>
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</tbody></table>
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<p>We can <a href="../simplifying-fractions.html">simplify</a> those fractions like this:</p>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td height="23"><span class="larger">Allie:</span></td>
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<td style="text-align:center;"><span class="intbl large"><em>21/7</em><strong>133/7</strong></span></td>
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<td style="text-align:center; width:30px;"> </td>
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<td class="larger" align="center">Mom:</td>
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<td style="text-align:center;"><span class="intbl large"><em>24/8</em><strong>152/8</strong></span></td>
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</tr>
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</tbody></table>
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<p>And we get this (please check that the calcs are correct):</p>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td height="23"><span class="larger">Allie:</span></td>
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<td style="text-align:center;"><span class="intbl large"><em>3</em><strong>19</strong></span></td>
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<td style="text-align:center; width:30px;"> </td>
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<td class="larger" align="center">Mom:</td>
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<td style="text-align:center;"><span class="intbl large"><em>3</em><strong>19</strong></span></td>
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</tr>
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</tbody></table>
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<p><i>"Oh!"</i> she said, <i>"the Ratios are the same".</i></p>
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<p><i>"So my foot is only as big as it should be for my height, and is not really too big."</i></p>
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<p> </p>
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<h2>Practice</h2>
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<p>You can practice your ratio skills by <a href="../ratio2.html">Making Some Chocolate Crispies</a></p>
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<p> </p>
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<div class="questions">1709, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 3603, 3604</div>
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<div class="related">
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<a href="../algebra/proportions.html">Proportions</a>
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<a href="../percentage.html">Percentages</a>
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<a href="../fractions.html">Fractions</a>
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<a href="golden-ratio.html">Golden Ratio</a>
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<a href="../ratio2.html">Ratio - Make Some Chocolate Crispies</a>
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</div>
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<div id="copyrt">Copyright © 2022 Rod Pierce</div>
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