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<h1>Multiplication of decimal fractions</h1>
<p><img src="https://imgoat.com/uploads/4b9ec30ad9/93411.png" width="362" height="200"/></p>
<p><a href="https://i.ytimg.com/vi/_reBMSgPxcw/hqdefault.jpg">Source</a></p>
<p>After finishing addition and subtraction of decimal fractions, we move on to multiplication of decimal numbers.</p>
<p>We've seen that addition and subtraction of decimal fractions are the same as addition and subtraction of whole numbers. When adding or subtracting decimal numbers, we have to remind our learners to ALWAYS place the decimal point underneath each other.</p>
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<p>Starting with multiplication of decimal numbers, it is also almost the same as multiplying whole numbers. </p>
<h2>Starting off with multiplying decimals with 10, 100 and 1000.</h2>
<p><img src="https://imgoat.com/uploads/4b9ec30ad9/93393.png" width="139" height="42"/></p>
<p>In this example, we have to multiply 1,1 with 10.</p>
<p>Multiplying with 10, 100 or 1000, we count how many zero's there are and move the decimal point to the right hand side. (It is mathematically incorrect to say that the decimal point moves, but I've seen that this is the only way that learners understand). If you explain to them that it is actually the digits that must move, they get confused and move to the wrong side or the wrong digits. </p>
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<p>Explain to your learners in a way that they will understand. </p>
<p>Getting back to the example, tell your learners if you multiply, you move the decimal point to the right.</p>
<p>1,1 x 10 = 11 (The decimal point moves 1 place to the right because 10 has one o)</p>
<p>When multiplying a decimal number with 100, you will move the decimal point 2 places because 100 has 2 zero's etc.</p>
<p><img src="https://imgoat.com/uploads/4b9ec30ad9/93394.png" width="226" height="110"/></p>
<p>In the above examples, we can see that multiplying with 100, we move the decimal point 2 places to the right.</p>
<p>Multiplying with 1000, we move the decimal point 3 places to the right.</p>
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<h2>What to do when you don't multiply with 10, 100 or 1000??</h2>
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<p><img src="https://imgoat.com/uploads/4b9ec30ad9/93397.png" width="287" height="205"/></p>
<ul>
<li>First, we write the sum vertically.</li>
<li>Count and see that 3,47 has 2 places behind the decimal point, 1,2 only has 1. (Keep this in mind until we calculate the answer.)</li>
<li>Let your learners forget about the decimals for now, write the numbers as whole numbers. 347 and 12</li>
<li>This means we can multiply 347 with 12.</li>
<li>Make sure your units, tens and hundreds are written underneath each other.</li>
<li>Multiply, starting at the units of the bottom number. Multiply the unit with each number at the top.</li>
<li>When you're done multiplying the units, remember to put a place holder for the units (0) under the first answer, as we are going to multiply with tens now.</li>
<li>Multiply the tens with each number at the top.</li>
<li>Add the two answers together.</li>
<li>The answer you get is 4164</li>
<li>Go back to the sum given and count how many decimal numbers there are in total.</li>
<li>The first number, 3,47 has 2 places behind the decimal point.</li>
<li>The second number, 1,2 only has 1 place behind the decimal point.</li>
<li>2 places + 1 place is equal to 3 places. This means that the answer must have 3 places behind the decimal point.</li>
<li>Our answer we got was 4164. Adding the decimal point now, we must have 3 places behind the decimal point. The answer will be 4,164</li>
</ul>
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<h3>In the next example we calculate the decimal sum the same way as above, this time the sum is just longer and more difficult. Learners have to concentrate calculating these sums.</h3>
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<p><img src="https://imgoat.com/uploads/4b9ec30ad9/93405.png" width="349" height="344"/></p>
<p>Again, let your learners forget about the decimal point while calculating the sum vertically. </p>
<ul>
<li>They can say it is 1473 x 392 , make sure the write the correct digits underneath each other. </li>
<li>Multiply with the bottom number first, starting at the units. </li>
<li>Multiply the units with every number at the top. </li>
<li> The answer you get is 2946.</li>
<li>Put a place holder (0) for the units and multiply the tens with each number at the top.</li>
<li>The answer you get is 132570. Make sure your learners carry the numbers over correctly and add correctly. With these answers they might start getting confused.</li>
<li>Multiply with the last digit, hundreds, but first add your place holder for the units and tens. This means 2 zero's</li>
<li>The answer you get will be 441900.</li>
<li>Now that we have multiplied all the numbers together, we can add all the answers. The final answer will be 577416.</li>
<li>Go back to the decimals given, and count how many decimal places are there in total.</li>
<li>The first decimal number have 3 places behind the comma and the second decimal has 2 places. In total there are 5.</li>
<li>The answer calculated must have 5 places behind the comma.</li>
<li>The final answer with the decimal must be 5,77416</li>
</ul>
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<h1>Conclusion:</h1>
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<ul>
<li>Learners must know how to multiply numbers using the vertical method.</li>
<li>When multiplying with 10,100 or 1000, learners don't have to calculate using the vertical method, they can move the decimal point to the right for the amount of zero's there are.</li>
<li>Remind your learners, when multiplying decimal numbers, they can forget about the decimal point at first and replace it at the end when they've calculated the answer.</li>
<li>Calculate how many places there must be by adding the total decimal points.</li>
</ul>
<p><img src="https://imgoat.com/uploads/4b9ec30ad9/93410.gif" width="562" height="141"/></p>
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