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Why Do We Do That? 3 Traditional Algorithms with Decimals

I went to one of the most beneficial decimal and fraction professional developments I have ever been to this summer.  I want to share what I learned with you so you can share it with your children.

1.  Traditionally adding and subtracting decimals:  Just line up the decimals to add or subtract.  Then just add and subtract like normal.  You may have to add zeros to the end of the decimal number on top if you have additional numbers on the bottom.  Why does this work?

Lining up the decimals is like adding like denominators. See:

Decimals1

2. Traditionally multiplying decimals:  Multiply the numbers like there is no decimal point.  Then count the places behind the decimal.  The number of decimal places in the numbers you multiplied is the number of decimal places in the product when you count from the back of the number.  Why does this work?

This works because you are counting the powers of ten in the denominator.  That is why there are three places behind the decimal!  See:

Decimals3-1

3.  Traditionally dividing decimals:  If their is a decimal in the divisor, move the decimal to the back of the number.  Then move the decimal that many places back in the dividend number.  Divide normally.  Then place the decimal on top of the “house” above where the decimal is in the dividend.  Why does this work?

Well, if you, again, turn the decimals into fractions, you can see what is happening.  If you divide straight across the fractions, you get the resulting 25 tenths.  Like with multiplication, this works the same.  You count the zeros OR powers of ten to know how many decimal places to include in the quotient.  See:

Decimals4-1

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