 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Session 9, Part A:
Models for the Multiplication and Division of Fractions

In This Part: Area Model for Multiplication | Try It Yourself | Area Model for Division
The Common Denominator Model for Division | Translating the Process to Decimals

You can extend what you've learned about operations and fractions to decimals as well. Remember that a terminating decimal can be thought of as a fraction with a power of 10 as the denominator (e.g., 0.4 = 4/10). Note 5

Why do we need to line up the decimal points when we add or subtract decimals?

 We need to line up the decimal points because we can only add or subtract if the units are the same. By aligning the decimal points, we make sure that we are adding or subtracting digits that have the same place values, just as we do when we add or subtract whole numbers.

Why do we count the decimal places when we multiply decimals?

 From the section on exponents in Session 3, we know that multiplication with exponents requires adding, or "counting," the exponents. So, for example, 0.2 • 0.03 in the exponential form is the following: 0.2 • 0.03 = 2/10 • 3/100 = 2 •10-1 • 3 • 10-2 The exponents are -1 and -2, which are one and two places, respectively, to the right of the decimal point. The product will then have an exponent that is the sum of -1 and -2 (i.e., -3), and is three places to the right of the decimal point. The product of 0.2 • 0.03 is 0.006: 0.2 • 0.03 = 6 • 10-3 = 0.006

Why do we move the decimal points when dividing with decimals?

 This process is related to finding equivalent fractions. You can think of the division as a fraction. Since the problem 2.5 0.05 is hard to visualize, write it as 2.5/0.05. You need a whole number in the denominator, so multiply by 100 to get a whole number. To compensate for multiplying the denominator by 100, you must also multiply the numerator by 100. That means that you actually multiplied by 100/100, or 1, which doesn't change the value of the fraction. Here's what the process looks like: 2.5/0.05 = (2.5 • 100)/(0.05 • 100) = 250/5 = 50   Session 9: Index | Notes | Solutions | Video