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How to Use Number Lines to Find Equivalent Fractions Dawn Galente, Arlington CSD 2012 This is a self-paced tutorial. Click the screen each time you want to see the next step. Click to Start

Start with a simple fraction like 1/3. Standard 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models….use this principle to recognize and generate equivalent fractions. Start with a simple fraction like 1/3. 1 3 2 Picture what this number line would look like if we broke each segment into 2 equal pieces. What fraction would this new line represent? 1 3 2 Now 2 out of 6 segments are shaded… 2/6. 2 6 4 1 3 5

I can find any number of equivalent fractions by simply breaking each segment on the line into smaller pieces. 1 2 Start with 1/2… 4 8 1 2 3 5 7 6 break each piece into 4 equal pieces… to get 4/8. x4 I have four times as many shaded segments now; 1 x 4= 4. 1 2 4 8 = x4 I have four times as many total segments now… 2 x 4 = 8.

What if I want to find a specific equivalent fraction? 3 5 ? 10 = Start with a model of the first fraction. Think: I have 5 total segments now. I need 10 total segments. 3 5 4 2 1 2 10 1 3 4 5 6 7 8 9 How can I break 5 segments into smaller segments so that I have 10? Break them into 2 segments each! 6 x2 3 5 10 = x2 How many shaded segments do I have now? 3 x 2 = 6.

= a b a b 4 8 = x4 x n a/b is equivalent to (n × a)/(n × b) means….. 1 2 = a b 4 8 1 2 3 5 7 6 x4 x n a b 4 8 =

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