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# Adding Fractions

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Adding Fractions with Different Denominators

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### Adding Fractions

1. 1. Norm Frankenberger<br />Adding Fractions<br />+<br />With Different Denominators<br />Adding Fractions<br />
2. 2. Adding Fractions<br />Norm Frankenberger<br />Summary Slide<br />Why Adding Fractions Is Important? <br />Identifying the Parts of a Fraction<br />The Most Important Rule<br />What If the Fractions You’re Adding Have Different Denominators<br />Choosing a Common Denominator<br />Converting Fractions to Equivalents<br />Equivalent Fractions<br />
3. 3. Why Adding Fractions Is Important?<br />In March 2008, a presidential panel reported after a two year study that “schools could improve students’ math scores by hammering home the basics, such as addition and multiplication, and then increasing the focus on fractions and geometry.<br />In addition the report stated…<br />Adding Fractions<br />Norm Frankenberger<br />
4. 4. Adding Fractions<br />Norm Frankenberger<br />“Difficulty with fractions (including decimals and percents) is pervasive and is a major obstacle to further progress in mathematics, including algebra.”<br />Success in algebra is linked to higher graduation rates and college enrollment.<br />Let’s get started!<br />
5. 5. Norm Frankenberger<br />Identifying the Parts of a Fraction<br />The top number is called the numerator.<br />The bottom number is called the denominator.<br />3<br />4<br /> numerator<br />denominator<br />Adding Fractions<br />
6. 6. Norm Frankenberger<br />The Most Important Rule<br /> You CANNOT add (or subtract) fractions unless the denominators are the same!<br />1<br />3<br />+ 1<br />4<br />does not add up to 2<br />7<br />Adding Fractions<br />
7. 7. Adding Fractions<br />Norm Frankenberger<br />What If the Fractions You’re Adding Have Different Denominators<br />You must choose a new common denominator <br />You must change the fractions into their equivalent forms.<br />
8. 8. Adding Fractions<br />Norm Frankenberger<br />Choosing a Common Denominator<br />1<br /> + 3<br />1<br />4<br />Go through the list of multiples of the two denominators and pick out the first number that appears in both lists.<br />This is the common denominator!<br />
9. 9. Adding Fractions<br />Norm Frankenberger<br />Converting Fractions to Equivalents<br /><ul><li> Put equal signs and the common denominator next to the original fractions
10. 10. Ask, “Three times what number equals twelve?”
11. 11. Answer: “Four”
12. 12. Now, whatever you do the bottom of the fraction, you must do to the top.
13. 13. Multiply the numerator times four</li></ul>x 4 =<br /> 12<br /> 12<br />1 <br /> + 3<br />1<br />4<br /> 4 <br />=<br />=<br />x 4 =<br />x 3 =<br /> 3 <br />x 3 =<br />Now repeat the same process with the second fraction.<br />
14. 14. Adding Fractions<br />Norm Frankenberger<br />Before we add the numerators…<br />Let’s take a closer look at equivalent fractions:<br />They are the mechanism by which we can change the original fractions into fractions with different denominators without losing the original value<br />If it wasn’t for equivalent fractions we could not add (or subtract) fractions.<br />
15. 15. Norm Frankenberger<br />Equivalent Fractions<br />Equivalent fractions allow us to change a fraction to a fraction with a different denominator but with the same value.<br />For example:<br />==<br /> ½ ½ ½<br />In other words, ½ = 2/4= 4/8<br />2/4<br />4/8<br />Adding Fractions<br />
16. 16. Norm Frankenberger<br />Now, Let’s Finish the Problem<br />Now, you add the numerators and put the total over the common denominator.<br />x 4 =<br /> 12<br /> 12<br />1 <br /> + 3<br />1<br />4<br /> 4 <br />=<br />=<br />x 4 =<br />x 3 =<br /> 3 <br />x 3 =<br />7 <br />12<br />Adding Fractions<br />
17. 17. Adding Fractions<br />Norm Frankenberger<br />I hope that helped and remember:<br />&quot;Numbers are your friends, <br />especially when they are<br /> on your paycheck.&quot;<br />