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# Algebraic fractions

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Examples and explanation of adding fractions with a common denominator, different denominators, multiplying fractions and dividing fractions.

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### Algebraic fractions

1. 1. Fractions<br /><ul><li>Adding with Common Denominators
2. 2. Adding with Different Denominators
3. 3. Multiplying
4. 4. Dividing</li></li></ul><li>Add straight across the top (numerators)<br />π¦6+2π¦6=<br />Β <br />If the base(denominator) is the sameβ¦<br />Add/Subtract Common Denominators<br />
5. 5. Can it be simplified?<br />3π¦6=<br />Β <br />
6. 6. 3Γ·3π¦6Γ·3=<br />Β <br />3<br />
7. 7. π¦6+2π¦6<br />= π¦+2π¦6<br />=3π¦6<br />=π¦2<br />Β <br />Add the numerators<br />Simplify<br />
8. 8.
9. 9. π¦6+2π¦5=<br />Β <br />Make the bases the same<br />(choose a common denominator)<br />Add/Subtract Different Denominators<br />
10. 10. Multiply top & bottom by the SAME number.<br />(changes the look not the fraction)<br />π¦Γ56Γ5+2π¦Γ65Γ6=<br />Β <br />30<br />
11. 11. Add straight across the top (numerators).<br />5π¦30+12π¦30=<br />Β <br />Now the base (denominator) is the sameβ¦<br />
12. 12. Can it be simplified?<br />17π¦30=<br />Β <br />
13. 13. π¦6+2π¦5<br />= π¦Γ56Γ5+2π¦Γ65Γ6<br />=Β 5π¦30+12y30<br />=17π¦30<br />Β <br />Make denominators the same<br />Multiply top and bottom by same number<br />Add the numerators<br />Simplify if you can!<br />
14. 14.
15. 15. Multiply straight across the top (numerators)<br />π¦2Γ43π₯=<br />Β <br />Multiply straight across the bottom <br />(denominators)<br />Multiply<br />
16. 16. Can it be simplified?<br />4π¦6π₯=<br />Β <br />
17. 17. 4Γ·2π¦6Γ·2π₯=<br />Β <br />2<br />
18. 18. Multiply numerators, <br />multiply denominators<br />π¦2Γ43π₯<br />= π¦Γ42Γ3π₯<br />=Β 4π¦6π₯<br />=2π¦3π₯<br />Β <br />Simplify<br />
19. 19.
20. 20. π¦2Γ·43π₯=<br />Β <br />Flip the secondfractionupside down<br />(invert)<br />Divide<br />
21. 21. Multiply straight across the top (numerators)<br />π¦2Γ3π₯4=<br />Β <br />Multiply straight across the bottom <br />(denominators)<br />
22. 22. Can it be simplified?<br />3π₯π¦8=<br />Β <br />
23. 23. Flip the second fraction<br />π¦2Γ·43π₯<br />= π¦2Γ3π₯4<br />=π¦Γ3π₯2Γ4<br />=Β 3π₯π¦8<br />Β <br />Multiply numerators, <br />multiply denominators<br />Simplify if you can!<br />