5 5by6 +3 9by10+2 4by15
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avadacrucio:
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Convert the mixed fraction into improper fractions:
![5 \frac{5}{6} + 3 \frac{9}{10} + 2 \frac{4}{15} \\ \\ = \frac{5 \times 6 + 5}{6} + \frac{3 \times 10 + 9}{10} + \frac{2 \times 15 + 4}{15} 5 \frac{5}{6} + 3 \frac{9}{10} + 2 \frac{4}{15} \\ \\ = \frac{5 \times 6 + 5}{6} + \frac{3 \times 10 + 9}{10} + \frac{2 \times 15 + 4}{15}](https://tex.z-dn.net/?f=5+%5Cfrac%7B5%7D%7B6%7D++%2B+3+%5Cfrac%7B9%7D%7B10%7D++%2B+2+%5Cfrac%7B4%7D%7B15%7D++%5C%5C++%5C%5C++%3D++%5Cfrac%7B5+%5Ctimes+6+%2B+5%7D%7B6%7D++%2B++%5Cfrac%7B3+%5Ctimes+10+%2B+9%7D%7B10%7D++%2B++%5Cfrac%7B2+%5Ctimes+15+%2B+4%7D%7B15%7D+)
![= \frac{30 + 5}{6} + \frac{30 + 9}{10} + \frac{30 + 4}{15} \\ \\ = \frac{3 5}{6} + \frac{39}{10} + \frac{34}{15} = \frac{30 + 5}{6} + \frac{30 + 9}{10} + \frac{30 + 4}{15} \\ \\ = \frac{3 5}{6} + \frac{39}{10} + \frac{34}{15}](https://tex.z-dn.net/?f=%3D++%5Cfrac%7B30+%2B+5%7D%7B6%7D++%2B++%5Cfrac%7B30+%2B+9%7D%7B10%7D++%2B++%5Cfrac%7B30+%2B+4%7D%7B15%7D+%5C%5C++%5C%5C++%3D+%5Cfrac%7B3+5%7D%7B6%7D++%2B++%5Cfrac%7B39%7D%7B10%7D++%2B++%5Cfrac%7B34%7D%7B15%7D)
Now, take LCM of denominators and add.
![= \frac{35 \times 5 + 39 \times 3 + 34 \times 2}{30} \\ \\ = \frac{175 + 117 + 68}{30} = \frac{35 \times 5 + 39 \times 3 + 34 \times 2}{30} \\ \\ = \frac{175 + 117 + 68}{30}](https://tex.z-dn.net/?f=+%3D+%5Cfrac%7B35+%5Ctimes+5+%2B+39+%5Ctimes+3+%2B+34+%5Ctimes+2%7D%7B30%7D++%5C%5C++%5C%5C++%3D++%5Cfrac%7B175+%2B+117+%2B+68%7D%7B30%7D+)
![= \frac{360}{30} \\ \\ = 12 = \frac{360}{30} \\ \\ = 12](https://tex.z-dn.net/?f=+%3D++%5Cfrac%7B360%7D%7B30%7D++%5C%5C++%5C%5C++%3D+12)
Now, take LCM of denominators and add.
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