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12 1/2 + 4 2/5 - 8 3/4 =

Guest Apr 20, 2017
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12 1/2 + 4 2/5 - 8 3/4 =

 

1.

\(\begin{array}{|rcll|} \hline && 12 \frac12 + 4 \frac25 - 8 \frac34 \\ &=& 12+4-8 + \frac12 + \frac25 - \frac34 \\ &=& 8 + 0.5 + 0.4 - 0.75 \\ &=& 8 + 0.15 \\ &=& 8.15 \\ &=& 8 \frac{15}{100} \\ &=& 8 \frac{3}{20} \\ \hline \end{array}\)

 

2.

\(\begin{array}{|rcll|} \hline && 12 \frac12 + 4 \frac25 - 8 \frac34 \\ &=& 12+4-8 + \frac12 + \frac25 - \frac34 \\ &=& 8 + \frac12\cdot \frac{10}{10} + \frac25\cdot \frac{4}{4} - \frac34\cdot \frac{5}{5} \\ &=& 8 + \frac{10}{20} + \frac{8}{20} - \frac{15}{20} \\ &=& 8 + \frac{10+8-15}{20} \\ &=& 8 \frac{3}{20} \\ \hline \end{array}\)

 

3.

\(\begin{array}{|rcll|} \hline && 12 \frac12 + 4 \frac25 - 8 \frac34 \\ &=& \frac{2\cdot 12+1}{2} + \frac{4\cdot 5+2}{5} + \frac{4\cdot 8+3}{4} \\ &=& \frac{25}{2} + \frac{22}{5} + \frac{35}{4} \\ &=& \frac{25}{2}\cdot \frac{10}{10} + \frac{22}{5}\cdot \frac{4}{4} - \frac{35}{4}\cdot \frac{5}{5} \\ &=& \frac{250}{20} + \frac{88}{20} - \frac{175}{20} \\ &=& \frac{250+88-175}{20} \\ &=& \frac{163}{20} \\ &=& 8 \frac{3}{20} \\ \hline \end{array}\)

 

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heureka  Apr 20, 2017

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