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Subtract $65\frac{1}{6}$ from $72\frac{2}{3}$. Express your answer as a mixed number. Solution 1: We use the fact that $65\frac{1}{6}$ =$65+\frac{1}{6}$ and $72\frac{2}{3}$=$72+\frac{2}{3}$ to get $$72\frac{2}{3}-65\frac{1}{6}=72+\frac{2}{3}-\left(65+\frac{1}{6}\right)=72+\frac{2}{3}-65-\frac{1}{6}.$$ Rearranging the terms we get \begin{align*} 72+\frac{2}{3}-65-\frac{1}{6}&=\left(72-65\right)+\left(\frac{2}{3}-\frac{1}{6}\right) \&=7+\left(\frac{2}{3}-\frac{1}{6}\right)=7+\left(\frac{4}{6}-\frac{1}{6}\right) \&=7+\frac{3}{6}=7+\frac{1}{2} \&=\boxed{7\frac{1}{2}}. \end{align*} Solution 2: We write $65\frac{1}{6}$ as a fraction by getting a common denominator of 6: $$65+\frac{1}{6}=\frac{390}{6}+\frac{1}{6}=\frac{391}{6}.$$ To subtract $\frac{391}{6}$ from $72\frac{2}{3}$, we first get a common denominator of 6 for $72\frac{2}{3}$ and then rewrite it as a fraction. Doing so, we get $$72+\frac{2}{3}=72+\frac{4}{6}=\frac{432}{6}+\frac{4}{6}=\frac{436}{6}.$$ By subtracting the two numbers, we get $$\frac{436}{6}-\frac{391}{6}=\frac{45}{6}.$$ When we divide 45 by 6 we get a quotient of 7 with a remainder of 3. When converting $\frac{45}{6}$ to a mixed number, we obtain $$\frac{45}{6}=\frac{42+3}{6}=\frac{42}{6}+\frac{3}{6}=7+\frac{3}{6}=7+\frac{1}{2}=\boxed{7\frac{1}{2}}.$$标签：
原文地址：http://www.cnblogs.com/shuxuejd/p/4533107.html
