6.6分数表达式求值

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  分数表达式求值

  

  [Figure 1]

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  Travis is sharing a pizza with his friends. The pizza was cut into eighths. Travis took one eighth first and then took two eighths. He was too full to eat one of the eighths, so he gave it to his friend. How much pizza did Travis eat? 
  ::Travis先吃八分之一,然后吃八分之二。他吃不饱,所以把披萨给了朋友。Travis吃了多少披萨?

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  In this concept, you will learn how to evaluate numerical expressions involving the sums and differences of fractions. 
  ::在此概念中,您将学会如何评估包含分数总和和差数的数字表达式。

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  Evaluating Expressions with Fractions
  ::带有分数的评价表达式

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  Some numerical expressions will involve both the  sum  and differences of fractions with common denominators. Evaluating the expression will involve more than one operation. To  evaluate  an expression means to find its value.
  ::有些数字表达式将包含带有共同分母的分数的总和和和差。 评估表达式将涉及不止一个操作。 要评价表达式, 则要评价查找其值的手段 。

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  Here is a  numerical expression .
  ::这里是一个数字表达式。

  $$\begin{array}{r}\frac{9}{10}-\frac{3}{10}+\frac{1}{10}\end{array}$$

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  Check that the fractions all have the same common denominators. In this example, they all have a  common denominator  of 10. When the fractions all have a common denominator, ignore the  denominator  and evaluate the numerators.
  ::检查分数都具有相同的共同分母。 在此示例中, 当分数都有一个共同分母时, 它们都有一个共同分母为 10 。 当分数都有一个共同分母时, 忽略分母并评估分子 。

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  Follow the  order  of operations. Resolve the operations with parenthesis first, and then add or subtract the fractions going from left to right. Start with finding the  difference  between the first two numerators, 9 and 3. Then, add 1 to the difference.
  ::遵循操作的顺序。 先用括号解析操作, 然后添加或减去从左到右的分数。 从找到前两个数字( 9 和 3) 之间的差数开始, 然后在差数中添加 1 。

  $$\begin{array}{r}9-3=6+1=7\end{array}$$

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  Put the result over the common denominator.
  ::将结果置于共同分母之上。

  $$\begin{array}{r}\frac{7}{10}\end{array}$$

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  Finally, write the fraction in  simplest form . The   of 7 and 10 is 1. The fraction is already in simplest form.
  ::最后, 以最简单的形式写入分数 。 7 和 10 是 1 。 分数已经以最简单的形式写入 。

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  Therefore, the value of the expression is  $\begin{array}{r}\frac{7}{10}\end{array}$ .
  ::因此,该表达式的价值是7 10。

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about Travis and the pizza.
  ::早些时候,你被问及 Travis和比萨饼的问题。

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  Travis first takes an eighth of the pizza, takes 2 more, but then gives one to his friend. Evaluate the expression to find out how much of the pizza Travis ate.
  ::Travis先吃八分之一的披萨,再多吃两块,然后再给他朋友吃。

  $\begin{array}{r}\frac{1}{8}+\frac{2}{8}-\frac{1}{8}=\underset{\_}{}\end{array}$

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  First, check if the fractions have a common denominator. The common denominator is 8.
  ::首先,检查分数是否有共同的分母。 共同的分母是 8 。

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  Then, add or subtract the numerators in order from left to right. 
  ::然后,将分子从左到右相加或减。

  1 + 2 = 3 - 1 = 2

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  Next, write the results as the  numerator  of the fraction.
  ::下一步,将结果写成分数的分子。

  $\begin{array}{r}\frac{2}{8}\end{array}$

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  Finally,  simplify  the fraction. The GCF of 2 and 8 s 2.
  ::最后,简化分数,全球合作框架为2和8秒2。

    $\begin{array}{r}\frac{2÷2}{8÷2}=\frac{1}{4}\end{array}$

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  Travis ate  $\begin{array}{r}\frac{1}{4}\end{array}$  of the pizza.
  ::Travis吃了14份披萨

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  Example 2
  ::例2

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  Evaluate the expression. Answer in simplest form.
  ::评估表达式,以最简单的形式回答。

  $\begin{array}{r}\frac{8}{9}+\frac{4}{9}-\frac{1}{9}\end{array}$

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  First, check if the fractions have a common denominator. They have a common denominator of 9.
  ::首先,检查分数是否有共同的分母。它们有一个共同的分母为 9。

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  Then, add or subtract the numerators in order from left to right. 
  ::然后,将分子从左到右相加或减。

  8 + 4 = 12 - 1 = 11

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  Next, write the result as  the numerator over the common denominator. 
  ::下一步,将结果写成共同分母上的分子。

  $\begin{array}{r}\frac{11}{9}\end{array}$

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  Finally, simplify the  improper fraction . Convert the improper fraction to a  mixed number . Remember that to convert an improper fraction to a mixed number,  divide  the numerator by the denominator. 
  ::最后,简化不当分数。 将不当分数转换成混合数。 记住, 要将不适当分数转换成混合数, 分子除以分母 。

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  $\begin{array}{r}11÷9=1\text{R}2=1\frac{2}{9}\end{array}$
  ::11 9 = 1 R 2 = 1 2 9

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  The final answer is  $\begin{array}{r}1\frac{2}{9}\end{array}$ .
  ::最后一个答案是 1 2 9 。

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  Example 3
  ::例3

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  Evaluate the expression:  $\begin{array}{r}\frac{6}{7}-\frac{2}{7}+\frac{1}{7}\end{array}$ . Answer in simplest form.
  ::评价表达式:6 7-2 7+1 7。回答最简单。

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  First, check if the fractions have a common denominator. They have a common denominator of 7.
  ::首先,检查分数是否有共同分母。它们有7个共同分母。

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  Then, add or subtract the numerators in order from left to right. 
  ::然后,将分子从左到右相加或减。

  6 - 2 = 4 + 1 = 5

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  Next, write the result as the numerator to the fraction.
  ::下一步,将结果写成分数中的分子。

    $\begin{array}{r}\frac{5}{7}\end{array}$

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  The final answer is  $\begin{array}{r}\frac{5}{7}\end{array}$ .
  ::最后一个答案是5 7。

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  Example 4
  ::例4

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  Evaluate the expression:  $\begin{array}{r}\frac{3}{4}+\frac{3}{4}-\frac{1}{4}\end{array}$ . Answer in simplest form.
  ::评价这一表述:3 4 + 3 4 - 14. 回答最简单。

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  First, check if the fractions have a common denominator. They have a common denominator of 9.
  ::首先,检查分数是否有共同的分母。它们有一个共同的分母为 9。

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  Then, add or subtract the numerators in order from left to right. 
  ::然后,将分子从左到右相加或减。

  3 + 3 = 6 - 1 = 5

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  Next, write the result as the numerator to the fraction.
  ::下一步,将结果写成分数中的分子。

    $\begin{array}{r}\frac{5}{4}\end{array}$  

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  Finally, simplify the fraction. Convert the improper fraction to a mixed number.
  ::最后,简化分数,将不适当的分数转换成混合数。

  $\begin{array}{r}\frac{5}{4}\end{array}$  =  $\begin{array}{r}1\frac{1}{4}\end{array}$

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  The final answer is  $\begin{array}{r}1\frac{1}{4}\end{array}$ .
  ::最后一个答案是11.4。

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  Example 5
  ::例5

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  Evaluate the expression:  $\begin{array}{r}\frac{7}{8}+\frac{3}{8}-\frac{2}{8}\end{array}$ . Answer in simplest form.
  ::评估表达式:7 8+3 8-2 8。回答最简单。

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  First, check if the fractions have a common denominator. They have a common denominator of 9.
  ::首先,检查分数是否有共同的分母。它们有一个共同的分母为 9。

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  Then, add or subtract the numerators in order from left to right. 
  ::然后,将分子从左到右相加或减。

  7 + 3 = 10 - 2 = 8

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  Next, write the result as the numerator to the fraction.
  ::下一步,将结果写成分数中的分子。

    $\begin{array}{r}\frac{8}{8}=1\end{array}$

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  Remember that a number over itself is equal to 1.
  ::记住一个数字本身等于1。

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  The final answer is 1.
  ::最后一个答案是1。

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  Review
  ::回顾

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  Evaluate the numerical expressions. Answer in simplest form.
  ::评估数字表达式。 以最简单的形式回答 。

  1. $\begin{array}{r}\frac{7}{9}+\frac{2}{9}-\frac{6}{9}\end{array}$
  2. $\begin{array}{r}\frac{3}{10}+\frac{4}{10}-\frac{1}{10}\end{array}$
  3. $\begin{array}{r}\frac{8}{9}+\frac{1}{9}-\frac{3}{9}\end{array}$
  4. $\begin{array}{r}\frac{8}{12}+\frac{1}{12}-\frac{4}{12}\end{array}$
  5. $\begin{array}{r}\frac{13}{14}+\frac{3}{14}-\frac{9}{14}\end{array}$
  6. $\begin{array}{r}\frac{9}{17}-\frac{5}{17}+\frac{3}{17}\end{array}$
  7. $\begin{array}{r}\frac{8}{11}+\frac{2}{11}-\frac{6}{11}\end{array}$
  8. $\begin{array}{r}\frac{13}{16}+\frac{1}{16}-\frac{6}{16}\end{array}$
  9. $\begin{array}{r}\frac{12}{17}-\frac{6}{17}+\frac{3}{17}\end{array}$
  10. $\begin{array}{r}\frac{8}{10}+\frac{9}{10}-\frac{7}{10}\end{array}$
  11. $\begin{array}{r}\frac{11}{14}+\frac{3}{14}-\frac{10}{14}\end{array}$
  12. $\begin{array}{r}\frac{19}{24}+\frac{13}{24}-\frac{20}{24}\end{array}$
  13. $\begin{array}{r}\frac{12}{13}+\frac{1}{13}-\frac{8}{13}\end{array}$
  14. $\begin{array}{r}\frac{23}{24}+\frac{1}{24}-\frac{12}{24}\end{array}$
  15. $\begin{array}{r}\frac{11}{15}+\frac{2}{15}-\frac{8}{15}\end{array}$

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  Review (Answers) 
  ::回顾(答复)

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  Click   to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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  Resources
  ::资源