6.3混合数和分数估计

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  混合数和分数估计

  

  [Figure 1]

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  Travis was practicing for the long jump. His first jump was  $\begin{array}{r}8\frac{3}{4}\end{array}$  feet. After practicing for a month, he was able to add  $\begin{array}{r}2\frac{1}{3}\end{array}$  feet to his record. About how many feet is Travis able to jump? Estimate the distance. 
  ::Travis正在练习长长的跳跃。 他的第一次跳跃是 8 3 4 英尺。 在练习了一个月后, 他能在记录上增加2 13 英尺。 关于Travis 能够跳多少英尺? 估计距离 。

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  In this concept, you will learn how to estimate the sums and differences of fractions and mixed numbers.
  ::在这个概念中,你将学会如何估计分数和混合数字的总数和差异。

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  Estimating Mixed Numbers and Fractions
  ::估计混合数字和分数

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  A  sum  is the answer in addition problem. You can also estimate the sum of fractions. To estimate a sum of two fractions,  round  the fractions to the nearest half. Here is an addition problem.
  ::一个总和是附加问题的答案。您也可以估算分数的总和。要估算两个分数的总和,请将分数四舍五入到最近的一半。这里是一个添加问题。

  $$\begin{array}{r}\frac{3}{8}+\frac{1}{7}=\underset{\_}{}\end{array}$$

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  First, round each fraction to the nearest half.
  ::首先,将每一分数圆到最近的一半。

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  Let’s start with  $\begin{array}{r}\frac{3}{8}\end{array}$ . For a whole divided into 8 parts,  $\begin{array}{r}\frac{1}{2}=\frac{4}{8}\end{array}$ .  $\begin{array}{r}\frac{3}{8}\end{array}$  is rounded to  $\begin{array}{r}\frac{1}{2}\end{array}$ .
  ::我们从3 8开始。整体分为8个部分,1 2 = 4 8。3 8四舍五入为1 2。

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  For a whole divided into 7 parts, one-half is between  $\begin{array}{r}\frac{3}{7}\end{array}$  and  $\begin{array}{r}\frac{4}{7}\end{array}$ .  $\begin{array}{r}\frac{1}{7}\end{array}$  is rounded 0. 
  ::整体分为7部分,半部分在3、7和4、7和7之间。

  $$\begin{array}{rl}\frac{3}{8}& \approx \frac{1}{2}\\ \frac{1}{2}& \approx 0\end{array}$$

  Then, rewrite the problem and find the sum.

  $$\begin{array}{r}\frac{1}{2}+0=\frac{1}{2}\end{array}$$

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  The estimate sum is  $\begin{array}{r}\frac{1}{2}\end{array}$ .
  ::估计数为12美元。

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  When estimating the sum of mixed numbers, round to the nearest whole number instead of the nearest half. Here is an addition problem involving mixed numbers. 
  ::当估算混合数字的总和时,将四舍五入到最近的整数,而不是最近的一半。这里还有一个涉及混合数字的额外问题。

  $$\begin{array}{r}3\frac{4}{5}+2\frac{1}{9}=\underset{\_}{}\end{array}$$

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  First, round each  mixed number  to the nearest whole number.
  ::首先,将每个混合数的四舍五入到最近的整数中。

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    $\begin{array}{r}3\frac{4}{5}\end{array}$   will either round down to 3 or up to 4. Look at the fraction part of the mixed number.  $\begin{array}{r}\frac{4}{5}\end{array}$  is greater than  $\begin{array}{r}\frac{1}{2}\end{array}$ . Round up to 4.
  ::3 4 5 将四舍五入到三舍三或四舍四。 看看混合数的分部分。 4 5 大于 12。 组四至四。

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  $\begin{array}{r}2\frac{1}{9}\end{array}$   will either round down to 2 or up to 3. One-ninth is a very small fraction and less than  $\begin{array}{r}\frac{1}{2}\end{array}$ . Round down to 2. 
  ::2 9 将四舍五入至 2 或最多 3 。 一十九是很小的一小部分,小于 12 。四舍五入到 2 。

  $$\begin{array}{rl}3\frac{4}{5}& \approx 4\\ 2\frac{1}{9}& \approx 2\end{array}$$

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  Then, rewrite the problem and find the sum.
  ::然后,重写问题 并找到金额。

  $$\begin{array}{r}4+2=6\end{array}$$

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  The estimate sum is 6.
  ::估计数总额为6。

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  When talking about a  difference , you are talking about subtraction. Estimating the difference of fractions and mixed numbers is similar to estimating sums. Round each fraction or mixed number and then subtract to find the estimate.
  ::当谈论差异时,您谈论的是减法。估计分数和混合数字的差数与估计总和相似。对每个分数或混合数字进行四舍五入,然后减去以找到估计数。

  $$\begin{array}{r}\frac{4}{5}-\frac{3}{7}=\underset{\_}{}\end{array}$$

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  First, round each fraction to the nearest half. 
  ::首先,将每一分数圆到最近的一半。

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  For a whole divided into 5 parts, one-half is between  $\begin{array}{r}\frac{2}{5}\end{array}$  and  $\begin{array}{r}\frac{3}{5}\end{array}$ .  $\begin{array}{r}\frac{4}{5}\end{array}$  is rounded to 1. 
  ::整体分为5个部分,半部分介于2个5个和3个5个5个5个之间。 4个4个5个四舍五入为1个。

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  For a whole divided into 7 parts, is one-half is between  $\begin{array}{r}\frac{3}{7}\end{array}$  and  $\begin{array}{r}\frac{4}{7}\end{array}$ .   $\begin{array}{r}\frac{3}{7}\end{array}$  is rounded to  $\begin{array}{r}\frac{1}{2}\end{array}$ .
  ::整体分为7个部分,一半在3、7和4、7和7之间。 3、7、7四舍五入至12。

  $$\begin{array}{rl}\frac{4}{5}& \approx 1\\ \frac{3}{7}& \approx \frac{1}{2}\end{array}$$

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  Then, rewrite the problem and subtract.
  ::然后重写问题再减

  $$\begin{array}{r}1-\frac{1}{2}=\frac{1}{2}\end{array}$$

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  The estimate difference is  $\begin{array}{r}\frac{1}{2}\end{array}$ .
  ::估计差额为12美元。

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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 practicing the long jump.
  ::早些时候,你遇到一个 Travis做长途跳跃的问题

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  Travis started at  $\begin{array}{r}8\frac{3}{4}\end{array}$  feet and was able to add  $\begin{array}{r}2\frac{1}{3}\end{array}$  feet to his long jump record. Round the numbers and add the numbers to find an estimate of his current long jump record. 
  ::Travis从8,3,4英尺开始,在长长的跳跃记录上又增加了2,13英尺。翻转数字并添加数字以寻找他目前长跳跃记录的估计值。

    $\begin{array}{r}8\frac{3}{4}+2\frac{1}{3}\end{array}$

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  First, round the mixed numbers to the nearest whole number. 
  ::首先,将混合数字四舍五入到最近的整数。

    $\begin{array}{r}8\frac{3}{4}\approx 9\\ 2\frac{1}{3}\approx 2\end{array}$

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  Then, rewrite the problem and add.
  ::然后,重写问题并添加。

    $\begin{array}{r}9+2=11\end{array}$

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  Travis can now jump approximately 11 feet.
  ::Travis现在可以跳大约11英尺了

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  Example 2
  ::例2

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  Estimate the difference:
  ::估计差异:

  $\begin{array}{r}6\frac{3}{4}-2\frac{1}{8}=\underset{\_}{}\end{array}$ .

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  First, round each mixed number to the nearest whole number. Look at the fraction part of each mixed number. 
  ::首先,将每个混合数的四舍五入到最近的整数。请看每个混合数的分部分。

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  $\begin{array}{r}\frac{3}{4}\end{array}$  is greater than  $\begin{array}{r}\frac{1}{2}\end{array}$ .  $\begin{array}{r}6\frac{3}{4}\end{array}$  rounds up to 7.
  ::3 4 大于 1 2 . 6 3 4 发到 7 。

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  $\begin{array}{r}\frac{1}{8}\end{array}$  is less than  $\begin{array}{r}\frac{1}{2}\end{array}$ .  $\begin{array}{r}2\frac{1}{8}\end{array}$  rounds down to 2.
  ::1 8 少于 1 2 。 2 2 18 发子弹, 降到 2 发子弹。

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  Then, rewrite the problem and subtract.
  ::然后重写问题再减

  $\begin{array}{r}7-2=5\end{array}$

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  The estimate sum is 5.
  ::估计数为5。

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  Example 3
  ::例3

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  Estimate the sum:  $\begin{array}{r}\frac{4}{9}+\frac{7}{8}=\underset{\_}{}\end{array}$ .
  ::估计总和:4 9+7 8=_。

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  First, round each fraction to the nearest half.
  ::首先,将每一分数圆到最近的一半。

    $\begin{array}{rl}\frac{4}{9}& \approx \frac{1}{2}\\ \frac{7}{8}& \approx 1\end{array}$

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  Then, rewrite the problem and add.
  ::然后,重写问题并添加。

    $\begin{array}{r}\frac{1}{2}+1=1\frac{1}{2}\end{array}$

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  The estimate sum is  $\begin{array}{r}1\frac{1}{2}\end{array}$ .
  ::估计数为1,12。

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  Example 4
  ::例4

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  Estimate the sum:  $\begin{array}{r}\frac{6}{7}+\frac{1}{11}=\underset{\_}{}\end{array}$ .
  ::估计总和:6 7+1 11=_。

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  First, round each fraction to the nearest half.
  ::首先,将每一分数圆到最近的一半。

  $\begin{array}{rl}\frac{6}{7}& \approx 1\\ \frac{1}{11}& \approx 0\end{array}$

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  Then, rewrite the problem and add.
  ::然后,重写问题并添加。

    $\begin{array}{r}1+0=1\end{array}$

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  The estimate sum is  $\begin{array}{r}1\end{array}$ .
  ::估计数为1。

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  Example 5
  ::例5

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  Estimate the difference:  $\begin{array}{r}5\frac{1}{3}-2\frac{3}{4}=\underset{\_}{}\end{array}$ .
  ::估计差数:5 1 3 - 2 3 4 = _。

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  First, round the mixed numbers to the nearest whole number.
  ::首先,将混合数字四舍五入到最近的整数。

    $\begin{array}{rl}5\frac{1}{3}& \approx 5\\ 2\frac{3}{4}& \approx 3\end{array}$

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  Then, rewrite the problem and find the difference.
  ::然后重写问题,找出差别

    $\begin{array}{r}5-3=2\end{array}$

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  The estimate difference is  $\begin{array}{r}2\end{array}$ .
  ::估计差额为2美元。

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  Review
  ::回顾

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  Estimate the following sums.
  ::估计以下数额。

  1. $\begin{array}{r}\frac{1}{5}+\frac{4}{5}=\underset{\_}{}\end{array}$
  2. $\begin{array}{r}\frac{8}{9}+\frac{4}{6}=\underset{\_}{}\end{array}$
  3. $\begin{array}{r}\frac{2}{9}+\frac{4}{5}=\underset{\_}{}\end{array}$
  4. $\begin{array}{r}\frac{3}{6}+\frac{2}{3}=\underset{\_}{}\end{array}$
  5. $\begin{array}{r}\frac{5}{6}+\frac{2}{3}=\underset{\_}{}\end{array}$
  6. $\begin{array}{r}\frac{1}{12}+\frac{9}{11}=\underset{\_}{}\end{array}$
  7. $\begin{array}{r}\frac{6}{12}+\frac{10}{11}=\underset{\_}{}\end{array}$
  8. $\begin{array}{r}1\frac{1}{10}+2\frac{1}{2}=\underset{\_}{}\end{array}$
  9. $\begin{array}{r}4\frac{2}{3}+5\frac{4}{5}=\underset{\_}{}\end{array}$
  10. $\begin{array}{r}7\frac{1}{9}+8\frac{1}{5}=\underset{\_}{}\end{array}$
  11. $\begin{array}{r}14\frac{5}{9}+8\frac{4}{5}=\underset{\_}{}\end{array}$
  12. $\begin{array}{r}4\frac{2}{3}+7\frac{1}{7}=\underset{\_}{}\end{array}$
  13. $\begin{array}{r}18\frac{1}{13}+7\frac{2}{10}=\underset{\_}{}\end{array}$
  14. $\begin{array}{r}11\frac{12}{13}+4\frac{1}{10}=\underset{\_}{}\end{array}$
  15. $\begin{array}{r}22\frac{5}{7}+11\frac{1}{5}=\underset{\_}{}\end{array}$

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  Estimate each difference.
  ::估计每个差异。

  16. $\begin{array}{r}\frac{4}{5}-\frac{1}{4}=\underset{\_}{}\end{array}$
  17. $\begin{array}{r}\frac{4}{5}-\frac{3}{4}=\underset{\_}{}\end{array}$
  18. $\begin{array}{r}\frac{9}{10}-\frac{3}{6}=\underset{\_}{}\end{array}$
  19. $\begin{array}{r}\frac{11}{12}-\frac{1}{7}=\underset{\_}{}\end{array}$
  20. $\begin{array}{r}\frac{10}{13}-\frac{1}{10}=\underset{\_}{}\end{array}$

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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