课程： 3.8混合数或分数减法估计

章节大纲

选择节常规

折叠展开
常规

全部折叠展开全部
- 选择活动新闻通告
  
  新闻通告讨论区
选择节混合数或分数减法估计

折叠展开
混合数或分数减法估计
Tessa is about to make some apple crisp. She is going to use walnuts in her crisp topping. She just opened a new bag of walnuts and the package says it contains $\begin{aligned} 4 \frac{1}{4} \end{aligned}$ cups of walnuts. She will be using $\begin{aligned} \frac{7}{8} \end{aligned}$ of a cup of walnuts in her apple crisp. How can Tessa estimate how many cups of walnuts she will have left after making her apple crisp? If her mom needs $\begin{aligned} 2 \frac{1}{2} \end{aligned}$ cups of walnuts to make candied walnuts, will she have enough to do that?
::Tessa正准备做苹果脆饼。她要用核桃做苹果脆饼。她刚打开了一袋胡桃,包子上说里面有414杯胡桃。她要用78杯核桃做苹果脆饼。 Tessa怎么估计她做苹果脆饼后会离开多少杯胡桃? 她妈妈需要212杯胡桃做罐头胡桃吗?

In this concept, you will learn how to estimate 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差异。

Estimating Differences of Fractions and Mixed Numbers
::分数和混合数字的估计差异

Recall that estimation is a method for finding an approximate solution to a problem. Even when you are asked to find an exact answer, estimation is a useful way to get an idea of a reasonable solution to a problem. Once you have found an exact answer, you can check your answer against the estimate.
::回顾估算是找到问题大致解决办法的一种方法。即使您被要求找到确切答案,估算也是找到合理解决问题办法的有用方法。一旦您找到准确答案,您可以对照估算来查看您的答复。

When working with fractions and mixed numbers, you can use the fraction benchmarks of 0, $\begin{aligned} \frac{1}{2} \end{aligned}$ , and 1 to help you to estimate differences.
::当使用分数和混合数字时,您可以使用 0、12和1 的分数基准来帮助您估算差异。

Here are the steps for estimating the differences of fractions and mixed numbers using benchmarks.
::以下是使用基准估计分数和混合数字差异的步骤。

Approximate the value of each fraction or mixed number using the benchmarks of 0, $\begin{aligned} \frac{1}{2} \end{aligned}$ , and 1.
::使用0、1、2和1的基准,接近每个分数或混合数的数值。

Subtract the approximated values to get an estimated difference .
::减去近似值以获得估计差异。

Here is an example.
::举一个例子。

Estimate the difference of $\begin{aligned} \frac{7}{8} - \frac{4}{9} \end{aligned}$ .
::估计差值为7 8 - 4 9。

First, approximate the value of each individual fraction.
::首先,大致相当于每一分数的数值。

$\begin{aligned} \frac{7}{8} \end{aligned}$ is approximately 1
::7 8 大约是 1

$\begin{aligned} \frac{4}{9} \end{aligned}$ is approximately $\begin{aligned} \frac{1}{2} \end{aligned}$
::4 9 大约是1 2

Next, subtract the approximated values.
::下一步,减去大致数值。

$\begin{aligned} 1 - \frac{1}{2} = \frac{1}{2} \end{aligned}$

The answer is $\begin{aligned} \frac{7}{8} - \frac{4}{9} \end{aligned}$ is approximately $\begin{aligned} \frac{1}{2} \end{aligned}$ .
::答案是7 8 - 4 9 大约是12。

Here is another example.
::下面是另一个例子。

Estimate the difference of $\begin{aligned} 5 \frac{7}{8} - 5 \frac{1}{16} \end{aligned}$ .
::估计差额为5 7 8 - 5 1 16。

First, approximate the value of each individual mixed number.
::首先,大约每个混杂数字的价值。

$\begin{aligned} 5 \frac{7}{8} \end{aligned}$ is approximately 6
::5 7 8 大约是 6

$\begin{aligned} 5 \frac{1}{16} \end{aligned}$ is approximately 5
::5 1 16 约 5

Next, subtract the approximated values.
::下一步,减去大致数值。

$\begin{aligned} 6 - 5 = 1 \end{aligned}$

The answer is $\begin{aligned} 5 \frac{7}{8} - 5 \frac{1}{16} \end{aligned}$ is approximately 1.
::答案是5 7 8 - 5 1 16 大约为 1。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Tessa and her apple crisp.
::早些时候,你得到一个问题关于苔莎和她的苹果杯。

Tessa just opened a new bag of walnuts that contains $\begin{aligned} 4 \frac{1}{4} \end{aligned}$ cups of walnuts. She will be using $\begin{aligned} \frac{7}{8} \end{aligned}$ of a cup of walnuts in her apple crisp. She wants to estimate how many cups of walnuts will be left after she makes her apple crisp. She needs to make sure her mom will have at least $\begin{aligned} 2 \frac{1}{2} \end{aligned}$ cups of walnuts to make candied walnuts later.
::Tessa刚刚打开了一袋新的胡桃,里面装有414杯胡桃。她将在苹果杯中用78杯胡桃。她想估计在她做苹果杯后还剩下多少杯胡桃。她需要确保她妈妈至少有212杯胡桃,以便以后做罐头胡桃。

Tessa needs to estimate the difference of $\begin{aligned} 4 \frac{1}{4} - \frac{7}{8} \end{aligned}$ .
::Tessa需要估计差额4,1,4,7,8。

First, she should approximate the value of each individual mixed number and fraction.
::首先,她应接近每个个别混合数和分数的价值。

$\begin{aligned} 4 \frac{1}{4} \end{aligned}$ is approximately 4
::1,4,4,4,大约4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,大约4,4,4,4,4,4,4,4,4,4,4,4,4,大约4,4,4,4,4,4,4,4,4,4,4,4,约4,4,4,4,4,4,4,4,4,4,4,约4,4,4,4,4,4,4,4,4,4,约4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,约4,4,4,4,4,约4,4,4,4,约4,4,4,4,4,4,4,4,4,4,4,约4,4,4,4,4,4,4,4,4,4,约4,4,4,4,4,4,4,约4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,约4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,约

$\begin{aligned} \frac{7}{8} \end{aligned}$ is approximately 1
::7 8 大约是 1

Next, Tessa should subtract the approximated values.
::其次,Tessa应减去大致数值。

$\begin{aligned} 4 - 1 = 3 \end{aligned}$

The answer is $\begin{aligned} 4 - 1 \end{aligned}$ is approximately 3. Tessa's mom should have enough walnuts to make her candied walnuts later.
::答案是4 -1大约是3 Tessa的妈妈应该有足够的核桃以后再做罐头核桃

Example 2
::例2

Estimate the difference of $\begin{aligned} 4 \frac{1}{15} - 2 \frac{3}{4} \end{aligned}$ .
::估计差额为4 1 15-2 3 4。

First, approximate the value of each individual mixed number.
::首先,大约每个混杂数字的价值。

$\begin{aligned} 4 \frac{1}{15} \end{aligned}$ is approximately 4
::4 1 15 约 4

$\begin{aligned} 2 \frac{3}{4} \end{aligned}$ is approximately 3
::2 3 4 大约3 3 4

Next, subtract the approximated values.
::下一步,减去大致数值。

$\begin{aligned} 4 - 3 = 1 \end{aligned}$

The answer is $\begin{aligned} 4 \frac{1}{15} - 2 \frac{3}{4} \end{aligned}$ is approximately 1.
::答案是4 1 15 - 2 3 4 大约为 1。

Example 3
::例3

Estimate the difference of $\begin{aligned} 6 \frac{5}{6} - \frac{9}{10} \end{aligned}$ .
::估计差额为6 5 6-9 10。

First, approximate the value of each individual mixed number and fraction.
::首先,大致相当于每个个别混合数和分数的数值。

$\begin{aligned} 6 \frac{5}{6} \end{aligned}$ is approximately 7
::6 5 6 6 大约是 7

$\begin{aligned} \frac{9}{10} \end{aligned}$ is approximately 1
::9 10 大约是 1

Next, subtract the approximated values.
::下一步,减去大致数值。

$\begin{aligned} 7 - 1 = 6 \end{aligned}$

The answer is $\begin{aligned} 6 \frac{5}{6} - \frac{9}{10} \end{aligned}$ is approximately 6.
::答案是6 5 6 6 - 9 10 大约是6。

Example 4
::例4

Estimate the difference of $\begin{aligned} \frac{8}{9} - \frac{1}{7} \end{aligned}$ .
::估计差值为8 9 - 1 7。

First, approximate the value of each individual fraction.
::首先,大致相当于每一分数的数值。

$\begin{aligned} \frac{8}{9} \end{aligned}$ is approximately 1
::8个是9个大约1个

$\begin{aligned} \frac{1}{7} \end{aligned}$ is approximately 0
::1 7 约 0 0

Next, subtract the approximated values.
::下一步,减去大致数值。

$\begin{aligned} 1 - 0 = 1 \end{aligned}$

The answer is $\begin{aligned} \frac{8}{9} - \frac{1}{7} \end{aligned}$ is approximately 1.
::答案是 8 9 - 1 7 大约是 1 。

Example 5
::例5

Estimate the difference of $\begin{aligned} 4 \frac{4}{5} - 1 \frac{2}{5} \end{aligned}$ .
::估计差额为4 4 5 - 1 2 5。

First, approximate the value of each individual mixed number.
::首先,大约每个混杂数字的价值。

$\begin{aligned} 4 \frac{4}{5} \end{aligned}$ is approximately 5
::4 4 5 约 5

$\begin{aligned} 1 \frac{2}{5} \end{aligned}$ is approximately $\begin{aligned} 1 \frac{1}{2} \end{aligned}$
::1 2 5 大约 1 1 2

Next, subtract the approximated values.
::下一步,减去大致数值。

$\begin{aligned} 5 - 1 \frac{1}{2} = 3 \frac{1}{2} \end{aligned}$

The answer is $\begin{aligned} 4 \frac{4}{5} - 1 \frac{2}{5} \end{aligned}$ is approximately $\begin{aligned} 3 \frac{1}{2} \end{aligned}$ .
::答案是4 4 5 - 1 2 5 大约是 3 1 2 。

Review
::回顾

Estimate the differences.
::估计差异。

$\begin{aligned} \frac{14}{16} - \frac{1}{11} \end{aligned}$

$\begin{aligned} \frac{28}{60} - \frac{6}{13} \end{aligned}$

$\begin{aligned} \frac{6}{7} - \frac{2}{145} \end{aligned}$

$\begin{aligned} \frac{32}{33} - \frac{5}{12} \end{aligned}$

$\begin{aligned} \frac{32}{33} - \frac{1}{12} \end{aligned}$

$\begin{aligned} 14 \frac{20}{21} - 3 \frac{18}{10} \end{aligned}$

$\begin{aligned} 2 \frac{1}{49} - 1 \frac{13}{14} \end{aligned}$

$\begin{aligned} 3 \frac{2}{21} - 2 \frac{6}{11} \end{aligned}$

$\begin{aligned} 4 \frac{8}{17} - \frac{71}{73} \end{aligned}$

$\begin{aligned} 2 \frac{1}{49} - 1 \frac{13}{14} \end{aligned}$

$\begin{aligned} 12 \frac{3}{4} - 11 \frac{1}{14} \end{aligned}$

$\begin{aligned} 23 \frac{6}{8} - 14 \frac{3}{4} \end{aligned}$

$\begin{aligned} 18 \frac{1}{9} - 12 \frac{3}{10} \end{aligned}$

$\begin{aligned} 22 \frac{1}{2} - 5 \frac{12}{34} \end{aligned}$

$\begin{aligned} 27 \frac{1}{5} - 18 \frac{7}{8} \end{aligned}$

Review (Answers)
::回顾(答复)

章节大纲

常规

混合数或分数减法估计

Estimating Differences of Fractions and Mixed Numbers ::分数和混合数字的估计差异

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Review (Answers) ::回顾(答复)

Estimating Differences of Fractions and Mixed Numbers
::分数和混合数字的估计差异

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Example 5
::例5

Review
::回顾

Review (Answers)
::回顾(答复)