课程： 7.8分数被整数除法

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选择节分数被整数除法

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分数被整数除法
Ray spends $\begin{aligned} \frac{1}{3} \end{aligned}$ of his day at work. He needs to divide his time equally between 3 different projects. How much time should Ray spend on each project? Find the answer in terms of hours.
::Ray每天工作13天,他需要把时间在3个不同的项目之间平均分配。 Ray每个项目要花多少时间? 找到按小时计算的答案。

In this concept, you will learn how to by whole numbers .
::在这个概念中,你将学习如何用整数来计算。

Dividing Fractions by Whole Numbers
::按整数排列的分数

Think about what is happening when you divide a fraction by a whole number. You are taking a part of something and splitting it up into more parts. Here is a division problem.
::想想当您将一个分数除以一个整数时会发生什么。您正在采取某种方式, 并将其分成更多的部分。这是一个分数问题。

$\begin{aligned} \frac{1}{2} \div 3 = \underline{} \end{aligned}$

This problem is asking you to take one-half and divide it into three parts. Here is a picture of one-half.
::这个问题要求你把一半分成三部分。这里是一半的图片。

Divide each half into three parts.
::每一半分成三部分。

Each section is $\begin{aligned} \frac{1}{6} \end{aligned}$ of the whole. One-half divided by 3 is $\begin{aligned} \frac{1}{6} \end{aligned}$ .
::每一节为16个整体,一半除以3为16个。

There are two things to remember when dividing fractions. The first is that you can solve the problem by using the inverse operation . The inverse or opposite of division is multiplication. The second is that you will multiply by the reciprocal of the divisor . Remember that the reciprocal of a fraction is a fraction with the numerator and denominator change places.
::当分割分数时有两点需要记住。首先, 您可以使用反向操作来解决问题。分数的反反反反是乘法。第二, 您会乘以差数的对等。记住一个分数的对等是分数的分数, 与数数和分数的变换位置是分数的分数。

To divide a fraction, multiply by the reciprocal of the divisor. Here is the division problem again.
::分割一个分数, 乘以对等的区划。这是分裂问题再次出现。

$\begin{aligned} \frac{1}{2} \div 3 = \underline{} \end{aligned}$

First, change the operation to multiplication and change 3 to its reciprocal. 3 can be written as the fraction $\begin{aligned} \frac{3}{1} \end{aligned}$ . The reciprocal of $\begin{aligned} \frac{3}{1} \end{aligned}$ is $\begin{aligned} \frac{1}{3} \end{aligned}$ .
::首先,将作业改为乘法,将3改为对等。 3可以写成第3部分第3部分第1部分。

$\begin{aligned} \frac{1}{2} \div 3 = \frac{1}{2} \times \frac{1}{3} \end{aligned}$

Then, multiply the fractions to solve.
::然后,将要解决的分数乘以。

$\begin{aligned} \frac{1}{2} \times \frac{1}{3} = \frac{1}{6} \end{aligned}$

The answer is the same as the diagram above. Dividing a fraction by whole number is the same as multiplying a fraction by the reciprocal of the divisor.
::答案与上面的图表相同。将一个分数按整数分解, 与将一个分数乘以一个分数乘以对等比数相同。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Ray's day at work.
::早些时候,你得到一个问题雷的一天在工作。

Ray needs to evenly divide $\begin{aligned} \frac{1}{3} \end{aligned}$ of his day between 3 projects. Divide $\begin{aligned} \frac{1}{3} \end{aligned}$ by 3 to find how much time he should spend on each project.
::Ray需要平分他一天的13分 3个项目。平分1 3 3 以找出他应该花多少时间在每一个项目上。

First, set up a division problem.
::首先,设置一个分裂问题。

$\begin{aligned} \frac{1}{3} \div 3 = \underline{} \end{aligned}$

Then, change the division problem. Multiply by the reciprocal of the divisor.
::然后,改变分裂问题。乘以对等的断层。

$\begin{aligned} \frac{1}{3} \div 3 = \frac{1}{3} \times \frac{1}{3} \end{aligned}$

Next, multiply the fractions.
::接下来,乘以分数。

$\begin{aligned} \frac{1}{3} \times \frac{1}{3} = \frac{1}{9} \end{aligned}$

Now find $\begin{aligned} \frac{1}{9} \end{aligned}$ of a day in terms of hours. One day is 24 hours. The word "of" tell you to multiply $\begin{aligned} \frac{1}{9} \end{aligned}$ by 24.
::以时数计,每天19小时。一天是24小时。 "of" 这个词告诉你乘以19乘以24。

$\begin{aligned} \frac{1}{9} \times 24 = \frac{1}{9^{3}} \times \frac{24^{8}}{1} = \frac{8}{3} = 2 \frac{2}{3} \end{aligned}$

Ray should spend $\begin{aligned} 2 \frac{2}{3} \end{aligned}$ hours on each project.
::Ray应该在每个项目上花2 2 3个小时

Example 2
::例2

Divide the fraction: $\begin{aligned} \frac{6}{8} \div 4 = \underline{} \end{aligned}$ . Answer in simplest form .
::除以分数: 6 8 4 = _. 回答最简单。

First, change the operation to multiplication and change 4 to its reciprocal.
::首先,将作业改为乘法,将4改为对等。

$\begin{aligned} \frac{6}{8} \div 4 = \frac{6}{8} \times \frac{1}{4} \end{aligned}$

Then, multiply the fractions.
::然后,乘以分数。

$\begin{aligned} \frac{6}{8} \times \frac{1}{4} = \frac{6}{32} \end{aligned}$

Next, simplify the fraction. The of 6 and 32 is 2.
::接下来,简化分数。6和32是2。

$\begin{aligned} \frac{6}{32} = \frac{3}{16} \end{aligned}$

The answer is $\begin{aligned} \frac{3}{16} \end{aligned}$ .
::答案是3 16。

Example 3
::例3

Divide the fraction: $\begin{aligned} \frac{1}{4} \div 2 = \underline{} \end{aligned}$ . Answer in simplest form.
::除以分数: 1 4 2 = _. 回答最简单。

First, change the expression. Multiply by the inverse of the divisor.
::首先,更改表达式。乘以 divisor 的反面。

$\begin{aligned} \frac{1}{4} \div 2 = \frac{1}{4} \times \frac{1}{2} \end{aligned}$

Then, multiply the fractions.
::然后,乘以分数。

$\begin{aligned} \frac{1}{4} \times \frac{1}{2} = \frac{1}{8} \end{aligned}$

The fraction is in simplest form.
::分数以最简单的形式出现。

The answer is $\begin{aligned} \frac{1}{8} \end{aligned}$ .
::答案是18岁

Example 4
::例4

Divide the fraction: $\begin{aligned} \frac{3}{4} \div 3 = \underline{} \end{aligned}$ . Answer in simplest form.
::除以分数: 3 4 + 3 = _. 回答最简单。

First, change the expression. Multiply by the inverse of the divisor.
::首先,更改表达式。乘以 divisor 的反面。

$\begin{aligned} \frac{3}{4} \div 3 = \frac{3}{4} \times \frac{1}{3} \end{aligned}$

Then, multiply the fractions. You can simplify the 3s before multiplying.
::然后,乘以分数。您可以在乘法之前简化 3 。

$\begin{aligned} \frac{3}{4} \times \frac{1}{3} = \frac{1}{4} \end{aligned}$

The fraction is in simplest form.
::分数以最简单的形式出现。

The answer is $\begin{aligned} \frac{1}{4} \end{aligned}$ .
::答案是14。

Example 5
::例5

Divide the fraction: $\begin{aligned} \frac{4}{5} \div 2 = \underline{} \end{aligned}$ . Answer in simplest form.
::除以分数: 4 5 = 2 = _. 回答最简单。

First, change the expression. Multiply by the inverse of the divisor.
::首先,更改表达式。乘以 divisor 的反面。

$\begin{aligned} \frac{4}{5} \div 2 = \frac{4}{5} \times \frac{1}{2} \end{aligned}$

Then, multiply the fractions.
::然后,乘以分数。

$\begin{aligned} \frac{4}{5} \times \frac{1}{2} = \frac{4}{10} \end{aligned}$

Next, simplify the fraction by the greatest common factor of 2.
::其次,将分数简化为2这一最大共同系数。

$\begin{aligned} \frac{4}{10} = \frac{2}{5} \end{aligned}$

The answer is $\begin{aligned} \frac{2}{5} \end{aligned}$ .

::答案是2 5。

Review
::回顾

Divide each fraction and whole number.
::将每个分数和整数除以。

$\begin{aligned} \frac{1}{2} \div 6 = \underline{} \end{aligned}$

$\begin{aligned} \frac{1}{4} \div 8 = \underline{} \end{aligned}$

$\begin{aligned} \frac{1}{3} \div 5 = \underline{} \end{aligned}$

$\begin{aligned} \frac{1}{3} \div 4 = \underline{} \end{aligned}$

$\begin{aligned} \frac{1}{2} \div 7 = \underline{} \end{aligned}$

$\begin{aligned} \frac{1}{5} \div 11 = \underline{} \end{aligned}$

$\begin{aligned} \frac{1}{2} \div 3 = \underline{} \end{aligned}$

$\begin{aligned} \frac{1}{4} \div 4 = \underline{} \end{aligned}$

$\begin{aligned} \frac{1}{9} \div 3 = \underline{} \end{aligned}$

$\begin{aligned} \frac{2}{3} \div 4 = \underline{} \end{aligned}$

$\begin{aligned} \frac{4}{7} \div 3 = \underline{} \end{aligned}$

$\begin{aligned} \frac{2}{5} \div 2 = \underline{} \end{aligned}$

$\begin{aligned} \frac{3}{7} \div 4 = \underline{} \end{aligned}$

$\begin{aligned} \frac{1}{5} \div 6 = \underline{} \end{aligned}$

$\begin{aligned} \frac{8}{9} \div 2 = \underline{} \end{aligned}$

$\begin{aligned} \frac{6}{7} \div 4 = \underline{} \end{aligned}$

Review (Answers)
::回顾(答复)

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。

Resources
::资源

章节大纲

常规

分数被整数除法

Dividing Fractions by Whole Numbers ::按整数排列的分数

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)

Resources ::资源

Dividing Fractions by Whole Numbers
::按整数排列的分数

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)

Resources
::资源