Section: 分数商 | 7.10分数商

Section outline

Corey is planning on making waffles. The recipe says to use $\begin{aligned} \frac{3}{4} \end{aligned}$ cups of flour, but Corey can only find the $\begin{aligned} \frac{1}{3} \end{aligned}$ -cup measuring cup. How many $\begin{aligned} \frac{1}{3} \end{aligned}$ -cups does Corey need to make his waffles?
::科里正计划制作华夫饼。食谱上说要用34杯面粉,但科里只能找到13杯杯杯子。科里需要多少13杯子来做华夫饼?

In this concept, you will learn how to divide a fraction by a fraction.
::在这个概念中,你会学会如何将一个分数除以一个分数。

Dividing Fractions
::分数分数

When dividing whole numbers and fractions, you first change the operation to multiplication and then change the divisor to its reciprocal . The same rule applies to dividing a fraction by another fraction. Here is a division problem.
::当分隔整数和分数时,您先将操作修改为乘法,然后将差数修改为对等。同一规则适用于将一个分数除以另一个分数。这里有一个分割问题。

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

Start by applying the first part of the rule and change the sign to multiplication. Then apply the second part of the rule, the reciprocal of one-third is three over one.
::从适用规则的第一部分开始,并将符号改为乘法。然后适用规则的第二部分,三分之一的对等为三乘一。

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

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

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

Next, simply the fraction. Convert the improper fraction a mixed number .
::接下来,简单的分数。将不适当的分数转换成混合数。

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

The quotient is $\begin{aligned} 1 \frac{1}{2} \end{aligned}$ .
::商数是1112

As long as you apply the rules, the problem is very straightforward and simple to figure out. Here is another one.
::只要你遵守规则,问题就简单明了。这是另一个问题。

$\begin{aligned} \frac{8}{9} \div \frac{1}{3} \end{aligned}$

First, change the operation and change $\begin{aligned} \frac{1}{3} \end{aligned}$ to its reciprocal.
::首先,改变行动,将13改为对等。

$\begin{aligned} \frac{8}{9} \div \frac{1}{3} = \frac{8}{9} \times \frac{3}{1} \end{aligned}$

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

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

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

$\begin{aligned} \frac{24}{9} = 2 \frac{5}{9} \end{aligned}$

The quotient is $\begin{aligned} 2 \frac{5}{9} \end{aligned}$ .
::商数是2 5 9

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Corey and his waffles.
::早些时候,你得到一个问题关于科里和他的华夫饼。

Corey needs to measure out $\begin{aligned} \frac{3}{4} \end{aligned}$ cups of flour for his waffles, but can only find a $\begin{aligned} \frac{1}{3} \end{aligned}$ measuring cup. Divide $\begin{aligned} \frac{3}{4} \end{aligned}$ by $\begin{aligned} \frac{1}{3} \end{aligned}$ to find how many $\begin{aligned} \frac{1}{3} \end{aligned}$ cups Corey should use.
::科里需要测量3 4 杯面粉作为他的华夫饼,但只能找到13杯。 3 4 乘 1 3 来找出科里应该使用多少13杯面粉。

First, write an expression.
::首先,写一个表达方式。

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

Then, change the operation to multiplication and change the divisor to its reciprocal.
::然后,将操作改变成乘法将断层改变成对等

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

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

$\begin{aligned} \frac{3}{4} \times \frac{3}{1} = \frac{9}{4} \end{aligned}$

Finally, convert the improper fraction to a mixed number.
::最后,将不当的分数转换成混合数。

$\begin{aligned} \frac{9}{4} = 2 \frac{1}{4} \end{aligned}$

Corey can use a little more than 2 of the $\begin{aligned} \frac{1}{3} \end{aligned}$ measuring cup to make his waffles.
::科里能用超过13个杯子中的2个来做他的华夫饼

Example 2
::例2

Divide the fractions: $\begin{aligned} \frac{4}{9} \div \frac{1}{2} \end{aligned}$ = _____. Answer in simplest form .
::除以分数: 4 9 1 2 = 。回答最简单。

First, change the operation to multiplication and $\begin{aligned} \frac{1}{2} \end{aligned}$ to its reciprocal.
::首先,将作业改为乘法,将乘法改为乘法,将乘法改为乘法,将乘法改为乘法。

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

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

$\begin{aligned} \frac{4}{9} \times \frac{2}{1} = \frac{8}{9} \end{aligned}$

The quotient is $\begin{aligned} \frac{8}{9} \end{aligned}$ .
::商数是 8 9 。

Example 3
::例3

Divide the fractions: $\begin{aligned} \frac{1}{4} \div \frac{3}{4} = \underline{} \end{aligned}$ . Answer in simplest form.
::除以分数:1 4+ 3 4 = _. 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。

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

Then, multiply.
::然后,乘数。

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

The quotient is $\begin{aligned} \frac{1}{3} \end{aligned}$ .
::商数是13

Example 4
::例4

Divide the fractions: $\begin{aligned} \frac{7}{8} \div \frac{1}{4} = \underline{} \end{aligned}$ . Answer in simplest form.
::除以分数: 7 8 1 4 = _. 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。

$\begin{aligned} \frac{7}{8} \div \frac{1}{4} = \frac{7}{8} \times \frac{4}{1} \end{aligned}$

Then, multiply.
::然后,乘数。

$\begin{aligned} \frac{7}{8^{2}} \times \frac{4^{1}}{1} = \frac{7}{2} \end{aligned}$

Next, convert the improper fraction to a mixed number.
::接下来,将不当的分数转换成混合数。

$\begin{aligned} \frac{7}{2} = 3 \frac{1}{2} \end{aligned}$

The quotient is $\begin{aligned} 3 \frac{1}{2} \end{aligned}$
::商数是3112

Example 5
::例5

Divide the fractions: $\begin{aligned} \frac{1}{4} \div \frac{1}{3} = \underline{} \end{aligned}$ . Answer in simplest form.
::除以分数:1 4+1 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。

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

Then, multiply.
::然后,乘数。

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

The quotient is $\begin{aligned} \frac{3}{4} \end{aligned}$ .

::商数是34

Review
::回顾

Divide the fractions. Answer in simplest form.
::除以分数。以最简单的形式回答。

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

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

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

$\begin{aligned} \frac{4}{7} \div \frac{1}{3} = \underline{} \end{aligned}$

$\begin{aligned} \frac{6}{8} \div \frac{1}{2} = \underline{} \end{aligned}$

$\begin{aligned} \frac{4}{9} \div \frac{1}{3} = \underline{} \end{aligned}$

$\begin{aligned} \frac{5}{6} \div \frac{1}{2} = \underline{} \end{aligned}$

$\begin{aligned} \frac{6}{10} \div \frac{1}{2} = \underline{} \end{aligned}$

$\begin{aligned} \frac{9}{18} \div \frac{1}{3} = \underline{} \end{aligned}$

$\begin{aligned} \frac{8}{9} \div \frac{1}{2} = \underline{} \end{aligned}$

$\begin{aligned} \frac{15}{16} \div \frac{1}{5} = \underline{} \end{aligned}$

$\begin{aligned} \frac{8}{11} \div \frac{3}{4} = \underline{} \end{aligned}$

$\begin{aligned} \frac{12}{16} \div \frac{3}{4} = \underline{} \end{aligned}$

$\begin{aligned} \frac{20}{24} \div \frac{3}{4} = \underline{} \end{aligned}$

$\begin{aligned} \frac{18}{20} \div \frac{4}{5} = \underline{} \end{aligned}$

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

Section outline

Dividing Fractions ::分数分数

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
::分数分数

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