课程： 5.8最简形式的分数

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最简形式的分数
Tessa made a pan of brownies for the sixth grade social. She cut the brownie pan into sixteen brownies. She sold 12 out of 16 brownies at the bake sale.
::Tessa为六年级的社交活动做了一块巧克力蛋糕她把巧克力饼切成十六块巧克力蛋糕,在蛋糕销售会上卖了16块巧克力蛋糕中的12块

What fraction of the brownies did she sell? What fraction did she not sell?
::她卖了多少块巧克力蛋糕?

In this concept, you will learn to write a fraction in simplest form .
::在此概念中,您将学会以最简单的形式写出一个分数。

Finding Fractions in Simplest Form
::以简单格式查找分数

Some fractions can describe large quantities. Simplifying a fraction can make it easier to understand its value. To simplify a fraction, divide the numerator and the denominator by a common factor. Sometimes you will also hear simplifying called reducing a fraction. A fraction that has been simplified by the is in simplest form . Remember that the greatest common factor (GCF) is the greatest factor that two or more numbers have in common.
::有些分数可以描述大数量。简化一个分数可以更容易理解其值。要简化一个分数, 将分子和分母除以一个共同系数。有时您也会听到简化的叫减少一个分数。一个以最简单的形式简化的分数。记住, 最大的共同系数( GCF) 是两个或两个以上数字共有的最大因素。

Here is a fraction.
::这里有一个分数。

$\begin{aligned} \frac{48}{60} \end{aligned}$

Simplify the fraction to better understand its value.
::简化分数以更好地了解其值。

First, find a common factor for the numerator and denominator.
::首先,找到分子和分母的共同系数。

48 – 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

60 – 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Then, divide by the GCF common factor. The GCF for 48 and 60 is 12
::然后,除以全球合作框架的共同因素。

$\begin{aligned} \frac{48 \div 12}{60 \div 12} = \frac{4}{5} \end{aligned}$

The simplest form of $\begin{aligned} \frac{48}{60} \end{aligned}$ is $\begin{aligned} \frac{4}{5} \end{aligned}$ .
::4860最简单的形式是4 5

Comparing fractions with different denominators can be difficult. Some fraction may look similar, but not be . You can compare fractions with different denominators by comparing them in their simplest form.
::将分数与不同的分母进行比较可能很困难。某些分数可能看起来相似, 但不是。您可以比较分数与不同的分母, 比较它们最简单的形式。

Here are two fractions.
::这里有两个部分。

$\begin{aligned} \frac{3}{6} \end{aligned}$ and $\begin{aligned} \frac{4}{8} \end{aligned}$
::3、6和4 8

Let’s simplify $\begin{aligned} \frac{3}{6} \end{aligned}$ . To do this, divide the numerator and denominator by the GCF. The GCF of 3 and 6 is 3.
::让我们简化3 6。要做到这一点,全球合作框架将数字和分母分开。全球合作框架3和6是3。

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

Let’s simplify $\begin{aligned} \frac{4}{8} \end{aligned}$ . To do this, divide the numerator and the denominator by the GCF. The GCF of 4 and 8 is 4.
::让我们简化4,8。要做到这一点,全球合作框架将分子和分母分开。全球合作框架是4,8是4。

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

Both $\begin{aligned} \frac{3}{6} \end{aligned}$ and $\begin{aligned} \frac{4}{8} \end{aligned}$ are equivalent to $\begin{aligned} \frac{1}{2} \end{aligned}$ . Therefore, $\begin{aligned} \frac{3}{6} \end{aligned}$ and $\begin{aligned} \frac{4}{8} \end{aligned}$ are also equivalent fractions.
::3 6 和 4 8 都相当于 1 2 。因此, 3 6 和 4 8 也是等分数。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Tessa and her brownies.
::早些时候,你得到一个问题关于苔莎和她的布朗尼。

Tessa sold 12 out of 16 brownies at the bake sale. Simply the fraction for the number brownies she sold and did not sell.
::Tessa在烤面包销售时卖掉16个巧克力蛋糕中的12个,仅是她卖掉但没有卖掉的巧克力蛋糕的分数。

First, write the fraction for the number of brownies that was sold.
::首先,写下出售的巧克力蛋糕数量的分数。

$\begin{aligned} \frac{12}{16} \end{aligned}$

Then, simplify the fraction by dividing both by the GCF. The GCF is 4.
::然后,简化分数,将两者除以全球合作框架,全球合作框架为4。

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

She sold $\begin{aligned} \frac{3}{4} \end{aligned}$ of the brownies
::她卖了34块巧克力蛋糕

Now, write the fraction for the number of brownies that was not sold.
::现在,写下未出售的巧克力蛋糕数量的分数。

$\begin{aligned} \frac{4}{16} \end{aligned}$

Then, simplify the fraction by dividing both by the GCF. The GCF is 4.
::然后,简化分数,将两者除以全球合作框架,全球合作框架为4。

$\begin{aligned} \frac{4}{16} = \frac{1}{4} \end{aligned}$

She did not sell $\begin{aligned} \frac{1}{4} \end{aligned}$ of the brownies.
::她没有卖14块巧克力蛋糕

Example 2
::例2

Simplify the fraction.
::简化分数。

$\begin{aligned} \frac{27}{36} \end{aligned}$

First, find the GCF of 27 and 36. The GCF for 27 and 36 is 9.
::第一,找到27和36的全球合作框架,27和36的全球合作框架为9。

27 – 1, 3, 9, 27

36 – 1, 2, 3, 4, 6, 9, 12, 18, 36

Then, divide both the numerator and the denominator by 9.
::然后,将分子和分母除以9。

$\begin{aligned} \frac{27 \div 9}{36 \div 9} = \frac{3}{4} \end{aligned}$

The simplest form of $\begin{aligned} \frac{27}{36} \end{aligned}$ is $\begin{aligned} \frac{3}{4} \end{aligned}$ .
::2736最简单的形式是34

Example 3
::例3

Simplify the fraction.
::简化分数。

$\begin{aligned} \frac{4}{20} \end{aligned}$

First, find the GCF of 4 and 20. The GCF for 4 and 20 is 4
::第一,发现全球合作框架为4个和20个,全球合作框架为4个和20个,全球合作框架为4个和20个,全球合作框架为4个

Then, divide both the numerator and the denominator by 4.
::然后,将分子和分母除以4。

The simplest form of $\begin{aligned} \frac{4}{20} \end{aligned}$ is $\begin{aligned} \frac{1}{5} \end{aligned}$ .
::最简单的形式是4 20是15

Solution: $\begin{aligned} \frac{1}{5} \end{aligned}$
::解决办法:1 5

Example 4
::例4

Simplify the fraction.
::简化分数。

$\begin{aligned} \frac{8}{16} \end{aligned}$

First, find the GCF of 8 and 16. The GCF for 8 and 16 is 8
::第一,找到8和16的全球合作框架,8和16的全球合作框架是8和16。

Then, divide both the numerator and the denominator by 8.
::然后,将分子和分母除以8。

The simplest form of $\begin{aligned} \frac{8}{16} \end{aligned}$ is $\begin{aligned} \frac{1}{2} \end{aligned}$ .
::最简单的形式是 8 16 是 12 。

Example 5
::例5

Simplify the fraction.
::简化分数。

$\begin{aligned} \frac{5}{15} \end{aligned}$

First, find the GCF of 5 and 15. The GCF for 5 and 15 is 5
::第一,发现全球合作框架为5和15,全球合作框架为5和15,全球合作框架为5和15,全球合作框架为5和15,全球合作框架为5和15,全球合作框架为5和15,全球合作框架为5和15

Then, divide both the numerator and the denominator by 5.
::然后,将分子和分母除以5。

The simplest form of $\begin{aligned} \frac{5}{15} \end{aligned}$ is $\begin{aligned} \frac{1}{3} \end{aligned}$ .
::最简单的形式是5 -15是13

Review
::回顾

Simplify each fraction. If the fraction is already in simplest form write simplest form for your answer.
::简化每个分数。如果分数已经以最简单的形式写入您回答的最简单的形式。

$\begin{aligned} \frac{8}{10} \end{aligned}$

$\begin{aligned} \frac{4}{10} \end{aligned}$

$\begin{aligned} \frac{2}{10} \end{aligned}$

$\begin{aligned} \frac{2}{12} \end{aligned}$

$\begin{aligned} \frac{3}{12} \end{aligned}$

$\begin{aligned} \frac{4}{9} \end{aligned}$

$\begin{aligned} \frac{5}{20} \end{aligned}$

$\begin{aligned} \frac{12}{24} \end{aligned}$

$\begin{aligned} \frac{12}{36} \end{aligned}$

$\begin{aligned} \frac{11}{44} \end{aligned}$

$\begin{aligned} \frac{20}{45} \end{aligned}$

$\begin{aligned} \frac{18}{20} \end{aligned}$

$\begin{aligned} \frac{12}{30} \end{aligned}$

$\begin{aligned} \frac{22}{40} \end{aligned}$

$\begin{aligned} \frac{35}{63} \end{aligned}$

Review (Answers)
::回顾(答复)

章节大纲

常规

最简形式的分数

Finding Fractions in Simplest Form ::以简单格式查找分数

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)

Finding Fractions in Simplest Form
::以简单格式查找分数

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)