Course: 6.4同分母分数和

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同分母分数和
Sarah is cleaning up after an art project. There are two boxes that still have clay in them. One box is $\begin{aligned} \frac{1}{5} \end{aligned}$ full. The other box is $\begin{aligned} \frac{3}{5} \end{aligned}$ full. How much clay is leftover? Can she combine the leftover clay into one box?
::Sarah正在清理一个艺术工程。有两个盒子里还有粘土。一个盒子里满了15个。另一个盒子里满了35个。剩下多少粘土? 她能把剩下的粘土合并成一个盒子吗 ?

In this concept, you will learn how to add fractions with like denominators .
::在这个概念中,你将学会如何添加分数和类似分母。

Adding Fractions with Like Denominators
::添加像分数一样的分数

Adding fractions with the same denominator is easy. Fractions with the same denominators are said to have like or common denominators . This means that the whole has been divided up into the same number of parts. If the denominator of two fractions is a six, then both of those fractions have been divided into six parts. The parts of each fraction are equivalent.
::使用相同分母添加分数是很容易的。使用相同分母的分数据说有相似的或共同的分母。这意味着整块被分成相同数量的部分。如果两个分母的分母是六, 那么这两个分母都分为六部分。每个分母的分母是等同的。

This picture shows two different fractions with like denominators.
::此图显示两个不同的分数, 有相似分母。

To add these two fractions, add the parts. Remember that the part in a fraction is the numerator . Here it is as a picture.
::添加这两个分数时, 请添加各个部分。记住, 分数中的部分是分子。这里是图像。

$\begin{aligned} \frac{2}{6} + \frac{4}{6} = \frac{6}{6} \end{aligned}$

The sum of both fractions is six-sixths. In this example, you can simplify or reduce the fraction to one whole. You can see that one whole figure is shaded in.
::两个分数的总和是六六分之六。在此示例中,您可以将分数简化或压缩为一个整体。您可以看到一个整数被阴影遮蔽。

$\begin{aligned} \frac{6}{6} = 1 \end{aligned}$

Therefore, the sum is 1.
::因此,数额为1。

Let’s look at another addition problem.
::让我们看看另一个附加问题。

$\begin{aligned} \frac{2}{8} + \frac{4}{8} = \underline{} \end{aligned}$

The first step is to check if the fractions have a common denominator . Both denominators are 8. Then, add the fractions. The sum of the fractions is the sum of the numerators over the common denominator.
::第一步是检查分数是否有共同的分母。两个分母都是 8 。然后, 添加分数。分数的总和是共同分母上的分子总和。

$\begin{aligned} 2 + 4 = 6 \end{aligned}$

The sum of the numerators is 6. Put the sum over the common denominator.
::计数器的总和是6. 将总和置于共同分母之上。

$\begin{aligned} \frac{6}{8} \end{aligned}$

Next, write the fraction in simplest form . 6 and 8 have the (GCF) of 2. Divide both the numerator and the denominator by 2 to simplify the fraction. If the GCF is 1, the fraction is already in simplest form.
::接下来,以最简单的形式写出分数。 6和8的分数为 2 的(GCF) 。将分子和分母除以 2 以简化分数。如果 GFP为 1, 则分数已经以最简单的形式出现。

$\begin{aligned} \frac{6 \div 2}{8 \div 2} = \frac{3}{4} \end{aligned}$

The sum is $\frac{3}{4}$ .
::数额是。

Remember that when adding fractions, you are only adding the parts of the whole. The denominator remains the same.
::记住, 当添加分数时, 您只是在添加整体的各个部分。分母保持不变。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Sarah and the leftover clay.
::早些时候,你曾为莎拉和剩下的粘土感到困扰。

Sarah needs to combine one box that is $\begin{aligned} \frac{1}{5} \end{aligned}$ full and another box that is $\begin{aligned} \frac{3}{5} \end{aligned}$ full. Add the fractions to find the total amount of leftover clay.
::Sarah需要将一个15整箱和另一个35整箱合并。添加分数以找到剩余粘土的总量。

First, check if the fractions have a common denominator. Both denominators are 5.
::首先,检查分数是否有共同的分母。两个分母都是5。

Then, add the fractions. Find the sum of the numerators over the common denominator.
::然后,添加分数。在共同分母上找到分子的总和。

$\begin{aligned} 1 + 3 = 4 \\ \frac{4}{5} \end{aligned}$

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

There is $\begin{aligned} \frac{4}{5} \end{aligned}$ box of clay left. Sarah can fit the leftover into one box.
::剩下45箱粘土 Sarah可以把剩菜放进一个盒子里

Example 2
::例2

Find the sum. Answer in simplest form.
::找到金额,回答最简单

$\begin{aligned} \frac{3}{10} + \frac{2}{10} + \frac{2}{10} = \underline{} \end{aligned}$ .

First, check if the fractions have a common denominator. All the denominators are 10.
::首先,检查分数是否有共同分母。所有分母为10。

Then, add the fractions. Find the sum of the numerators over the common denominator.
::然后,添加分数。在共同分母上找到分子的总和。

$\begin{aligned} 3 + 2 + 2 = 7 \\ \frac{7}{10} \end{aligned}$

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

The sum is $\begin{aligned} \frac{7}{10} \end{aligned}$ .
::总额是7 10。

Example 3
::例3

Find the sum: $\begin{aligned} \frac{1}{7} + \frac{2}{7} = \underline{} \end{aligned}$ . Answer in simplest form.
::查找总和: 1 7+ 2 7 = _. 回答最简单。

First, check if the fractions have a common denominator. Both are 7.
::首先,检查分数是否有共同的分母。这两个分母都是7个。

Then, add the fractions. Find the sum of the numerators over the common denominator.
::然后,添加分数。在共同分母上找到分子的总和。

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

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

The sum is $\begin{aligned} \frac{3}{7} \end{aligned}$ .
::总共是3 7。

Example 4
::例4

Find the sum: $\begin{aligned} \frac{3}{9} + \frac{1}{9} = \underline{} \end{aligned}$ . Answer in simplest form.
::查找总和: 3 9 + 1 9 = _. 回答最简单。

First, check if the fractions have a common denominator. Both are 9.
::首先,检查分数是否有共同的分母。这两个分母都是9个。

Then, add the fractions. Find the sum of the numerators over the common denominator.
::然后,添加分数。在共同分母上找到分子的总和。

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

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

The sum is $\begin{aligned} \frac{4}{9} \end{aligned}$ .
::金额是4 9。

Example 5
::例5

Find the sum: $\begin{aligned} \frac{2}{10} + \frac{3}{10} = \underline{} \end{aligned}$ . Answer in simplest form.
::查找总和: 2 10+ 3 10 = _. 回答最简单。

First, check if the fractions have a common denominator. Both are 10.
::首先,检查分数是否有共同的分母。这两个分母都是10个。

Then, add the fractions. Find the sum of the numerators over the common denominator.
::然后,添加分数。在共同分母上找到分子的总和。

$\begin{aligned} 2 + 3 = 5 \\ \frac{5}{10} \end{aligned}$

Next, simplify the fraction. The GCF of 5 and 10 is 5. Divide the numerator and the denominator by 5.
::接下来,简化分数。全球合作框架5和10是5,分子和分母除以5。

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

The sum is $\begin{aligned} \frac{1}{2} \end{aligned}$ .
::金额是12。

Review
::回顾

Find the sum. Answer in simplest form.
::找到金额,回答最简单

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

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

$\begin{aligned} \frac{4}{7} + \frac{2}{7} = \underline{} \end{aligned}$

$\begin{aligned} \frac{5}{11} + \frac{4}{11} = \underline{} \end{aligned}$

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

$\begin{aligned} \frac{4}{10} + \frac{1}{10} = \underline{} \end{aligned}$

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

$\begin{aligned} \frac{5}{6} + \frac{3}{6} = \underline{} \end{aligned}$

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

$\begin{aligned} \frac{5}{10} + \frac{1}{10} = \underline{} \end{aligned}$

$\begin{aligned} \frac{6}{13} + \frac{4}{13} = \underline{} \end{aligned}$

$\begin{aligned} \frac{9}{10} + \frac{1}{10} = \underline{} \end{aligned}$

$\begin{aligned} \frac{6}{9} + \frac{1}{9} = \underline{} \end{aligned}$

$\begin{aligned} \frac{8}{12} + \frac{1}{12} = \underline{} \end{aligned}$

$\begin{aligned} \frac{10}{20} + \frac{4}{20} = \underline{} \end{aligned}$

$\begin{aligned} \frac{11}{18} + \frac{5}{18} = \underline{} \end{aligned}$

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

General

同分母分数和

Adding Fractions with Like Denominators ::添加像分数一样的分数

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

Adding Fractions with Like Denominators
::添加像分数一样的分数

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