Section: 不同分母分数和 | 6.7不同分母分数和

Section outline

Larry is building a skateboard ramp in his backyard. At first, he used a $\begin{aligned} \frac{3}{8} \end{aligned}$ inch thick piece of plywood. It didn't feel sturdy enough so he is replacing it with something that is $\begin{aligned} \frac{1}{2} \end{aligned}$ inch thicker that what he originally used. How thick will the ramp be?
::拉里在后院建滑板坡。起初, 他用了38英寸厚的胶合板。感觉不够坚固, 所以他用比他原先使用的要厚12英寸的东西替换。坡道会有多厚?

In this concept, you will learn how to add fractions with different denominators.
::在这个概念中,你会学习如何添加分数,分母不同。

Adding Fractions with Different Denominators
::添加有不同分数的分数

Fractions that have the same denominator have a common denominator . To add fractions with a common denominator, you find the sum over the numerators over the common denominator. Not all addition problems will involve fractions with common denominators.
::具有相同分母的分数有一个共同分母。要添加带有共同分母的分分数,您可以在共同分母上找到数字总和。并非所有添加问题都涉及带有共同分母的分数。

Here is an addition problem.
::还有一个附加问题。

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

One-half and one-fourth have different denominators and represent different quantities of a whole.
::一半和四分之一的分母有不同的分母,代表一个整体的不同数量。

To add fractions with different denominators, you will need to rewrite the fractions so that they have a common denominator before finding the sum.
::要添加具有不同分母的分数, 您需要重写分数, 以便在找到总和前有共同分母。

The first step is to the find the least common multiple (LCM) of the denominators, 2 and 4. Remember that the LCM is the smallest multiple that is shared by the numbers being compared. This LCM will become the lowest common denominator (LCD) for the fractions.
::第一步是找到分母中最小的多重(LCM),即2和4。记住,LCM是被比较的数字所共享的最小的多个。 LCM将成为分数中最小的公分母(LCD)。

List the multiples of 2 and 4.
::列出 2 和 4 的倍数。

2: 2, 4 , 6, 8, 10 . . .

4: 4 , 8, 12, 16 . . .

The least common multiple of 2 and 4 is 4.
::2和4的最小常见乘数是4。

Then, rewrite each fraction with the common denominator of 4. Multiply the numerator and the denominator of $\begin{aligned} \frac{1}{2} \end{aligned}$ by 2 to find the equivalent fraction..
::然后将每个分数重写为 4 的共同分母。乘以分子和1 2 2 的分母, 以找到相等的分母。

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

The second fraction, $\begin{aligned} \frac{1}{4} \end{aligned}$ , is already written in terms of fourths.
::第二个分数,14, 已经以四分之一的写法写成。

$\begin{aligned} \frac{2}{4} + \frac{1}{4} \end{aligned}$

Now you can add the fractions with common denominators.
::现在您可以添加带有共同分母的分数。

$\begin{aligned} \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \end{aligned}$

Finally, simplify the fraction, if possible. The $\begin{aligned} \frac{3}{4} \end{aligned}$ is a fraction in simplest form .
::最后,尽可能简化分数。3 4是最简单的分数。

The sum is $\begin{aligned} \frac{3}{4} \end{aligned}$ .
::金额是3 4。

You can add any number of fractions with unlike denominators as long as you rewrite the fractions with a common denominator.
::只要用共同的分母重写分母,您就可以添加含有不同分母的分数数。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Larry and his ramp.
::早些时候,你得到一个问题关于拉里和他的斜坡。

Larry started with $\begin{aligned} \frac{3}{8} \end{aligned}$ inch plywood, but wanted something $\begin{aligned} \frac{1}{2} \end{aligned}$ inch thicker. Add the measurements to find the total thickness of the ramp.
::拉里用38英寸的胶合板开始, 但想要更厚的12英寸。添加测量数据以找到斜坡的总厚度。

$\begin{aligned} \frac{3}{8} + \frac{1}{2} = \underline{} \end{aligned}$

First, check the denominators. The denominators are 8 and 2. The LCD is 8.
::首先,检查分母。分母是8和2。

Then, rewrite the fractions with the common denominator.
::然后用共同分母重写分数。

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

$\begin{aligned} \frac{3}{8} + \frac{4}{8} \end{aligned}$

Next, add the fractions.
::下一步,添加分数。

$\begin{aligned} \frac{3}{8} + \frac{4}{8} = \frac{7}{8} \end{aligned}$

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

The skate ramp will be $\begin{aligned} \frac{7}{8} \end{aligned}$ inch thick.
::滑板斜坡将厚78英寸

Example 2
::例2

Find the sum.
::找到数额。

$\begin{aligned} \frac{2}{7} + \frac{3}{9} = \underline{} \end{aligned}$

First, check for a common denominator. The denominators are 7 and 9 and are not common. Find the LCD using the LCM of 7 and 9.
::首先,检查一个共同的分母。分母是 7 和 9 , 并不常见。请使用 7 和 9 的 LCM 查找 LCD 。

7 – 7, 14, 21, 28, 35, 42, 49, 56, 63

9 – 9, 18, 27, 36, 45, 54, 63

The LCD is 63.
::LCD是63岁。

Then, rewrite the fractions. Find the with the denominator 63.
::然后重写分数。用分母63找到分母63。

$\begin{aligned} \frac{2}{7} = \frac{18}{63} \\ \frac{3}{9} = \frac{21}{63} \end{aligned}$

$\begin{aligned} \frac{18}{63} + \frac{21}{63} \end{aligned}$

Next, add the fractions. Add the numerators over the common denominator.
::下一步,添加分数。在共同分母上添加分子。

$\begin{aligned} \frac{18}{63} + \frac{21}{63} = \frac{39}{63} \end{aligned}$

Finally, simplify the fraction. The GCF of 39 and 63 is 3. Divide the numerator and the denominator by 3.
::最后,简化分数:全球合作框架39和63是3,分子和分母除以3。

$\begin{aligned} \frac{39 \div 3}{63 \div 3} = \frac{13}{21} \end{aligned}$

The sum is $\begin{aligned} \frac{13}{21} \end{aligned}$ .
::总数是13 21。

Example 3
::例3

Find the sum: $\begin{aligned} \frac{1}{2} + \frac{2}{6} = \underline{} \end{aligned}$ . Answer in simplest form.
::查找总和:1、2+2 6 = _。回答最简单。

First, check the denominators. The denominators are 2 and 6. The LCD is 6.
::首先,检查分母,分母是2和6,液晶为6。

Then, rewrite the fractions with the common denominator.
::然后用共同分母重写分数。

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

$\begin{aligned} \frac{3}{6} + \frac{2}{6} \end{aligned}$

Next, add the fractions.
::下一步,添加分数。

$\begin{aligned} \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \end{aligned}$

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

The sum is $\begin{aligned} \frac{5}{6} \end{aligned}$ .
::总额是5 6。

Example 4
::例4

Find the sum: $\begin{aligned} \frac{2}{3} + \frac{1}{9} = \underline{} \end{aligned}$ . Answer in simplest form.
::查找总和: 2 3+ 1 9 = _. 回答最简单。

First, check the denominators. The denominators are 3 and 9. The LCD is 9.
::首先,检查分母。分母是3和9, 液晶显示器是9。

Then, rewrite the fractions with the common denominator.
::然后用共同分母重写分数。

$\begin{aligned} \frac{2}{3} & = \frac{6}{9} \end{aligned}$

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

Next, add the fractions.
::下一步,添加分数。

$\begin{aligned} \frac{6}{9} + \frac{1}{9} = \frac{7}{9} \end{aligned}$

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

The sum is $\begin{aligned} \frac{7}{9} \end{aligned}$ .
::金额是7 9。

Example 5
::例5

Find the sum: $\begin{aligned} \frac{4}{5} + \frac{1}{3} = \underline{} \end{aligned}$ . Answer in simplest form.
::查找总和: 4 5 + 1 3 = _. 回答最简单。

First, check the denominators. The denominators are 5 and 3. The LCD is 15.
::首先,检查分母。分母是5和3。液晶显示器是15。

Then, rewrite the fractions with the common denominator.
::然后用共同分母重写分数。

$\begin{aligned} \frac{4}{5} & = \frac{12}{15} \\ \frac{1}{3} & = \frac{5}{15} \end{aligned}$

$\begin{aligned} \frac{12}{15} + \frac{5}{15} \end{aligned}$

Next, add the fractions.
::下一步,添加分数。

$\begin{aligned} \frac{12}{15} + \frac{5}{15} = \frac{17}{15} \end{aligned}$

Finally, simplify the fraction. Convert the improper fraction to a proper fraction .
::最后,简化分数,将不当分数转换成适当的分数。

$\begin{aligned} \frac{17}{15} = 1 \frac{2}{15} \end{aligned}$

The sum is $\begin{aligned} 1 \frac{2}{15} \end{aligned}$ .
::金额是12 15。

Review
::回顾

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

$\begin{aligned} \frac{3}{4} + \frac{1}{2} = \underline{} \end{aligned}$

$\begin{aligned} \frac{6}{7} + \frac{1}{2} = \underline{} \end{aligned}$

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

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

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

$\begin{aligned} \frac{3}{6} + \frac{1}{3} = \underline{} \end{aligned}$

$\begin{aligned} \frac{6}{8} + \frac{1}{3} = \underline{} \end{aligned}$

$\begin{aligned} \frac{4}{7} + \frac{1}{2} = \underline{} \end{aligned}$

$\begin{aligned} \frac{4}{5} + \frac{1}{2} = \underline{} \end{aligned}$

$\begin{aligned} \frac{3}{7} + \frac{1}{6} = \underline{} \end{aligned}$

$\begin{aligned} \frac{5}{8} + \frac{2}{3} = \underline{} \end{aligned}$

$\begin{aligned} \frac{6}{7} + \frac{1}{3} = \underline{} \end{aligned}$

$\begin{aligned} \frac{9}{12} + \frac{1}{6} = \underline{} \end{aligned}$

$\begin{aligned} \frac{8}{10} + \frac{1}{2} = \underline{} \end{aligned}$

$\begin{aligned} \frac{6}{7} + \frac{3}{4} = \underline{} \end{aligned}$

$\begin{aligned} \frac{3}{4} + \frac{2}{6} = \underline{} \end{aligned}$

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

Adding Fractions with Different Denominators ::添加有不同分数的分数

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 Different Denominators
::添加有不同分数的分数

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