同分母分数的差异

Danny and Sam are training for a race. In 5 minutes, Danny is able to run  $\begin{array}{r}\frac{5}{8}\end{array}$  of a mile. Sam is able to run  $\begin{array}{r}\frac{3}{8}\end{array}$  of a mile. How far is Danny from Sam after 5 minutes?
::Danny和Sam正在训练比赛 5分钟后 Danny就能跑580英里

In this concept, you will learn about subtracting fractions with  like denominators .
::在此概念中, 您将学习如何以类似分母来减分数 。

Subtracting Fractions with Like Denominators
::与类似分数器的减法分数

You can also subtract fractions with  common denominators  - that is, fractions with denominators that are the same. As long as the denominators are the same, you can find the  difference  by subtracting the numerators.
::您也可以用共同分母来减去分母,即分母与分母相同。只要分母相同,您可以通过减去分子来找到差异。

Here are two fractions. The fractions have a  common denominator , 8. Each whole is divided into 8 parts.
::这是两个分数。 分数有一个共同的分母, 8 。 每个整体分为八个部分 。

[Figure 2]

[Figure 3]

Here is a subtraction problem with the two fractions.
::这是两个部分的减法问题 。

To solve this problem, find the difference of the numerators over the common denominator.
::为了解决这个问题, 找到点数对共同分母的区别 。

Then, write the fraction in  simplest form . The   (GCF) of 3 and 8 is 1. The fraction is in simplest form.
::然后以最简单的形式写出分数。 3和8的( GCF) 是 1 。 分数是最简单的形式 。

Therefore, the difference  is  $\begin{array}{r}\frac{3}{8}\end{array}$ .
::因此,差别是3 8。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Danny and Sam, who are training for a race.
::早些时候,你被问及丹尼和山姆的问题, 他们正在参加比赛的训练。

In 5 minutes, Danny can run  $\begin{array}{r}\frac{5}{8}\end{array}$  mile and Sam can run  $\begin{array}{r}\frac{3}{8}\end{array}$  mile. Find the difference to see how much farther Danny will be after 5 minutes. 
::5分钟后,丹尼可以跑58英里,山姆可以跑38英里。

$\begin{array}{r}\frac{5}{8}-\frac{3}{8}=\underset{\_}{}\end{array}$

First, check if the fractions have common denominators. Both are 8.
::首先,检查分数是否有共同的分母。这两个分母都是8个。

Then, subtract the fractions. Find the difference of the numerators over the common denominator.
::然后,减去分数。找出在共同分母上点数的差数。

  $\begin{array}{r}5-3=2\end{array}$

  $\begin{array}{r}\frac{2}{8}\end{array}$

Next,  simplify  the fraction. The GCF of 2 and 8 is 2.  Divide  the  numerator  and the  denominator  by 2. 
::接下来,简化分数。全球合作框架2和8是2,分子和分母除以2。

   $\begin{array}{r}\frac{2÷2}{8÷2}=\frac{1}{4}\end{array}$

Danny will be  $\begin{array}{r}\frac{1}{4}\end{array}$  of a mile farther than Sam.
::丹尼将比山姆远14英里

Example 2
::例2

Find the difference:  $\begin{array}{r}\frac{9}{12}-\frac{5}{12}=\underset{\_}{}\end{array}$ . Answer in simplest form.
::查找差异: 9 12 - 5 12 = _. 回答最简单。

First, check if the fractions have a common denominator. Both denominators are 12. 
::首先,检查分数是否有共同的分母。 两个分母都是12个。

Then, subtract the fractions. Find the difference of the numerators over the common denominator. 
::然后,减去分数。找出在共同分母上点数的差数。

  $\begin{array}{r}9-5=4\end{array}$

$\begin{array}{r}\frac{4}{12}\end{array}$

Next, simplify the fraction. The GCF of 4 and 12 is 4. Divide the numerator and the denominator by 4.
::接下来,简化分数。全球合作框架4和12是4. 分子和分母除以4。

  $\begin{array}{r}\frac{4÷4}{12÷4}=\frac{1}{3}\end{array}$

The difference is  $\begin{array}{r}\frac{1}{3}\end{array}$ .
::差别是13

Example 3
::例3

Find the difference:  $\begin{array}{r}\frac{6}{7}-\frac{2}{7}=\underset{\_}{}\end{array}$ . Answer in simplest form.
::查找差异: 6 7 - 2 7 = _. 回答最简单。

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

Then, subtract the fractions. 
::然后,扣除分数。

$\begin{array}{r}6-2=4\end{array}$

  $\begin{array}{r}\frac{4}{7}\end{array}$

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

The difference is  $\begin{array}{r}\frac{4}{7}\end{array}$ .
::差别是4 7。

Example 4
::例4

Find the difference:  $\begin{array}{r}\frac{5}{9}-\frac{2}{9}=\underset{\_}{}\end{array}$ . Answer in simplest form.
::查找差异: 5 9 - 2 9 = _. 回答最简单。

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

Then, subtract the fractions. 
::然后,扣除分数。

  $\begin{array}{r}5-2=3\end{array}$

  $\begin{array}{r}\frac{3}{9}\end{array}$

Next, simplify the fraction. The GCF of 3 and 9 is 3.
::接下来,简化分数,全球合作框架3和9是3。

  $\begin{array}{r}\frac{3÷3}{9÷3}=\frac{1}{3}\end{array}$

The difference is  $\begin{array}{r}\frac{1}{3}\end{array}$ .
::差别是13

Example 5
::例5

Find the difference:  $\begin{array}{r}\frac{8}{10}-\frac{4}{10}=\underset{\_}{}\end{array}$ . Answer in simplest form.
::查找差异: 8 10 - 4 10 = _. 回答最简单。

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

Then, subtract the fractions. 
::然后,扣除分数。

  $\begin{array}{r}8-4=4\end{array}$

  $\begin{array}{r}\frac{4}{10}\end{array}$

Next, simplify the fraction. The GCF of 4 and 10 is 2.
::接下来,简化分数,全球合作框架4和10是2。

  $\begin{array}{r}\frac{4÷2}{10÷2}=\frac{2}{5}\end{array}$

The difference is  $\begin{array}{r}\frac{3}{5}\end{array}$ .
::差异是3 5。

Review
::回顾

Find the difference. Answer in simplest form.
::找出不同之处 回答最简单

1. $\begin{array}{r}\frac{6}{7}-\frac{3}{7}=\underset{\_}{}\end{array}$
2. $\begin{array}{r}\frac{6}{12}-\frac{4}{12}=\underset{\_}{}\end{array}$
3. $\begin{array}{r}\frac{13}{18}-\frac{3}{18}=\underset{\_}{}\end{array}$
4. $\begin{array}{r}\frac{7}{8}-\frac{6}{8}=\underset{\_}{}\end{array}$
5. $\begin{array}{r}\frac{4}{8}-\frac{2}{8}=\underset{\_}{}\end{array}$
6. $\begin{array}{r}\frac{10}{12}-\frac{6}{12}=\underset{\_}{}\end{array}$
7. $\begin{array}{r}\frac{11}{13}-\frac{6}{13}=\underset{\_}{}\end{array}$
8. $\begin{array}{r}\frac{10}{20}-\frac{5}{20}=\underset{\_}{}\end{array}$
9. $\begin{array}{r}\frac{16}{18}-\frac{5}{18}=\underset{\_}{}\end{array}$
10. $\begin{array}{r}\frac{12}{14}-\frac{2}{14}=\underset{\_}{}\end{array}$
11. $\begin{array}{r}\frac{8}{9}-\frac{3}{9}=\underset{\_}{}\end{array}$
12. $\begin{array}{r}\frac{7}{11}-\frac{3}{11}=\underset{\_}{}\end{array}$
13. $\begin{array}{r}\frac{9}{20}-\frac{7}{20}=\underset{\_}{}\end{array}$
14. $\begin{array}{r}\frac{12}{24}-\frac{8}{24}=\underset{\_}{}\end{array}$
15. $\begin{array}{r}\frac{7}{28}-\frac{2}{28}=\underset{\_}{}\end{array}$

Review (Answers) 
::回顾(答复)