5.7等效分数

章节大纲

• 选择节常规

  折叠 展开

  常规

  全部折叠 展开全部

  • 选择活动新闻通告

    

    新闻通告 讨论区
• 选择节等效分数

  折叠 展开

  等效分数

  

  [Figure 1]

  播放段落

  After the party, there was still  $\begin{array}{r}\frac{3}{4}\end{array}$  of the cake left over. Mike wants people to take some cake home with them. If there are 9 people, how much of the cake will each person take with them?
  ::派对之后,还有34个蛋糕剩下了。迈克希望人们带一些蛋糕回家。如果有9个人,每人要带多少蛋糕?

  播放段落

  In this concept, you will learn to find an equivalent fraction.
  ::在这个概念中,你会学会找到一个相等的分数。

  播放段落

  Finding Equivalent Fractions
  ::查找等等价分数

  播放段落

  A  fraction  is a part of a whole. It describes the relationship between a part of something and the whole thing. A fraction has two numbers separated by a fraction bar. The top number is called the  numerator  and tells you how many parts there are out of the whole. The bottom number is the  denominator . It tells you how many parts the whole has been divided into.
  ::一个分数是整体的一部分。 它描述某物的一部分和整个物之间的关系。 一个分数用一个分数条分隔了两个数字。 最高数字称为分子, 并告诉你整体中有多少部分。 底数是分母。 它告诉了您整个体被分割成多少部分 。

  播放段落

  Here is a fraction.
  ::这里有一个分数。

  $$\begin{array}{r}\frac{4}{5}\end{array}$$

  播放段落

  There are 4 parts and the whole is divided into 5 parts. Fractions can also be represented as a picture.
  ::有4个部分,整个部分分为5个部分,也可以以图示表示。

  播放段落

  Here is a picture of a fraction.
  ::这是一小部分的图片。

  

  [Figure 2]

  播放段落

  The whole has been divided into ten parts. This is our denominator. Five out of ten are shaded. This is our numerator.
  ::整部分分为十部分,这是我们的分母,十分之五是阴暗的,这是我们的分子。

  $$\begin{array}{r}\frac{5}{10}\end{array}$$

  播放段落

  The fraction for the parts that are not shaded would also be  $\begin{array}{r}\frac{5}{10}\end{array}$ . Notice that half of the image is shaded. Remember that a half is also written as the fraction  $\begin{array}{r}\frac{1}{2}\end{array}$ . Therefore,  $\begin{array}{r}\frac{5}{10}\end{array}$  is the same as  $\begin{array}{r}\frac{1}{2}\end{array}$ . When two fractions have the same value, the fractions are  equivalent fractions .
  ::未遮蔽部分的分数也将是 5 10 。 请注意, 图像的一半是遮蔽的。 记住, 一半也写成分数 1 2 。 因此, 5 10 和 12 相同。 当两个分数的值相同时, 分数是相等的分数 。

  播放段落

  The bars below visually represent equivalent fractions.
  ::下面的栏目表示相等的分数。

  

  [Figure 3]

  播放段落

  The shaded part of each bar represents a fraction that is equivalent to one half.
  ::每个横条的阴暗部分代表一个分数,等于一半。

  $$\begin{array}{r}\frac{1}{2}=\frac{2}{4}=\frac{3}{6}=\frac{4}{8}\end{array}$$

  播放段落

  To find equivalent fractions, multiply the numerator and denominator by the same number. If the numerator and denominator have a common factor other than 1, you can also  divide  the numerator and denominator by a common factor.
  ::要找到相等的分数,请将分子和分母乘以相同数字。如果分子和分母有一个除1以外的共同系数,也可以将分子和分母除以一个共同系数。

  播放段落

  Here is a fraction.
  ::这里有一个分数。

  $$\begin{array}{r}\frac{6}{12}\end{array}$$

  播放段落

  Find two equivalent fractions by multiplying or dividing.
  ::通过乘法或除法查找两个相等的分数。

  播放段落

  First, multiply the numerator and denominator by the same number. Let’s choose 2.
  ::首先,将分子和分母乘以相同数字。让我们选择 2。

  $$\begin{array}{r}\frac{6\times 2}{12\times 2}=\frac{12}{24}\end{array}$$

  播放段落

  The numbers 6 and 12 have common  factors .
  ::6号和12号有共同因素。

  $$\begin{array}{r}\begin{array}{rcl}& & 6-\underset{\_}{1},\underset{\_}{2},\underset{\_}{3},\underset{\_}{6}\\ & & 12-\underset{\_}{1},\underset{\_}{2},\underset{\_}{3},4,\underset{\_}{6},12\end{array}\end{array}$$

  播放段落

  Let’s try dividing to find a second equivalent fraction.
  ::让我们试着分割以找到第二个等值分数 。

  播放段落

  First, divide the numerator and denominator by a common factor. Let’s choose 3.
  ::首先,将分子和分母除以一个共同因素。让我们选择 3 。

  $$\begin{array}{r}\frac{6÷3}{12÷3}=\frac{2}{4}\end{array}$$

  播放段落

  Two equivalent fraction for  $\begin{array}{r}\frac{6}{12}\end{array}$  is  $\begin{array}{r}\frac{12}{24}\end{array}$  and  $\begin{array}{r}\frac{2}{4}\end{array}$ .
  ::6 12 2等量分数为 12 24 和 2 4 。

  $$\begin{array}{r}\frac{6}{12}=\frac{12}{24}=\frac{2}{4}\end{array}$$

  播放段落

  Examples
  ::实例

  播放段落

  Example 1
  ::例1

  播放段落

  Earlier, you were given a problem about Mike and the cake.
  ::之前,你得到一个问题 关于迈克和蛋糕。

  播放段落

  Mike wants to evenly divide  $\begin{array}{r}\frac{3}{4}\end{array}$  of the cake between 9 people. Find an equivalent fraction of  $\begin{array}{r}\frac{3}{4}\end{array}$  where the numerator equals 9.
  ::Mike想在9人之间平均分配3 4个蛋糕。 找到相当于3 4的分数, 分子数等于9。

  播放段落

  Multiply the numerator and denominator by the same number.
  ::用相同数字乘以分子和分母。

  $$\begin{array}{r}\frac{3\times 3}{4\times 3}=\frac{9}{12}\end{array}$$

  播放段落

  If Mike divides the leftover cake evenly between 9 people, each person will take home  $\begin{array}{r}\frac{1}{12}\end{array}$  of the original cake.
  ::如果麦克把剩下的蛋糕平分在9个人之间, 每个人都会带回家 12个原来的蛋糕。

  播放段落

  Example 2
  ::例2

  播放段落

  Find an equivalent fraction.
  ::找一个相等的分数。

  $$\begin{array}{r}\frac{3}{4}\end{array}$$

  播放段落

  Multiply the numerator and denominator by the same number. Let’s choose 2.
  ::用相同数字乘以分子和分母。让我们选择 2。

  $$\begin{array}{r}\begin{array}{rcl}\frac{3\times 2}{4\times 2}& =& \frac{6}{8}\\ \frac{6}{8}& =& \frac{3}{4}\end{array}\end{array}$$

  播放段落

  An equivalent fraction of  $\begin{array}{r}\frac{3}{4}\end{array}$  is  $\begin{array}{r}\frac{6}{8}\end{array}$ .
  ::3 4的相等部分是6 8。

  播放段落

  Example 3
  ::例3

  播放段落

  Find an equivalent fraction for the following fraction.
  ::查找以下分数的等效分数 。

  $$\begin{array}{r}\frac{1}{4}\end{array}$$

  播放段落

  Multiply the numerator and denominator by the same number.
  ::用相同数字乘以分子和分母。

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

  播放段落

  An equivalent fraction for  $\begin{array}{r}\frac{1}{4}\end{array}$  is  $\begin{array}{r}\frac{2}{8}\end{array}$ .
  ::1 4 的相等分数是 2 8 。

  播放段落

  Example 4
  ::例4

  播放段落

  Find an equivalent fraction for the following fraction.
  ::查找以下分数的等效分数 。

  $$\begin{array}{r}\frac{2}{3}\end{array}$$

  播放段落

  Multiply the numerator and denominator by the same number.
  ::用相同数字乘以分子和分母。

  $$\begin{array}{r}\frac{2\times 3}{3\times 3}=\frac{6}{9}\end{array}$$

  播放段落

  An equivalent fraction for  $\begin{array}{r}\frac{2}{3}\end{array}$  is  $\begin{array}{r}\frac{6}{9}\end{array}$ .
  ::2 3 的相等分数是 6 9 。

  播放段落

  Example 5
  ::例5

  播放段落

  Find an equivalent fraction for the following fraction.
  ::查找以下分数的等效分数 。

  $$\begin{array}{r}\frac{8}{10}\end{array}$$

  播放段落

  Divide the numerator and denominator by a common factor, 2.
  ::将分子和分母除以一个共同系数2。

  $$\begin{array}{r}\frac{8÷2}{10÷2}=\frac{4}{5}\end{array}$$

  播放段落

  An equivalent fraction for  $\begin{array}{r}\frac{8}{10}\end{array}$  is  $\begin{array}{r}\frac{4}{5}\end{array}$ .
  ::8 10 的相等分数是 4 5 。

  播放段落

  Review
  ::回顾

  播放段落

  Find an equivalent fraction for the following fractions.
  ::查找以下各分数的等效分数 。

  1. $\begin{array}{r}\frac{1}{2}\end{array}$  
  2. $\begin{array}{r}\frac{1}{3}\end{array}$  
  3. $\begin{array}{r}\frac{1}{4}\end{array}$  
  4. $\begin{array}{r}\frac{1}{5}\end{array}$  
  5. $\begin{array}{r}\frac{2}{3}\end{array}$  
  6. $\begin{array}{r}\frac{2}{5}\end{array}$  
  7. $\begin{array}{r}\frac{3}{4}\end{array}$  
  8. $\begin{array}{r}\frac{3}{10}\end{array}$  
  9. $\begin{array}{r}\frac{2}{9}\end{array}$  
  10. $\begin{array}{r}\frac{2}{7}\end{array}$  

  播放段落

  Determine if each pair of fractions is equivalent. Use true or false as your answer.
  ::确定每对分数是否相等。 请使用真实或虚假的答案 。

  播放段落
  11. $\begin{array}{r}\frac{1}{2}\text{ and }\frac{3}{6}\end{array}$  
      ::1 2和3 6
  播放段落
  12. $\begin{array}{r}\frac{2}{3}\text{ and }\frac{4}{9}\end{array}$  
      ::2、3和4 9
  播放段落
  13. $\begin{array}{r}\frac{2}{5}\text{ and }\frac{4}{20}\end{array}$  
      ::2、5和4 20
  播放段落
  14. $\begin{array}{r}\frac{3}{7}\text{ and }\frac{9}{21}\end{array}$  
      ::3、7和9 21
  播放段落
  15. $\begin{array}{r}\frac{5}{9}\text{ and }\frac{25}{45}\end{array}$  
      ::5、9和25 45

  播放段落

  Review (Answers) 
  ::回顾(答复)

  播放段落

  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 。

  播放段落

  Resources
  ::资源