Course: 5.7等效分数 | The Way To Learn

Section outline

Select section General

Collapse Expand
General

Collapse all Expand all
- Select activity 新闻通告
  
  新闻通告 Forum
Select section 等效分数

Collapse Expand
等效分数
After the party, there was still $\begin{aligned} \frac{3}{4} \end{aligned}$ 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?

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。

Finding Equivalent Fractions
::查找等等价分数

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。

Here is a fraction.
::这里有一个分数。

$\begin{aligned} \frac{4}{5} \end{aligned}$

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。

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

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。

$\begin{aligned} \frac{5}{10} \end{aligned}$

The fraction for the parts that are not shaded would also be $\begin{aligned} \frac{5}{10} \end{aligned}$ . Notice that half of the image is shaded. Remember that a half is also written as the fraction $\begin{aligned} \frac{1}{2} \end{aligned}$ . Therefore, $\begin{aligned} \frac{5}{10} \end{aligned}$ is the same as $\begin{aligned} \frac{1}{2} \end{aligned}$ . 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。

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

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。

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

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。

Here is a fraction.
::这里有一个分数。

$\begin{aligned} \frac{6}{12} \end{aligned}$

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

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。

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

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

$\begin{aligned} \begin{array}{rcl} 6 - \underline{1}, \underline{2}, \underline{3}, \underline{6} \\ 12 - \underline{1}, \underline{2}, \underline{3}, 4, \underline{6}, 12 \end{array} \end{aligned}$

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。

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 。

$\begin{aligned} \frac{6 \div 3}{12 \div 3} = \frac{2}{4} \end{aligned}$

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

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

Examples
::实例

Example 1
::例1

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。

Mike wants to evenly divide $\begin{aligned} \frac{3}{4} \end{aligned}$ of the cake between 9 people. Find an equivalent fraction of $\begin{aligned} \frac{3}{4} \end{aligned}$ 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。

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

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

If Mike divides the leftover cake evenly between 9 people, each person will take home $\begin{aligned} \frac{1}{12} \end{aligned}$ 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。

Example 2
::例2

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

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

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。

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

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

Example 3
::例3

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

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

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

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

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

Example 4
::例4

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

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

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

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

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

Example 5
::例5

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

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

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。

$\begin{aligned} \frac{8 \div 2}{10 \div 2} = \frac{4}{5} \end{aligned}$

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

Review
::回顾

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

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

$\begin{aligned} \frac{1}{3} \end{aligned}$

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

$\begin{aligned} \frac{1}{5} \end{aligned}$

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

$\begin{aligned} \frac{2}{5} \end{aligned}$

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

$\begin{aligned} \frac{3}{10} \end{aligned}$

$\begin{aligned} \frac{2}{9} \end{aligned}$

$\begin{aligned} \frac{2}{7} \end{aligned}$

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。

$\begin{aligned} \frac{1}{2} and \frac{3}{6} \end{aligned}$
::1 2和3 6

$\begin{aligned} \frac{2}{3} and \frac{4}{9} \end{aligned}$
::2、3和4 9

$\begin{aligned} \frac{2}{5} and \frac{4}{20} \end{aligned}$
::2、5和4 20

$\begin{aligned} \frac{3}{7} and \frac{9}{21} \end{aligned}$
::3、7和9 21

$\begin{aligned} \frac{5}{9} and \frac{25}{45} \end{aligned}$
::5、9和25 45

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

等效分数

Finding Equivalent Fractions ::查找等等价分数

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

Finding Equivalent Fractions
::查找等等价分数

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