课程： 8.7心理数学解决比例

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选择节心理数学解决比例

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心理数学解决比例
Chase works in the stockroom of a grocery store. It takes him 20 minutes to stock 3 shelves. He has 9 more shelves to stock. His shift ends in 1 hour. Can Chase finish stocking the shelves before his shift ends?
::大通在一家杂货店的仓库里工作,他需要20分钟才能储存3个货架。他还有9个货架要储存。他的轮班在1小时后结束。大通能在轮班结束前完成架子的储存吗?

In this concept, you will learn how to use mental math to solve proportions.
::在这个概念中,你将学会如何使用心理数学来解决比例问题。

Using Mental Math to Solve Proportions
::使用精神数学解决比例

You can find equal ratios without having to write the multiplication or division on paper. Mental math is the calculation that goes on inside your head and can be used to find the unknown quantity in an equation.
::您可以找到相等的比例, 而不必在纸张上写入乘数或分数。智商数学是您脑中的计算方法, 可以用来在方程式中找到未知的数量。

Here is a proportion with an unknown quantity, $\begin{aligned} x \end{aligned}$ . Solve the proportion by finding the value of $\begin{aligned} x \end{aligned}$ using mental math.
::这里有一个比例,数量未知, x。通过使用心理数学找到 x 的值来解答比例。

$\begin{aligned} \frac{25 campers}{1 tent} = \frac{75 campers}{x tents} \end{aligned}$

First, look at the relationship between the numerators, 25 campers to 75 campers. Think, “What can I multiply 25 by to get 75. 25 times 3 equals 75.” Remember, a proportion is two equal ratios. You multiply both the numerator and the denominator by the same number to get an equivalent ratio.
::首先,请看看计数员、25个露营员和75个露营员之间的关系。想想,“我可以乘25个乘75个乘25个乘25个乘35个乘3等于75个。”记住,比例是两个等比。用相同数字乘25个阵营员和75个露营员以获得同等比率。

Next, multiply the given number of tents by 3 to find the equivalent number of tents needed for 75 campers. Think, “1 times 3 equals 3.”
::其次,将给定的帐篷数乘以3,以找到75个露营者所需的同等数量的帐篷。想想,“ 1乘以3等于3 ” 。

You need 3 tents for 75 campers.
::75辆露营车需要3个帐篷

Here is another proportion with a missing quantity. Solve the proportion using mental math.
::这是另一个缺少数量的比例。使用心理数学解决比例。

$\begin{aligned} \frac{4}{8} = \frac{x}{16} \end{aligned}$

First, look at the fraction $\begin{aligned} \frac{4}{8} \end{aligned}$ . 4 is half of 8. Think, “What is half of 16? Half is 16 is 8.”
::首先,看看第4点 8点 4点是8点的一半想想,“16点的一半是什么? 一半是16点是8点。”

The value of $\begin{aligned} x \end{aligned}$ is 8.
::x 值为 8 。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Chase at the grocery store.
::早些时候,你在杂货店遇到切斯的问题

Chase takes 20 minutes to stock 3 shelves. Can he finish 9 shelves before his shift ends in an hour? Write a proportion and use mental math to solve for $\begin{aligned} x \end{aligned}$ .
::大通要花20分钟才能存满3个书架。他能在轮班前一小时完成9个书架吗? 写一个比例,用心理数学解答 x 。

First, write a proportion using the known values with minutes in the numerator and shelves in the denominator.
::首先,使用分母中的分子数和架子中的已知值与分钟的比例写一个比例。

$\begin{aligned} \frac{20}{3} = \frac{x}{9} \end{aligned}$

Next, look at the relationship of the denominators. Think, “What number multiplied by 3 equals 9? 3 times 3 equals 9.”
::接下来,看看分母之间的关系。想想,“乘以多少乘以3等于9?3乘以3等于9?”

Then, multiply the known numerator by 3 to find the unknown quantity. Think, “20 times 3 equals 60. It will take 60 minutes.”
::然后将已知的分子数乘以 3 以找到未知的数量。想想, “ 20乘以 3等于 60 分钟 , 需要 60 分钟。 ”

It will take Chase 60 minutes, or 1 hour, to stock 9 shelves. Chase will finish before his shift is over.
::大通要花60分钟或1小时才存9个货架,大通在下班前完成。

Example 2
::例2

Solve the proportion using mental math: $\begin{aligned} \frac{2}{3} = \frac{x}{33} \end{aligned}$ .
::使用心理数学解决比例:2 3 = x 33 。

First, look at the relationship between the denominators. Think, “What can I multiply 3 by to get 33? 3 times 11 equals 33.”
::首先,看看分母之间的关系。想想,“我乘3能乘多少?3乘3等于33?3乘11等于33。”

Next, multiply the given numerator by 11 to find the unknown quantity. Think “2 times 11 equals 22.”
::下一步, 将给定的分子乘以 11 以找到未知的数量。想象“ 2乘以 11 等于 22 ” 。

The value of $\begin{aligned} x \end{aligned}$ is 22.
::x 值为 22 。

Example 3
::例3

Solve the proportion using mental math: $\begin{aligned} \frac{1}{4} = \frac{x}{16} \end{aligned}$ .
::使用心理数学解决比例:14=x16。

First, look at the fraction $\begin{aligned} \frac{1}{4} \end{aligned}$ . Think, “1 over 4 is the same as one-fourth. One-fourth of 16 is 4.”
::首先,看看第14项。想想,“1+4与四分之一相同,16的四分之一为4。”

The value of $\begin{aligned} x \end{aligned}$ is 4.
::x 值为 4 。

Example 4
::例4

Solve the proportion using mental math: $\begin{aligned} \frac{3}{9} = \frac{x}{18} \end{aligned}$ .
::使用心理数学解决比例:3 9=x18。

First, look at the relationship between the denominators. Think, “What can I multiply 9 by to get 18? 9 times 2 equals 18.”
::首先,看看这些分母之间的关系。想想,“我能乘以9乘以18吗?9乘以2等于18?”

Then, multiply the given numerator to find the unknown quantity. Think, “3 times 2 equals 6.”
::然后,将给定的分子乘以数以找到未知的数量。想想,“3乘以2等于6”

The value of $\begin{aligned} x \end{aligned}$ is 6.
::x 值为 6 。

Example 5
::例5

Solve the proportion using mental math: $\begin{aligned} \frac{5}{15} = \frac{1}{x} \end{aligned}$ .
::使用心理数学解决比例:5 15= 1 x 。

First, look at fraction $\begin{aligned} \frac{5}{15} \end{aligned}$ . 5 and 15 are multiples of 5 and can be simplified by dividing both the numerator and denominator by 5.
::首先,看看第5项、第15项、第5项和第15项是5项的倍数,可以通过将分子和分母除以5来简化。

Think, “5 divided by 5 is 1 and 15 divided by 5 is 3. $\begin{aligned} \frac{5}{15} \end{aligned}$ can be simplified and is equal to $\begin{aligned} \frac{1}{3} \end{aligned}$ .”
::想想,“5”除以5是1,15除以5是3,515可以简化,等于13。”

The value of $\begin{aligned} x \end{aligned}$ is 3.

::x 值为 3 。

Review
::回顾

Solve the following proportions using mental math.
::使用心理数学解决以下比例。

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

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

$\begin{aligned} \frac{1}{3} = \frac{4}{x} \end{aligned}$
::1 3 = 4 x

$\begin{aligned} \frac{2}{3} = \frac{x}{6} \end{aligned}$
::2 3 =x 6

$\begin{aligned} \frac{1}{2} = \frac{x}{16} \end{aligned}$
::1 2 = x 16

$\begin{aligned} \frac{5}{6} = \frac{x}{12} \end{aligned}$
::5 6 = x 12

$\begin{aligned} \frac{14}{16} = \frac{x}{8} \end{aligned}$
::14 16 = x 8

$\begin{aligned} \frac{1}{2} = \frac{x}{18} \end{aligned}$
::1 2 = x 18

$\begin{aligned} \frac{1}{4} = \frac{x}{20} \end{aligned}$
::1 4 = x 20

$\begin{aligned} \frac{1}{4} = \frac{x}{24} \end{aligned}$
::1 4 =x 24

$\begin{aligned} \frac{1}{4} = \frac{x}{40} \end{aligned}$
::1 4 = x 40

$\begin{aligned} \frac{2}{4} = \frac{x}{40} \end{aligned}$
::2 4 = 40 = 40

$\begin{aligned} \frac{25}{50} = \frac{2}{x} \end{aligned}$
::25 50=2x

$\begin{aligned} \frac{4}{12} = \frac{x}{48} \end{aligned}$
::4 12 = x 48

$\begin{aligned} \frac{6}{7} = \frac{36}{x} \end{aligned}$
::6 7 = 36 x

Review (Answers)
::回顾(答复)

章节大纲

常规

心理数学解决比例

Using Mental Math to Solve Proportions ::使用精神数学解决比例

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)

Using Mental Math to Solve Proportions
::使用精神数学解决比例

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)