Course: 3.2 乘数司变换的单位数

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乘数司变换的单级数
Solving Equations with Multiplication and Division
::用乘数和除数解决等号

Suppose you are selling pizza for $1.50 a slice and you can get eight slices out of a single pizza. How much money do you get for a single pizza? It shouldn’t take you long to figure out that you get $\begin{aligned} 8 \times $ 1.50 = $ 12.00 \end{aligned}$ . You solved this problem by multiplying. Here’s how to do the same thing algebraically, using $\begin{aligned} x \end{aligned}$ to stand for the cost in dollars of the whole pizza.
::假设你卖披萨一切 1.50美元,你可以从一个披萨中取出八片。你能得到多少钱买一个披萨?你不必花很长时间就能发现你得到8x1.50美元=12.0美元。你通过乘法解决问题。这里是如何做同样的事情代数,用x来支付整个披萨的美元成本。

Solving Equations
::溶解等量

1. Solve $\begin{aligned} \frac{1}{8} \cdot x = 1.5 \end{aligned}$ .
::1. 解决18x=1.5。

Our $\begin{aligned} x \end{aligned}$ is being multiplied by one-eighth. To cancel that out and get $\begin{aligned} x \end{aligned}$ by itself, we have to multiply by the reciprocal , 8. Don’t forget to multiply both sides of the equation .
::我们的x正乘以八分之一。要取消它并自己得到x, 我们必须乘以对等, 8。不要忘了将等式的两边乘以。

$\begin{aligned} 8 (\frac{1}{8} \cdot x) & = 8 (1.5) \\ x & = 12 \end{aligned}$

::8(18xx)=8(1.5)x=12

2. Solve $\begin{aligned} 0.25 x = 5.25 \end{aligned}$ .
::2. 解决0.25x=5.25。

0.25 is the decimal equivalent of one fourth, so to cancel out the 0.25 factor we would multiply by 4.
::0.25是小数数等于四分之一,所以要取消0.25系数,我们将乘以4。

$\begin{aligned} 4 (0.25 x) & = 4 (5.25) \\ x & = 21 \end{aligned}$

::4(0.25x)=4(5.25x)=21

Solving by division is another way to isolate $\begin{aligned} x \end{aligned}$ . Suppose you buy five identical candy bars, and you are charged $3.25. How much did each candy bar cost? You might just divide $3.25 by 5, but let’s see how this problem looks in algebra.
::以分部解决是隔离 x 的另一种方式。假设你买了5个相同的糖果棒,你却要付3. 25美元。每个糖果棒要花多少钱? 你只需将3. 25美元除以5美元,但让我们看看代数里这个问题如何看待。

3. Solve $\begin{aligned} 5 x = 3.25 \end{aligned}$ .
::3. 解决5x=3.25。

To cancel the 5, we divide both sides by 5.
::为了取消5项,我们把双方除以5。

$\begin{aligned} \frac{5 x}{5} & = \frac{3.25}{5} \\ x & = 0.65 \end{aligned}$

::5x5=3.255x=0.65

4. Solve $\begin{aligned} 1.375 x = 1.2 \end{aligned}$ .
::4. 解决1.375x=1.2。

Divide by 1.375
::除以1.375

$\begin{aligned} x & = \frac{1.2}{1.375} \\ x & = 0.8 \bar{72} \end{aligned}$

::-==============================================================================================================================

Notice the bar above the final two decimals; it means that those digits recur, or repeat. The full answer is 0.872727272727272....
::注意最后两个小数点上方的栏; 这意味着这些位数会重复, 或者重复。完整答案是 0. 87272727272727722....

Examples
::实例

Example 1
::例1

$\begin{aligned} \frac{9 x}{5} = 5 \end{aligned}$
::9x5=5

$\begin{aligned} \frac{9 x}{5} \end{aligned}$ is equivalent to $\begin{aligned} \frac{9}{5} \cdot x \end{aligned}$ , so to cancel out that $\begin{aligned} \frac{9}{5} \end{aligned}$ , we multiply by the reciprocal, $\begin{aligned} \frac{5}{9} \end{aligned}$ .
::9x5等于95xx, 所以取消95, 我们乘以对等, 59。

$\begin{aligned} \frac{5}{9} (\frac{9 x}{5}) & = \frac{5}{9} (5) \\ x & = \frac{25}{9} \end{aligned}$

::59(9x5)=59(5)x=259

Example 2
::例2

$\begin{aligned} 7 x = \frac{5}{11} \end{aligned}$ .
::7x=511. 7x=511.

Divide both sides by 7.
::双方除以7。

$\begin{aligned} x & = \frac{5}{11.7} \\ x & = \frac{5}{77} \end{aligned}$

::x=511.7x=577

Review
::回顾

For 1-5, solve the following equations for $\begin{aligned} x \end{aligned}$ .
::对于 1-5, 解答 x 的以下方程式。

$\begin{aligned} 7 x = 21 \end{aligned}$
::7x=21

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

$\begin{aligned} \frac{5 x}{12} = \frac{2}{3} \end{aligned}$
::5x12=23

$\begin{aligned} 0.01 x = 11 \end{aligned}$
::0.01x=11

$\begin{aligned} \frac{- 2 x}{9} = \frac{10}{3} \end{aligned}$
::- 2x9=103

For 6-10, solve the following equations for the unknown variable.
::对于 6-10, 解析未知变量的下列方程式。

$\begin{aligned} 21 s = 3 \end{aligned}$
::21s=3 21s=3

$\begin{aligned} - 7 a = - 5 \end{aligned}$
::-7a5

$\begin{aligned} \frac{7 f}{11} = \frac{7}{11} \end{aligned}$
::7f11=711

$\begin{aligned} 6 r = \frac{3}{8} \end{aligned}$
::6r=38

$\begin{aligned} \frac{9 b}{16} = \frac{3}{8} \end{aligned}$
::9b16=38

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。

Section outline

General

乘数司变换的单级数

Solving Equations with Multiplication and Division ::用乘数和除数解决等号

Solving Equations ::溶解等量

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Review ::回顾

Review (Answers) ::回顾(答复)

Solving Equations with Multiplication and Division
::用乘数和除数解决等号

Solving Equations
::溶解等量

Examples
::实例

Example 1
::例1

Example 2
::例2

Review
::回顾

Review (Answers)
::回顾(答复)