整数的绝对值

[Figure 1]

Jeremiah just moved to Boston with his family. He wants to practice Aikido, but he's not sure which dojo to pick. The distance on the bus is probably the deciding factor, but some of them are Outbound, some are Inbound, and some are both. He lives near the Washington St. stop on the Green Line. He finds one dojo in Porter Square and one near the Davis stop on the Red Line. He finds one on Mass Ave, one out at Forest Hills on the Orange Line, and one at Brookline on the Green Line. Which dojo should he pick?
::Jeremiah刚和家人搬到波士顿。 他想要练习Aikido, 但他不确定哪个道场可以选择。 公共汽车上的距离可能是决定性因素, 但有些是外向的, 有些是内向的, 有些是内向的, 有些是两者兼而有之。 他住在Washington St的绿线上。 他在波特广场找到一个道祖, 在红线上的戴维斯站附近找到一个道祖。 他在Mass Ave上发现了一个道道, 一个在橙线上的森林山, 一个在绿线上的布鲁克林。 他应该选哪个道祖?

In this concept, you will learn how to take the absolute value of integers. 
::在这个概念中,你会学会如何使用整数的绝对值。

Taking Absolute Value of Integers
::采用整数绝对值

An  integer  is any  positive  whole number or its opposite. Here, opposite means sign. So a positive integer has a negative opposite and vice versa.
::整数是正整数或正整数。 这里, 反整数是指符号。 正整数是负整数, 反整数是负整数, 反整数是正整数。

A  positive number  is a number greater than  zero . It can be written with or without a + symbol in front of it. A gain in something is written with a positive number. 
::正数是大于零的数。 它可以在前面有或没有 + 符号来写。 某事物的增益会写成正数 。

A  negative number  is a number that is less than zero. It is always written with a - symbol in front of it. A loss is written with a negative number. 
::负数是一个小于零的数字。它总是在前面写上一个符号。损失则用负数写上。

A  number line  is a line on which numbers are marked at intervals, used to illustrate simple numerical operations. Using a number line allows you to see where a number is in relationship to other numbers and from zero.
::数字行是用于说明简单数字操作的间隔标记数字的线条。使用数字行可以显示数字与其他数字的关系,从零到零。

If you look at this number line, you will see that 2 is two units away from zero. Each little line on the number line is a unit. But -2 is also two units away from zero. Even though these numbers have different signs, they are both two units away from zero.
::如果看这个数字线, 你会看到 2 是 0 之间的两个单位。 数字线上的每个小行都是 单位。 但是 - 2 也是 零 之间的两个单位。 尽管这些数字有不同的信号, 但它们都是 零 之间的两个单位 。

The  absolute value  of a number is the distance that the integer is from zero. The symbol for absolute value is two parallel lines surrounding the quantity, like this:  $\begin{array}{r}|5|\end{array}$ .
::一个数字的绝对值是整数从零的距离。绝对值的符号是围绕数量的两个平行线条,例如: 5 。

In this example,   $\begin{array}{r}|5|\end{array}$ , the absolute value of 5 is 5 because five is five units away from zero.
::5的绝对值是5 因为5的单位离零是5个单位。

Here is another example.
::下面是另一个例子。

$\begin{array}{r}|-9|=\underset{\_}{}\end{array}$

The absolute value of negative nine is the number of units that -9 is from zero. It is nine units from zero. So the absolute value of -9 is 9.
::负 9 的绝对值为 - 9 个单位数, 零为 - 9 个单位数。 零为 9 个单位数。 绝对值为 - 9 个单位数为 9 个单位数。 因此, 绝对值为 - 9 个单位数为 9 个单位数 。

$\begin{array}{r}|-9|=9\end{array}$

Distance from 0 is always a positive quantity. So in practice, all you need to do to find the absolute value is to take away the negative sign. The absolute value of a positive integer will just be that integer. The absolute value of a negative integer will just be that integer without the negative sign.
::从 0 到 0 的距离总是正数 。 因此在实践中, 要找到绝对值, 您需要做的就是取消负数符号。 正数整数的绝对值就是这个整数。 负数整数的绝对值就是那个没有负数符号的整数 。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Jeremiah and his Aikido dilemma.
::早些时候,你得到一个问题 关于耶利米和他的相基多两难困境。

He can't decide which dojo is the fewest bus stops from his house near Washington St. He has found dojos at Porter, Davis, Mass Ave., Forest Hills, and Brookline.
::他无法决定哪个道场是他在华盛顿街附近的 家里的 最少的公交车站 他已经在波特、戴维斯、马斯艾夫、森林山和布鲁克林 找到了道场

First, to solve this problem, he figures out how many stops Inbound and Outbound each dojo would require him to travel.  
::首先,为了解决这个问题,他想方设法 有多少个入境和出境的道场 需要他去旅行。

To get to Porter Square, he has to go Inbound 18 stops on the Green Line. Then he transfers to the Red Line at Park Street and goes Out bound 5 stops. To get to Davis, he does the same but goes Outbound 6 stops. To get to Mass Ave he goes Inbound 18 stops on the Green Line, then he transfers to the Red Line and goes Inbound another stop, then he transfers to the Orange Line at Downtown Crossing and goes Outbound 4 stops. To get to Forest Hills, he does the same but goes Outbound 10 stops, instead. But to get to Brookline Village, he only has to go Inbound 13 stops on the Green Line and then he can get off at Kenmore and go 3 stops Outbound on the D.
::为了到达波特广场,他必须前往绿线上的18个路口。然后他又转往公园街的红线,然后到5个路口。为了到达戴维斯,他也这样做了,但往外走6个路口。为了到达弥撒Ave,他到绿线上的18个路口,然后他到红线,再到另一个路口,然后到下城十字路口的橙线,然后到4个路口。为了到达森林山,他也这样做了,但到了10个路口,相反。但是为了到达布鲁克林村,他只需到绿线上的13个路口,然后他就可以到肯莫尔,然后到3个路口,到D路口。

Next, he decides that any stops going Inbound from his house are positive values and any stops Outbound are negative. Using this convention, he makes a chart.
::接下来,他决定任何从他家入境的停留都是积极的价值观,任何从他家入境的停留都是消极的。他利用这个公约做了一张图表。

Then, because he only cares about the total number of stops and not what direction they are in, he sets up a series of addition problems using absolute values and solves them.
::然后,因为他只关心停停的总数, 而不关心停停的方向, 他用绝对值设置了一系列的附加问题, 并解决了这些问题。

 Porter: $\begin{array}{r}18+\left|-5\right|=23\end{array}$   
::波特:18+___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Mass Ave:  $\begin{array}{r}18+\left|-6\right|=24\end{array}$
::Mass Ave: 18 + + + + + - 6 = 24

Davis:   $\begin{array}{r}18+1+\left|-4\right|=23\end{array}$
::戴维斯:18 + 1 + + + + + + + - 4 = 23

Forest Hills:   $\begin{array}{r}18+1+\left|-10\right|=29\end{array}$
::森林山:18+1++______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Brookline Village:   $\begin{array}{r}13+\left|-3\right|=16\end{array}$
::布鲁克林村:13++____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________#16

Finally, he compares the number of total stops. He concludes that the Brookline Village dojo has the fewest total stops, so he will practice there.
::最后,他比较了总停车站的数量。他的结论是布鲁克林村的停车站数量最少,因此他将在那里练习。

Example 2
::例2

Find the absolute value.
::找到绝对值。

$\begin{array}{r}|-270|=\underset{\_}{}\end{array}$

First, remember that the absolute value is just the distance a value is from zero.
::首先,记住绝对值只是一个数值与零的距离。

In this case, that is 270.
::在这种情况下,就是270个。

Next, remember that the distance is always a positive value.
::接下来,请记住,距离总是一个正值。

Then, write the absolute value as a positive distance from zero.
::然后,将绝对值写成从零的正距离。

The absolute value of  $\begin{array}{r}-270\end{array}$  is 270.
::270的绝对值为270。

Example 3
::例3

Find the absolute value.
::找到绝对值。

$\begin{array}{r}|-10|=\underset{\_}{}\end{array}$

First, determine what the distance is.
::首先,确定距离。

In this case, it is 10.
::在这种情况下,是10个。

Then, remember that the distance is always a positive number.
::那么,记住距离总是正数。

The answer is 10.
::答案是10个

Example 4
::例4

Find the absolute value.
::找到绝对值。

$\begin{array}{r}|25|=\underset{\_}{}\end{array}$

First, determine what the distance is.
::首先,确定距离。

In this case, it is 25.
::在这种情况下,是25个。

The answer is 25.
::答案是25岁

Example 5
::例5

Find the absolute value.
::找到绝对值。

$\begin{array}{r}|-2|=\underset{\_}{}\end{array}$

First, determine what the distance is.
::首先,确定距离。

In this case, it is 2.
::在这种情况下,是2。

Then, remember that the distance is always a positive number.
::那么,记住距离总是正数。

Therefore, the answer is 2.
::因此,答案是2。

Review
::回顾

Identify the absolute value of integers. Use a number line for reference.
::指定整数的绝对值。使用数字行进行引用。

[Figure 4]

1. $\begin{array}{r}|6|\end{array}$
2. $\begin{array}{r}|-6|\end{array}$
3. $\begin{array}{r}|-21|\end{array}$
4. $\begin{array}{r}|8|\end{array}$
5. $\begin{array}{r}|12|\end{array}$
6. $\begin{array}{r}|-7|\end{array}$
7. $\begin{array}{r}|-17|\end{array}$
8. $\begin{array}{r}|17|\end{array}$
9. $\begin{array}{r}|4|\end{array}$
10. $\begin{array}{r}|-4|\end{array}$
11. $\begin{array}{r}|-204|\end{array}$
12. $\begin{array}{r}|44|\end{array}$
13. $\begin{array}{r}|144|\end{array}$
14. $\begin{array}{r}|-144|\end{array}$
15. $\begin{array}{r}|-290|\end{array}$

Review (Answers) 
::回顾(答复)