Course: 4.2整数的绝对值

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整数的绝对值
Victor's grandparents live in Moscow, Russia. They told him that in the winters the high temperatures average around $\begin{aligned} - 10^{\circ} C \end{aligned}$ while in the summers the high temperatures average around $\begin{aligned} 23^{\circ} C \end{aligned}$ . In science class Victor learned that in Celsius, water freezes at $\begin{aligned} 0^{\circ} C \end{aligned}$ . How could Victor use absolute value to determine which temperature is closer to the freezing point of water, $\begin{aligned} 0^{\circ} C \end{aligned}$ ?
::Victor的祖父母住在俄罗斯莫斯科。他们告诉他,冬天,气温平均在-10°C左右,夏季,气温平均在-23°C左右。在科学课上,Victor了解到,在摄氏度,水冻结在0°C。Victor如何使用绝对值来确定哪一种温度更接近水的冷点,0°C?

In this concept, you will learn how to find the absolute value of an integer and you will learn how to find the opposite of an integer.
::在这个概念中,你会学会如何找到整数的绝对值, 你会学会如何找到整数的相反值。

Finding the Absolute Value of Integers
::查找整数的绝对值

The absolute value of a number is its distance from zero on the number line . The symbol for absolute value is $\begin{aligned} | | \end{aligned}$ .
::数字的绝对值是数字线上与零的距离。绝对值的符号是\\\\\\\\\\\\。

Let's look at an example.
::让我们举个例子。

$\begin{aligned} | - 3 | \end{aligned}$

This is read as “the absolute value of -3”. To figure out the absolute value of -3, think about how far the number -3 is from zero. -3 is 3 units from zero on the number line. This means the absolute value of -3 is 3.
::这被解读为“-3的绝对值” , 要计算-3的绝对值, 想想数字- 3从零到零的绝对值。 - 3 从数字行的零到3个单位。这意味着 - 3的绝对值是3。

The answer is $\begin{aligned} | - 3 | = 3 \end{aligned}$ .
::答案是 3 = 3 = 3 = 3 = 3 = 3 = = 3 = = 3 = = = 3 = = 3 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

Let's look at another example.
::让我们再举一个例子。

$\begin{aligned} | 3 | \end{aligned}$

This is read as “the absolute value of 3”. 3 is 3 units from zero on the number line. This means the absolute value of 3 is 3.
::“绝对值为3”。 3 数字线从零到零是3个单位,3 绝对值为3。

The answer is $\begin{aligned} | 3 | = 3 \end{aligned}$ .
::答案是 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = 3 = = 3 = 3 = 3 = 3 = = 3 = 3 = = 3 = 3 = = 3 = = 3 = = 3 = = 3 = = 3 = = 3 = = = 3 = = = 3 = = = = 3 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

Notice that both $\begin{aligned} | - 3 | \end{aligned}$ and $\begin{aligned} | 3 | \end{aligned}$ are equal to 3. This is because both -3 and 3 are 3 units from zero on the number line.
::请注意 3 和 3 和 3 都等于 3 , 这是因为 3 和 3 是 3 和 3 的 3 。

Keep in mind that the absolute value of a number will always be a positive value. This is because all numbers will always be a positive number of units away from zero on the number line.
::记住数字的绝对值总是正值。这是因为所有数字总是正数, 而不是数字线上的零。

In general, any positive integer and its opposite will have the same absolute value. To find the opposite of an integer, just change its sign either from positive to negative or from negative to positive.
::一般来说,任何正整数及其相反的正整数都将具有相同的绝对值。要找到整数的相反值,只需将其符号从正向负或正向正向改变为正。

Let's look at an example.
::让我们举个例子。

Find the opposite of -16.
::发现与 -16相反。

-16 is a negative integer. To find its opposite, change the negative sign to a positive sign.
::-16是负整数。要发现相反的,将负符号改为正符号。

The answer is that the opposite of -16 is +16 or 16.
::答案是 -16的反比是+16或16。

Let's look at another example.
::让我们再举一个例子。

Find the opposite of 900.
::发现对面的900。

900 is a positive integer. It's the same as +900. To find its opposite, change the positive sign to a negative sign.
::900 是正整数。与 +900 相同。要找到相反的, 将正符号改为负符号。

The answer is that the opposite of 900 is -900.
::答案是,900的对面是 -900。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Victor, who has grandparents in Moscow.
::早些时候,你被问及维克多的问题, 维克多在莫斯科有祖父母。

The winter temperature there is around $\begin{aligned} - 10^{\circ} C \end{aligned}$ while the summer temperature is around $\begin{aligned} 23^{\circ} C \end{aligned}$ . Victor wondered which of these temperatures is closer to the freezing point of water, $\begin{aligned} 0^{\circ} C \end{aligned}$ .
::冬天的温度在-10°C左右, 夏季的温度在23°C左右。 Victor想知道其中哪一种温度更接近水的冷点, 0°C。

First, consider the winter temperature of $\begin{aligned} - 10^{\circ} C \end{aligned}$ .
::首先,考虑冬季温度 - 10°C。

$\begin{aligned} | - 10 | = 10 \end{aligned}$ .

This means that $\begin{aligned} - 10 ° C \end{aligned}$ is 10 degrees away from the freezing point of water.
::这意味着-10°C离水冷点10摄氏度。

Next, consider the summer temperature of $\begin{aligned} 23 ° C \end{aligned}$ .
::接下来,考虑夏季温度 23°C。

$\begin{aligned} | 23 | = 23 \end{aligned}$

This means that $\begin{aligned} 23^{\circ} C \end{aligned}$ is 23 degrees away from the freezing point of water.
::这意味着23°C离水冷点有23度。

The answer is that because $\begin{aligned} | - 10 | \end{aligned}$ is less than $\begin{aligned} | 23 | \end{aligned}$ , the winter temperature is closer to the freezing point of water.
::答案是,因为 - - - - - - - - - - 23 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 23 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Example 2
::例2

Find the absolute value.
::找到绝对值。

$\begin{aligned} | - 234 | \end{aligned}$

First, read the expression. This expression is read as “the absolute value of -234”.
::首先,读读这个表达式。这个表达式被解读为“ -234的绝对值”。

Next, you should think about how far the integer -234 is from zero on the number line. -234 is 234 units from zero on the number line. This means that the absolute value of -234 is 234.
::接下来,你应该考虑数字行的整数 -234 与零相差多少。 -234 是数字行的零 234 个单位。这意味着 -234 的绝对值是 234 个单位。

Remember that in general, the absolute value of a number will always be positive.
::总的说来,一个数字的绝对值永远是正数。

The answer is 234.
::答案是234

Example 3
::例3

Find the absolute value.
::找到绝对值。

$\begin{aligned} | 22 | \end{aligned}$

First, read the expression. This expression is read as “the absolute value of 22”.
::首先,读读这个表达方式,这一表达方式被解读为“22的绝对值”。

Next, you should think about how far the integer 22 is from zero on the number line. 22 is 22 units from zero on the number line. This means that the absolute value of 22 is 22.
::接下来,你应该考虑数字行的整数22从零到零的距离。22是数字行从零到零的22个单位。这意味着22的绝对值是22。

Notice that our sign didn't change. The absolute value of a number will always be positive.
::注意我们的标志没有改变数字的绝对值总是正数

The answer is 22.
::答案是22。

Example 4
::例4

Find the absolute value.
::找到绝对值。

$\begin{aligned} | - 222 | \end{aligned}$

First, read the expression. This expression is read as “the absolute value of -222”.
::首先,读读这个表达方式。这个表达方式被解读为“222的绝对值”。

Next, you should think about how far the integer -222 is from zero on the number line. -222 is 222 units from zero on the number line. This means that the absolute value of -222 is 222.
::接下来,你应该考虑数字线上的整数 - 222 与零相差多少。 - 222 是数字线上的零 222 个单位。这意味着 - 222 的绝对值是 222 。

Remember that the absolute value of a number will always be positive.
::记住数字的绝对值总是正数。

The answer is 222.
::答案是222

Example 5
::例5

Find the opposite of -18.
::发现与 -18相反。

First, notice that -18 is a negative integer. To find its opposite, change the negative sign to a positive sign.
::首先, 请注意 - 18 是负整数。要找到相反的, 请将负符号改为正符号。

The answer is 18.
::答案是18岁

Review
::回顾

Write the opposite of each integer.
::每整数写相反的文字。

20

-7

22

-34

0

-9

14

25

Find the absolute value of each integer.
::查找每个整数的绝对值。

$\begin{aligned} | 13 | \end{aligned}$

$\begin{aligned} | - 11 | \end{aligned}$

$\begin{aligned} | - 5 | \end{aligned}$

$\begin{aligned} | 17 | \end{aligned}$

$\begin{aligned} | - 9 | \end{aligned}$

Review (Answers)
::回顾(答复)

Section outline

General

整数的绝对值

Finding the Absolute Value of Integers ::查找整数的绝对值

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)

Finding the Absolute Value of Integers
::查找整数的绝对值

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)