章节大纲

  • 常规

    全部折叠 展开全部

  • 数轴上的整数比较

    lesson content

    Alyson and her son, Gage, are tired of Vermont winters, so they decide to get a small winter home somewhere warm. After looking around, they come up with a short list of places that are within their price range. But there's a catch. Alyson gets altitude sickness, so they want to pick the place that has the lowest altitude. Which place should they pick?
    ::Alyson和她的儿子Gage厌倦了佛蒙特州的冬天,所以他们决定去一个温暖的冬天家。在环顾四周之后,他们提出了一份价格范围内的短清单。但是有一个陷阱。Alyson病得很高,所以他们想选择一个最低高度的地方。他们应该选择哪个地方?

    Brawley, CA: altitude -112ft
    ::布朗利,CA:高度-112ft

    Eldorado, NM: altitude 6,677ft
    ::Eldorado,NM:高度6,677ft

    Punta Gorda, FL: altitude 10 ft
    ::Punta Gorda, FL:高度10英尺

    Holtville, CA: altitude -10 ft
    ::加利福尼亚州霍特维尔:高度 - 10英尺

    In this concept, you will learn how to compare and  order  integers using a  number line . 
    ::在此概念中, 您将学习如何使用数字行比较和排序整数 。

    Comparing Integers on a Number Line
    ::在数字行上比较整数

    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。

    This number line shows the integers from -5 to 5.
    ::此数字行显示 - 5 到 5 的整数 。

    lesson content

    Number lines are useful for comparing integers. Just plot the integers on the line and then check to see which one is furthest to the right. That one is the greatest. The one furthest to the left is the least. Note, this means that a positive number is always greater than (>) a negative number. (The sideways V opens in the direction of the bigger number.)
    ::数字行可用于比较整数。 只需在线上绘制整数, 然后检查看哪个向右最远。 这是最大的。 左边最远的是最小的。 注意, 这意味着正数总是大于( >)负数。 (侧面 V 向较大数字方向打开) 。

    Here is an example.
    ::举一个例子。

    -6 ____ 2

    First draw a number line.
    ::首先绘制数字行。

    Next, plot both integers on it.
    ::下一张图 上面画两个整数

    Then, decide which one is further to the right.
    ::然后,决定谁在右边。

    In this case, the 2 is further to the right. That means it is greater than -6.
    ::在此情况下, 2 是 向右 。 这意味着它大于 - 6 。

    The answer is -6 < 2.
    ::答案是 -6 < 2。

    Here is another example.
    ::下面是另一个例子。

    17 ____10

    First draw a number line.
    ::首先绘制数字行。

    Next, plot both integers on it.
    ::下一张图 上面画两个整数

    Then, decide which one is further to the right.
    ::然后,决定谁在右边。

    In this case, the 17 is further to the right. That means it is greater than 10.
    ::在这种情况下,17人更接近权利,即超过10人。

    The answer is 17 > 10.
    ::答案是17 > 10。

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

    -5 ____ -6

    First draw a number line.
    ::首先绘制数字行。

    Next, plot both integers on it.
    ::下一张图 上面画两个整数

    Then, decide which one is further to the right.
    ::然后,决定谁在右边。

    In this case, the -5 is further to the right. That means it is greater than -6.
    ::在这种情况下,5比权利更进一步,这意味着它大于6。

    The answer is -5 > -6.
    ::答案是 -5 > -6。

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Alyson and Gage's house-hunt dilemma.
    ::早些时候,你遇到了一个问题 关于Alyson和Gage的家访困境。

    They want to get a winter home that is at the lowest elevation possible. Their four options are:
    ::他们想要一个位于最低海拔的冬季家庭。他们有四个选择:

    Brawley, CA: altitude -112ft
    ::布朗利,CA:高度-112ft

    Eldorado, NM: altitude 6,677ft
    ::Eldorado,NM:高度6,677ft

    Punta Gorda, FL: altitude 10 ft
    ::Punta Gorda, FL:高度10英尺

    Holtville, CA: altitude -10 ft
    ::加利福尼亚州霍特维尔:高度 - 10英尺

    In order to decide which one to buy, Gage makes a number line.
    ::为了决定买哪一个, Gage 做了一个数字行 。

    It is easy to see from this number line that Eldorado is the highest altitude, then Punta Gorda, then Holtville, then Brawley.
    ::从这个数字线很容易看出 埃尔多拉多是最高海拔, 然后是蓬塔戈尔达, 然后是霍尔特维尔, 然后是布朗利。

    Brawley, CA has the lowest altitude, so it is the place that they pick.
    ::布朗利 CA的高度最低 所以这是他们选的地方

    Example 2
    ::例2

    Jessie loses fifteen dollars playing video games. Carmen loses twenty-five dollars. Who has the bigger loss?
    ::卡门损失了25美元 谁的损失更大?

    First, write both losses as integers.
    ::首先,将两个损失都写成整数。

    Since losses are represented by negative integers, Jessie= − 15  and Carmen= − 25
    ::由于损失以负整数表示,Jessie= - 15和Carmen=- 25

    Next, draw a number line and plot both integers on it.
    ::下一步,绘制数字线并绘制数字的整数。

    Then, compare the two points. The one further to the left is the smaller number, or the bigger loss.
    ::然后,比较两个点。左边一个是较小的数字,或者更大的损失。

    In this case, -25 is further to the left so it is the smaller integer.
    ::在这种情况下, -25在左侧,所以是小整数。

    This can also be written: 
    ::这也可以写成:

      − 25 < − 15

    Example 3
    ::例3

    Decide which is greater using < or > symbols: -6 ____ 8.
    ::使用 < 或 > 符号决定哪个更大: - 6 _ 8 。

    First, draw a number line and plot both points on it.
    ::首先,绘制一个数字线,并绘制上面的两个点。

    Next, decide which point is further to the left.
    ::下一步,决定左侧是哪个点。

    In this case, -6 is further to the left, so it is smaller than 8.
    ::在这种情况下, -6离左侧更远,因此小于8。

    That means -6<8.
    ::意思是 -6<8

    The answer is <.
    ::答案是 < 。

    Example 4
    ::例4

    Decide which is greater using < or > symbols: -99 ____ -9.
    ::使用 < 或 > 符号: - 99___ - 9决定哪个更大: - 99___-9。

    First, draw a number line and plot both points on it.
    ::首先,绘制一个数字线,并绘制上面的两个点。

    Next, decide which point is further to the left.
    ::下一步,决定左侧是哪个点。

    In this case, -99 is much further to the left than -9, so it is smaller.
    ::在这种情况下,-99比-9远得多,因此小得多。

    That means, -99<-9.
    ::意思是 99 -9

    The answer is <.
    ::答案是 < 。

    Example 5
    ::例5

    Decide which is greater using < or > symbols: 12 ____ 6.
    ::决定使用 < 或 > 符号的数值更大: 12 _ 6。

    First, draw a number line and plot both points on it.
    ::首先,绘制一个数字线,并绘制上面的两个点。

    Next, decide which point is further to the left.
    ::下一步,决定左侧是哪个点。

    In this case, 6 is further to the left so it is smaller.
    ::在这种情况下,6个在左侧,小于6个。

    That means 6<12. Or, re-written: 12>6.
    ::意思是6<12。或者,改写:12>6。

    The answer is >.

    ::答案是 > 。

    Review
    ::回顾

    Draw a number line, and compare each pair of integers using the symbols for greater than and less than.
    ::绘制数字行,并用大于和小于的符号比较每对整数。

    1. 18 ____ 22
    2. -12 ____ 12
    3. -14 ____ -16
    4. -20 ____ -33
    5. 19 ____ -1
    6. 0 ____ -3
    7. -27 ____ -28
    8. -233 ____ -300
    9. -765 ____ -745
    10. -234 _____ -300

    Write integers and then use inequality symbols to compare each pair of values.
    ::写入整数,然后使用不平等符号比较每一对数值。

    1. A loss of 16 and a loss of 29
      ::损失 16 损失 16 损失 29 损失
    2. A loss of 18 and a gain of 28
      ::损失18和收益28
    3. A loss of 27 and a loss of 10
      ::损失27项,损失10项
    4. A loss of 16 and a gain of 12
      ::损失16和收益12
    5. A loss of 90 and a loss of 99
      ::90损失和99损失

    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