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  • 数轴上的整数和

    lesson content

    Cooper is having a great time getting to know his pen pal, Riley, in New Zealand. They are both the same age and love sports. Cooper wants to call Riley, but he's having a hard time figuring out when it would be OK to call him because of the time zone  difference .
    ::库珀在新西兰的笔友Riley正在玩得很开心。他们都是同龄人,热爱运动。库珀想给莱利打电话,但他很难确定什么时候可以打电话给他,因为时区差异很大。

    Cooper figures that it would be best if someone called  him  some time after he got home from school at 3pm and before he went to bed at 10pm. He knows that New Zealand is 18 hours ahead of Santa Fe, NM, where Cooper lives, but he doesn't know what time that makes it in New Zealand.
    ::他知道新西兰比Cooper住的地方NM的Santa Fe要早18小时, 但他不知道什么时候能到新西兰。

    In this concept, you will learn how to add integers using a  number line .
    ::在此概念中,您将学习如何使用数字行添加整数。

    Adding Integers Using a Number Line
    ::使用数字行添加整数

    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。

    lesson content

    Number lines are useful tools for visualizing simple arithmetic operations, especially addition and subtraction. Start at the position indicated by the first number. If the second number is negative, move that many units to the left. If it's positive, move that many units to the right. The final mark is the answer.
    ::数字行是可视化简单算术操作的有用工具, 特别是添加和减法。 从第一个数字所显示的位置开始。 如果第二个数字为负数, 将许多单位移动到左边。 如果数字为正数, 将许多单位移动到右边。 最后的标记是答案 。

    Here is an example of using a number line in addition.
    ::下面是加用数字行的例子。

    -5 + 7 = ____

    First, mark the initial integer.
    ::首先,标记初始整数。

    lesson content

    Next, move seven units in the positive direction.
    ::接下来,向积极方向移动七个单位

    The result is +2. 
    ::结果是+2。

    That is the answer of this addition.
    ::这是这一补充的答案。

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

    6 + -9 = _____

    First, mark the initial integer, +6.
    ::首先,标记初始整数,+6。

    lesson content

    Next, move to left (the negative direction) 9 units.
    ::下一步,移动到左边(负向) 9 个单元。

    The final mark is at -3.
    ::最后的标记是 -3

    The answer is -3.
    ::答案是 -3

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Cooper and his time zone difficulty.
    ::早些时候,你得到一个问题 关于库珀 和他的时区困难。

    He wants to call his friend, Riley, in New Zealand some time between 3pm and 10pm, but he doesn't know what time that is in Santa Fe, where he lives. He knows Santa Fe is 18 hours later than New Zealand.
    ::他想给他在新西兰的朋友莱利打个电话,下午3点到10点之间,但他不知道他住的地方圣达菲的时间。他知道圣达菲比新西兰晚18小时。

    In  order  to solve this problem, Cooper can use number lines and addition.
    ::为了解决这一问题,Cooper可以使用数字行和加号。

    First, Cooper can draw a special number line that repeats every twelve hours.
    ::首先,库珀可以画一个特殊的号码线,每12小时重复一次。

    Next, to figure out the early limit, Cooper marks 3pm and then adds 18 hours.
    ::接下来,想出早期限制,Cooper下午3点,然后加18小时。

    3 pm + 18 hours = 9 am
    ::下午3时+18小时=上午9时

    So, 3pm in New Zealand is 9am in Santa Fe.
    ::所以,新西兰下午3点 在圣达菲是早上9点

    Then, he repeats this process to find the later limit.
    ::然后,他重复了这个过程 以找到后期的限制。

    10 pm + 18 hours = 4pm
    ::上午10时+18时=4时

    So, if Cooper wants to call Riley some time between the time Riley comes home from school at 3pm and before he goes to bed at 10pm, Cooper will have to call him between 9am and 4pm. But Cooper, himself, doesn't get home until 3pm. So he concludes that the only time he can call Riley is as soon as he gets home from school at 3pm.
    ::所以,如果Cooper想给Riley打个电话 从Riley下午3点放学回家到晚上10点睡觉之前的一段时间, Cooper必须在9点到4点之间给他打电话。 但是Cooper本人到下午3点才回家。所以他的结论是,他唯一能给Riley打电话的时间是下午3点放学回家之后。

    Example 2
    ::例2

    Draw a number line from -6 to 9 and use it to find the  sum .
    ::从 -6 到 9 绘制数字行, 并用它来查找总和 。

    − 5 + − 1 + 7  = _____

    First, draw the number line. 
    ::首先,绘制数字线。

    Next, start at -5 and move 1 to the left.
    ::下一步,从5 -5开始,向左移动1

    Then, add 7 to the right.
    ::然后右边加7

    You are now at +1.
    ::您现在在+1 中 。

    The answer is  1 .
    ::答案是1。

    Example 3
    ::例3

    Draw a number line and use it to find the sum.
    ::绘制数字行,然后用它来查找总和。

    -5 + 9 = ____

    First, draw the number line. 
    ::首先,绘制数字线。

    Next, start at -5 and move 9 to the right.
    ::下一步,从5 -5开始,向右移动9。

    You are now at +4.
    ::您现在在+4。

    The answer is 4.
    ::答案是4。

    Example 4
    ::例4

    Draw a number line and use it to find the sum.
    ::绘制数字行,然后用它来查找总和。

    -1 + -8 = ____

    First, draw the number line. 
    ::首先,绘制数字线。

    Next, start at -1 and move 8 to the left.
    ::接下来,从 -1开始,向左移动8。

    You are now at -9.
    ::你现在在 -9。

    The answer is -9.
    ::答案是 -9

    Example 5
    ::例5

    Draw a number line and use it to find the sum.
    ::绘制数字行,然后用它来查找总和。

    5 + -7 = ____

    First, draw the number line. 
    ::首先,绘制数字线。

    Next, start at 5 and move 7 to the left.
    ::接下来,从5点开始,往左移7

    You are now at -2.
    ::你现在在 -2。

    The answer is -2.

    ::答案是 -2

    Review
    ::回顾

    Add the following integers that have the same sign by using a number line. You may figure out a pattern. If so, try finding the sums without a number line.
    ::使用数字行添加具有相同符号的以下整数。您可以找出一个模式。如果是,请尝试找到没有数字行的数值。

    1. 6 + 7 = _____
    2. -9 + -7 = _____
    3. -3 + -4 = _____
    4. 5 + 12 = _____
    5. -12 + -23 = _____
    6. 27 + 11 = _____
    7. -34 + -13 = _____
    8. 25 + 16 = _____
    9. -9 + -29 = _____
    10. -16 + -12 = _____

    Add the following integers using a number line. Notice that they have different signs.
    ::使用数字行添加以下整数。请注意它们有不同的符号。

    1. -9 + 3 = _____
    2. -7 + 5 = _____
    3. 1 + -12 = _____
    4. 3 + -8 = _____
    5. -19 + 11 = _____
    6. 7 + -12 = _____
    7. 23 + -10 = _____
    8. -4 + 16 = _____
    9. 15 + -18 = _____
    10. -15 + 9 = _____

    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