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  • 不同符号整数的和

    lesson content

    Collette has just moved to New York City for school and can't quite believe how expensive everything is. She had $1000 in her bank account when she got to the city. She makes $520 at the coffee shop where she works her first two weeks in the city. That's supposed to be automatically deposited into her account on the 14th of the month. Her rent is $1250. It is supposed to be taken out on the 16th of the month. Will she have enough money in her account to cover the withdrawal?
    ::科莱特刚搬到纽约市上学,无法相信每件东西有多贵。 她到了城里时,银行帐户里有1000美元。 她在咖啡店里挣了520美元, 她头两个星期在城里工作。 这应该自动存入她每月14号的帐户。 她的租金是1 250美元。 她的租金应该是1 250美元。 她的帐户里有足够的钱来支付提款费吗?

    In this concept, you will learn to add integers with different signs.
    ::在此概念中, 您将学会添加带有不同符号的整数 。

    Adding Integers with Different Signs
    ::添加带有不同符号的整数

    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。

    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。

    One way to add integers with different signs is to ignore the sign and find the  difference  between the two integers. Then give the answer the sign of the bigger integer.
    ::添加带有不同符号的整数的一个方法就是忽略符号并找到两个整数之间的差别。然后给答案大整数的符号。

    Here is an example:
    ::以下是一个例子:

    8 + -3 = ____

    First, ignore the sign and find the difference between the two numbers. Difference means to subtract.
    ::首先,忽略符号, 找到两个数字之间的差。 差异意味着要减去 。

    8 - 3 = 5.

    Next, determine which of the original integers was bigger.
    ::下一步,确定哪个原始整数更大。

    8 is bigger than 5.
    ::8 大于 5 。

    Then, check the sign of the integer that is bigger.
    ::然后,检查整数的符号 更大的。

    The sign of 8 is "+". 
    ::8的符号是"+"

    Finally, assign the answer that sign.
    ::最后, 指定那个标志的答案 。

    The answer is positive 5.
    ::答案是正5。

    You can check your work by using a  number line .
    ::您可以使用数字线查看您的工作 。

    lesson content

    Start with positive 8.
    ::从正8开始

    lesson content

    Add a negative three to that by moving three units to the left.
    ::将三个单位移到左边,再加一个负三。

    The answer is 5.
    ::答案是5。

    Here is another example:
    ::以下是另一个例子:

    -9 + 4 = ____

    First, ignore the signs and find the difference between the two values.
    ::首先,忽略这些迹象,找出这两个价值观之间的差别。

    9 - 4 = 5

    Next, determine which integer is bigger.
    ::下一步,决定哪个整数更大。

    9 is bigger than 4.
    ::9大于4。

    Then, check the sign of that original integer.
    ::然后,检查那个原始整数的符号。

    9 was negative.
    ::9是负数。

    Finally, assign that sign to the answer.
    ::最后,把那个标志指定给答案。

    The answer is -5.
    ::答案是 -5

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Collette and her money troubles.
    ::早些时候,你得到一个问题 关于科莱特和她的钱问题。

    She has to figure out if she is going to have enough money in her bank account on the 16th to make her rent of $1,250. Her bank account started with $1000 and she made $520 at work. Will she have enough?
    ::她必须弄清楚她是否有足够的钱在16号的银行帐户上赚到1,250美元的租金。她的银行帐户从1000美元开始,她在工作中赚到520美元。她有足够的钱吗?

    First, she writes all the relevant quantities as positive and negative integers.
    ::首先,她将所有相关数量都写成正数和负数整数。

    Her bank account starts positive, so that is: +1000. Her earnings are added to that, so they are positive, as well: +520. Her rent will be taken from her account, so that is a negative integer: -1250.
    ::她的银行账户开始呈正数,也就是说:+1000。她的收入加起来,所以是正数,还有:+520。她的房租将从她的账户中扣除,也就是说负数整数: - 1250。

    Next, she checks that her wages will be in the bank before her rent comes out. Since they come in the 14th, they should be. Then she adds what she starts with to her wages. 
    ::接下来,她检查她的工资在她房租出来之前会在银行里。自从他们到14号以后,应该有。然后,她将工资加到她的工资上。

    1000 + 520 = 1520

    Then, she adds the positive  amount  in her bank account to the negative amount to be taken out to see if she has enough.
    ::然后,她又将银行账户中的正数加上负数,再加到负数,看她是否有足够的钱。

    1520 + − 1250 =

    To do this problem, first she takes the difference of the two numbers, ignoring the signs:
    ::为了解决这个问题,首先,她拿两个数字的差数,忽略了迹象:

    1520 − 1250 = 270

     Next, she checks the sign of the original integers.
    ::接下来,她检查原始整数的符号。

    The positive was bigger. That means the final answer will be positive. 
    ::积极程度更大,这意味着最终答案将是肯定的。

    She concludes, that her final bank account will be a positive number, which means that there will still be money in her account. This means, she will have enough money in her account to cover her rent.
    ::她的结论是,她最后的银行账户将是一个正数,这意味着她的账户中还会有钱,这意味着她的账户中有足够的钱来支付房租。

    Example 2
    ::例2

    Find the  sum .
    ::找到数额。

    -2 + 8 = _____

    First, ignore the signs and find the difference between the two values.
    ::首先,忽略这些迹象,找出这两个价值观之间的差别。

    8 - 2 = 6

    Next, decide which integer is bigger.
    ::下一步,决定哪个整数更大。

    8 is bigger than 2.
    ::8 大于 2。

    Then, check the original sign of that integer.
    ::然后,检查那个整数的原始符号。

    8 is positive.
    ::8是积极的。

    Finally, assign the answer that sign.
    ::最后, 指定那个标志的答案 。

    The answer is 6.
    ::答案是6个

    Example 3
    ::例3

    Find the sum.
    ::找到数额。

    7 + -13 = ____

    First, ignore the signs and find the difference between the two values.
    ::首先,忽略这些迹象,找出这两个价值观之间的差别。

    13 - 7 = 6

    Next, determine which integer is bigger.
    ::下一步,决定哪个整数更大。

    13 is bigger than 7.
    ::13大于7。

    Then, check the sign of that original integer.
    ::然后,检查那个原始整数的符号。

    13 was negative.
    ::13是负数。

    Finally, assign that sign to the answer.
    ::最后,把那个标志指定给答案。

    The answer is -6.
    ::答案是 -6

    Example 4
    ::例4

    Find the sum.
    ::找到数额。

    -22 + 10 = ____

    First, ignore the signs and find the difference between the two values.
    ::首先,忽略这些迹象,找出这两个价值观之间的差别。

    22 - 10 = 12

    Next, determine which integer is bigger.
    ::下一步,决定哪个整数更大。

    22 is bigger than 10.
    ::22大于10。

    Then, check the sign of that original integer.
    ::然后,检查那个原始整数的符号。

    22 was negative.
    ::22是负数。

    Finally, assign that sign to the answer.
    ::最后,把那个标志指定给答案。

    The answer is -12.
    ::答案是 -12

    Example 5
    ::例5

    Find the sum.
    ::找到数额。

    -1 + 16 = ____

    First, ignore the signs and find the difference between the two values.
    ::首先,忽略这些迹象,找出这两个价值观之间的差别。

    16 - 1 = 15

    Next, determine which integer is bigger.
    ::下一步,决定哪个整数更大。

    16 is bigger than 1.
    ::16大于1。

    Then, check the sign of that original integer.
    ::然后,检查那个原始整数的符号。

    16 was positive.
    ::16是肯定的。

    Finally, assign that sign to the answer.
    ::最后,把那个标志指定给答案。

    The answer is +15.

    ::答案是+15。

    Review
    ::回顾

    Add the following pairs of integers.
    ::添加以下几对整数。

    1. 12 + − 4
    2. − 24 + 14
    3. 32 + − 4
    4. − 52 + 14
    5. 67 + − 64
    6. 55 + − 64
    7. 78 + − 84
    8. 99 + − 104
    9. − 112 + 114
    10. − 19 + − 4 + 12
    11. − 32 + − 24 + 65
    12. 98 + − 12 + − 34
    13. 70 + − 34 + 23
    14. 82 + − 54 + 27
    15. 98 + − 34 + − 18

    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