Section outline

  • lesson content

    Serena and her dad have to build a fence to keep their cows in their pasture and out of the road. Together they walk the line of the new fence, measuring out and marking every three feet where the fence posts will go. But then her dad gets called in for a phone call. He leaves her with the tape measure, the poles, and a shovel and tells her to go ahead and start digging the holes. To figure out the depth he tells her that about half what's left above ground should go below. She measures the poles and finds that they're each 60 inches long.  How can Serena figure out how deep the holes need to be?
    ::Serena和她的爸爸必须修建一道栅栏,让他们的奶牛留在牧场和道路之外。他们一起走在新栅栏的线条上,测量和标记每三英尺的栅栏去的地方。但随后她父亲接到电话。他给她留下带子、杆子和铲子,并告诉她继续挖洞。为了了解他告诉她,地面上剩下的一半应该到下面去。她测量了杆子,发现它们每60英寸长。Serena怎么能知道洞有多深?

    In this concept, you will learn how to find the opposites of integers. 
    ::在这个概念中,你会学会如何找到整数的反面。

    Finding Opposites of Integers
    ::查找整数的对手

    Finding the opposite of an integer is useful in many different contexts. If you spend $20, the person who takes your money gains it. If a boat floats half below water and half above it, then the distance below the water is the opposite of the distance above it. All of this can be described using opposite integers.
    ::查找整数的相反点在许多不同的背景下是有用的。 如果您花费20美元, 取钱的人就可以得到。 如果一艘船舶在水下漂浮一半, 水下漂浮一半, 水下距离与水上距离相对。 所有这些都可以用相反的整数来描述。

    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. Profit, increase, and income are all examples of words that mean positive.
    ::正数是大于零的数。 它可以在前面用或不用+符号书写。 某事物的增益是用正数书写。 利润、 增长和收入都是表示正数的字词例子。

    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. Decrease, spend, and decline are examples of words that mean negative.
    ::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。 减少、 花费和下降是表示负数的字数的例子。

    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。

    Let's look at an example.
    ::让我们举个例子。

    Write the opposite of -15.
    ::写反比15。

    First, determine whether the given integer is positive or negative.
    ::首先,确定给定整数是正数还是负数。

    This example has a "-" out front, so it is negative.
    ::这个例子的前面有一个" -", 所以它是负的。

    Next, figure out what the opposite sign is.
    ::下一步,找出相反的标志是什么。

    The opposite of negative is positive.
    ::反倒相反的是积极的。

    Then, re-write the original integer with the opposite sign.
    ::然后用相反的符号重写原始整数。

    The answer is +15 or 15.
    ::答案是+15或15。

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

    Find the opposite of 500 feet above sea level.
    ::发现海拔500英尺的对面

    First, determine whether the original number is positive or negative.
    ::首先,确定原始数字是正数还是负数。

    "Above sea level" is positive, since sea level is zero.
    ::"波及海平面"是正数 因为海平面是零

    Next, write the original example as a positive integer.
    ::下一步,将原始示例写成正整数。

    It is +500.
    ::这是+500。

    Then, write it with the opposite sign.
    ::那就用相反的符号写吧

    The answer is -500.
    ::答案是 -500

    In this example, -500 means 500 feet below sea level.
    ::例如,500表示海平面下500英尺以下。

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Serena and her fence making.
    ::早些时候,有人给了你一个问题 关于瑟琳娜和她的栅栏制造。

    The posts are each 60 inches long and her dad tells her that half as much of the post should go in the ground as stays above. Serena realizes that the post can be divided into three even pieces. One that needs to fit in the hole. And two that are above ground.
    ::塞雷娜意识到这个职位可以被分成三块。一个需要放在洞里,而两个在地上。

    In  order  to figure out how much of the post goes underground, she divides the length 60 by 3.
    ::为了弄清楚这篇文章有多少内容被转入地下, 她将60比3的长度除以3。

    The piece that needs to fit in the hole is 20inches.
    ::需要装在洞里的碎片是20英寸

    Next, she re-writes that as a positive integer.
    ::接下来,她重写为正整数

    It is +20.
    ::这是+20。

    Then, she figures out that a hole dug into the ground is a negative integer because it is below ground-level.
    ::然后,她发现挖进地面的洞是一个负整数, 因为它在地面以下。

    So, in order for the +20 of the pole to fit in the hole, the hole needs to be -20.
    ::所以,为了让电线杆的 +20 适应洞口, 洞口必须是 -20 。

    In other words, she needs to dig the whole 20 inches deep.
    ::换句话说,她需要挖 整个20英寸深。

    Example 2
    ::例2

    Alec spends $15 buying lemonade to sell at his stand. In order to break even, he needs to sell the opposite. Write the integer that represents how much Alec needs to sell.
    ::艾力克花了15美元买柠檬水 在他的摊位出售。为了实现平衡,他需要卖反面。写下代表艾力克需要卖多少的整数。

    First, write the original number as an integer.
    ::首先,将原始编号写成整数。

    Alec "spends" the money. This means it's negative. The original integer is -15.
    ::Alec "spends" the money. 原始整数是 - 15 。

    Next, find the opposite sign.
    ::下一个,找到相反的标志。

    In this case, it is positive.
    ::在这种情况下,这是积极的。

    Then, write the opposite integer.
    ::然后,写反整数。

    The answer is +15. This means that Alec needs to make, or gain, $15 in order to break even.
    ::答案是+15。这意味着亚历克需要挣15美元,或者获得15美元才能实现平衡。

    Write the opposite of each example.
    ::每个例子的写法正好相反。

    Example 3
    ::例3

    A loss of 34.
    ::损失34美元

    First, determine whether the given integer is positive or negative.
    ::首先,确定给定整数是正数还是负数。

    "Loss" means negative.
    ::"损失"的意思是负的。

    Then, write the original integer.
    ::然后,写原整数。

    It is -34
    ::是 -34号

    Finally, write the opposite.
    ::最后,写反了。

    The answer is  + 34 .
    ::答案是+34。

    Example 4
    ::例4

    998

    First, determine whether the given integer is positive or negative.
    ::首先,确定给定整数是正数还是负数。

    Since there is no sign, you can assume it is positive.
    ::由于没有迹象,你可以假定这是积极的。

    It can also be written as +998.
    ::也可以以+998写成。

    Then, write the opposite.
    ::那就反写反写吧

    The answer is   − 998 .
    ::答案是- 998。

    Example 5
    ::例5

    67 feet above sea level
    ::海拔67英尺以上海平面

    First, determine whether the given integer is positive or negative.
    ::首先,确定给定整数是正数还是负数。

    "Above sea level" means positive.
    ::"波及海平面"是积极的

    Then, write the original integer.
    ::然后,写原整数。

    It is +67.
    ::这是+67。

    Finally, write the opposite.
    ::最后,写反了。

    The answer is   − 67 .

    ::答案是 - 67

    Review
    ::回顾

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

    1. A loss of 18
      ::损失18
    2. A gain of 22
      ::22项收益
    3. -78
    4. 999
    5. -87
    6. 30 feet below the surface of the ocean
      ::海洋表面下30英尺处
    7. A rise of 15 feet
      ::升起15英尺
    8. 25 feet below sea level
      ::海平面下25英尺
    9. 80 feet above ground
      ::地面80英尺以上
    10. 100 feet deep
      ::100英尺深
    11. A profit of ten dollars
      ::10块钱的利润
    12. The hill had a grade of 15%
      ::山丘的等级是15%
    13. -987
    14. 65
    15. -1,298