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  • 代表不同情况的整数

    lesson content

    Michele lives in Salt Lake City, Utah. In school she learned that Salt Lake City is 4,300 feet above sea level. Michele is going on vacation with her family to Death Valley in California. Her mom told her that Death Valley has the lowest land in North America and a portion of it lies 282 feet below sea level. How could Michele represent the locations of Salt Lake City and Death Valley with respect to sea level using integers?
    ::米凯勒住在犹他州的盐湖城。她在学校里得知盐湖城海拔4,300英尺。Michelle正与家人一起度假前往加利福尼亚州的死谷。她妈妈告诉她,死谷是北美最低的土地,其中一部分位于海平面以下282英尺。Michelle如何用整数代表盐湖城和死亡谷的海平面位置?

    In this concept, you will learn how to write integers to represent real world situations.
    ::在这个概念中,你将学会如何写出整数来代表现实世界的情况。

    Writing Integers to Represent Real World Situations
    ::代表真实世界状况的书写集成器

    Integers  are a set of numbers that include the  positive   whole numbers  (1, 2, 3, 4, 5, ...), their opposites (-1, -2, -3, -4, -5, ...) and  zero . This  number line  shows the integers from -5 to 5.
    ::整数是一组数字,包括正整数(1, 2, 3, 4, 4, 5, ......)、正反数(1, 2, 3, 3, 4, 5, 5)和零。此数字线显示的是 - 5 到 5 的整数。

    lesson content

    You can use integers to help represent many real world situations, such as:
    ::您可以使用整数来帮助代表许多真实世界的情况,例如:

    • Increases and decreases in temperature.
      ::温度的增减。
    • Profits and losses of money
      ::利润和金钱损失
    • Locations above and below sea level.
      ::海平面上和海平面以下的位置。

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

    Suppose the temperature outside a ski lodge was  3 ∘ F  below  0 ∘ F . You want to express that temperature with an integer.
    ::假设滑雪小屋外的温度在0°F以下是3°F。您想用整数表示温度。

    To write this as an integer, first you should look for key words. The word “below” means the integer will be negative. Therefore, the temperature is  − 3 ∘ F  .
    ::要将此写成一个整数, 首先您应该查找关键字。 “ 下面” 表示整数为负值。 因此, 温度为 - 3 °F 。

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

    A fisherman is sitting 2 feet above the surface of a lake on a boat. The hook on his fishing pole is floating 6 feet below the lake’s surface. Use integers to represent the position of the fisherman and his hook.
    ::渔民坐在渔船上湖面上方2英尺处。 钓鱼杆上的钩子漂在湖面下方6英尺处。 使用整数代表渔夫及其钩子的位置。

    The surface of the lake can be represented by the integer 0.
    ::湖泊表面可以用整数 0 表示。

    The fisherman is sitting above the surface. The word “above” means the integer will be positive. The position of the fisherman is +2 or 2.
    ::渔民正坐在表面之上。“以上”一词表示整数为正数。渔民的位置是+2或2。

    The hook is floating below the surface. The word “below” means the integer will be negative. You can represent the position of the hook as -6.
    ::钩子在表面下浮动。“以下”一词表示整数为负。您可以将钩子的位置表示为-6。

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Michele, who was traveling to Death Valley.
    ::早些时候,你得到一个问题 关于Michelle, 谁旅行到死亡谷。

    Michele knows that Salt Lake City is 4,300 feet above sea level, while parts of Death Valley are 282 feet below sea level. Michele wanted to figure out how to represent these locations with respect to sea level using integers.
    ::Michele知道盐湖城比海平面高4,300英尺,而死亡谷的部分地区比海平面低282英尺。 Michele想了解如何用整数来代表海平面上的这些位置。

    First, consider Salt Lake City. It is above sea level so you will use a positive integer. With respect to sea level, Salt Lake City is +4,300 or 4,300.
    ::首先,考虑盐湖城。它是在海平面之上,所以你将使用正整数。关于海平面,盐湖城是+4,300或4,300。

    Next, consider Death Valley. It is below sea level so you will use a negative integer. With respect to sea level, Death Valley is -282.
    ::接下来,请考虑死亡谷。它位于海平面以下, 所以您将使用负整数。 关于海平面, 死亡谷是 - 282 。

    The answer is 4,300 for Salt Lake City and -282 for Death Valley.
    ::答案是盐湖城4300块 死亡谷282块

    Example 2
    ::例2

    Express the following situation using integers.
    ::使用整数表示下列情况。

    John gained 15 dollars, but then he lost 20 dollars.
    ::约翰赚了15美元 但后来他损失了20美元

    First, look for key words in  order  to determine if your integers will be positive or negative. To “gain” means to get more, so that will be a positive integer. “Lost” means to have less, so that will be a negative integer.
    ::首先,寻找关键字以决定您的整数是正数还是负数。 “ 增益” 意味着获取更多, 也就是正整数。 “ 损失” 意味着更少, 也就是负整数。

    Now, you can write your answer:
    ::现在,你可以写下你的答案:

    +15 represents the gain.
    ::+15 表示增益。

    -20 represents the loss.
    ::-20代表损失

    The answer is +15 gain and -20 loss.
    ::答案是+15收益和 -20损失。

    Example 3
    ::例3

    Express the following using an integer.
    ::使用整数表示如下。

    An increase of $200.00.
    ::增加200美元。

    First, look for key words. The word “increase” means to go up, so you will use a positive integer.
    ::首先,寻找关键词。“增加”一词意味着上升,所以您将使用正整数。

    The answer is +200 or 200.
    ::答案是+200或200。

    Example 4
    ::例4

    Express the following using an integer.
    ::使用整数表示如下。

    Down 10%.
    ::10%下调

    First, look for key words. The word “down” means you will need to use a negative integer.
    ::首先,查找关键词。“下方”一词表示您需要使用负整数。

    The answer is -10%.
    ::答案是 -10%。

    Example 5
    ::例5

    Express the following using an integer.
    ::使用整数表示如下。

    50 feet below sea level.
    ::海平面下50英尺

    First, look for key words. The word “below” means you will need to use a negative integer.
    ::首先,查找关键词。“以下”一词表示您需要使用负整数。

    The answer is -50.
    ::答案是 -50

    Review
    ::回顾

    Write each as an integer.
    ::以整数书写 。

    1. 10 degrees below zero
      ::零下10度
    2. 50 ∘ F  
      ::50 _______________________________________________________________________________________________________________________________________
    3. A loss of $20.00
      ::损失20美元
    4. 35 feet below the surface
      ::地表下35英尺处
    5. 120 feet below sea level
      ::海平面下120英尺
    6. An altitude of 15,000 feet
      ::高度为15,000英尺

    Use two integers and an operation to represent each situation.
    ::使用两个整数和一个操作来代表每个情况。

    1. A loss of 20 and a gain of 15.
      ::损失20块,收益15块
    2. A gain of 15, then a loss of twenty.
      ::得15分 然后损失20分
    3. A gain of 20 and a gain of 35.
      ::增益20 增益35
    4. A loss of 19 and another loss of 30.
      ::损失19项,损失30项。
    5. An altitude of 30,000 feet and another height of 15,000 feet
      ::高度为30 000英尺,另一高度为15 000英尺
    6. A loss of 15,000 feet and another loss of 12,000 feet.
      ::损失了15,000英尺,又损失了12,000英尺。
    7. A depth of 60 feet at the bottom of a lake and then rising up 15 feet above the bottom.
      ::湖底深60英尺 然后从底部上爬上15英尺
    8. A depth of 15 feet and then another descent of 20 feet below the surface of the water.
      ::深15英尺,然后又下沉20英尺 水面下。
    9. The hikers climbed to 1500 feet and then hiked another 1000 feet.
      ::徒步者爬到1500英尺,然后又爬了1 000英尺。