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  • 通过数轴计算整数的差

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    Jamie earned ten dollars cutting grass for his aunt, but he owes his brother twelve dollars from a movie that they went to last week. Does Jamie still owe his brother money if he gives him the whole ten dollars he made? If so, how much does he still owe? If not, how much does he have left over?
    ::杰米为姨妈赚了10美元割草,但他从他们上星期去看的电影中欠他弟弟12美元。 杰米还欠他弟弟10美元吗?如果是的话,他还欠他多少?如果不是,还剩下多少?

    In this concept, you will learn to use a  number line  to find the  difference  between integers.
    ::在此概念中,您将学会使用数字行来查找整数之间的差异。

    Subtracting Integers Using a Number Line
    ::使用数字行减法整数

    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。

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    Number lines are useful tools for visualizing simple arithmetic operations, especially addition and subtraction. Here is an example of using a number line for subtraction.
    ::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。这里用数字行来减法的例子。

    -6 – 2 = ____

    First, mark the location of the first integer.
    ::首先,标记第一个整数的位置。

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    Next, subtract two from this value. Subtraction means to move to the left. 
    ::接下来,从此值中减去两个。减法意味着向左移动。

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    The final mark is at -8.
    ::最后的标记是 -8

    The answer is -6 – 2 = -8.
    ::答案是 -6 -2 = -8。

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

    2 – 9 = ____

    First, make a mark at the initial integer.
    ::首先,在初始整数处打一个标记。

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    Next, subtract 9. Subtract means to move to the left.
    ::减去9. 减法表示向左移动。

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    The final mark is at -7.
    ::最后标记是 -7

    The answer is 2 – 9 = -7.
    ::答案是 2 - 9 = -7。

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Jamie.
    ::早些时候,你得到一个问题 杰米。

    He made ten dollars mowing his aunt's grass, but he owes his brother twelve. If he gives his brother his ten, does he still owe him money?
    ::他拔了十美元的姑姑的草,但他欠他弟弟十二块钱。如果他给他弟弟十块钱,他还欠他钱吗?

    First, write a number sentence to represent the problem.
    ::首先,写一个句子来代表问题。

    Jamie earned $10.00. He owes his brother $12.00.
    ::杰米赚了10.00美元 他欠他弟弟12.00美元

    10 - 12 = ____

    Next, draw the problem on a number line.
    ::下一步,请在数字行上标出问题。

    Start at positive ten and then subtract 12. This means you move twelve units toward the negative side of the number line.
    ::从正十点开始,再减去12点,这意味着将12个单位移到数字行的负面。

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    10 – 12 = -2

    Then, notice whether the answer is positive or negative.
    ::然后,注意回答是正面的还是负面的。

    In this case, it is negative, so the answer is yes, Jaime still owes more money. He owes his brother $2.00.
    ::在这种情况下,这是否定的,所以答案是肯定的,詹姆还欠更多的钱,他欠他弟弟两美元。

    Example 2
    ::例2

    Write a number sentence for this situation and then use a number line to solve it.
    ::在此情况下写一个数字句, 然后用数字行来解决这个问题 。

    Marcy lost 12 gems from a small jewel bag. Then she lost another four gems. How many did she lose?
    ::Marcy从一个小珠宝袋中丢失了12颗宝石 然后又失去了4颗宝石 她损失了多少?

    To write this expression, use  negative numbers  for losses.
    ::写此表达式时, 请使用负数表示损失 。

    First, write the original number of gems lost as an integer.
    ::首先,写下丢失的宝石的原始数量,作为整数。

    − 12

    Next write the additional number of gems lost as an integer.
    ::下一步写下损失的更多宝石的整数 。

    − 4

    Then, put them together in an expression.
    ::然后,把他们集合起来,

    − 12 − 4  

    Then, draw a number line. 
    ::然后绘制数字线。

    Finally, start at -12 and move 4 to the left.
    ::最后,从 -12开始,向左移动4

    You are now at -16.
    ::你现在在 -16。

    The answer is -16.
    ::答案是 -16

    Use a number line to evaluate the following problems.
    ::使用数字行来评估下列问题。

    Example 3
    ::例3

    4 – 10 = ____

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

    Next, start at 4 and move 10 to the left.
    ::下一步,从4开始,向左移动10

    You are now at -6.
    ::你现在在 -6。

    The answer is -6.
    ::答案是 -6

    Example 4
    ::例4

    -9 – 3 = ____

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

    Next, start at -9 and move 3 to the left.
    ::接下来,从 -9开始,往左移动3

    You are now at -12.
    ::你现在在 -12。

    The answer is -12.
    ::答案是 -12

    Example 5
    ::例5

    -12 – 4 = ____

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

    Next, start at -12 and move 4 to the left.
    ::接下来,从 -12开始,向左移动4

    You are now at -16.
    ::你现在在 -16。

    The answer is -16.

    ::答案是 -16

    Review
    ::回顾

    Find each difference by using a number line.
    ::使用数字行查找每个差异。

    1. − 5 − 2
    2. 7 − 12
    3. − 5 − 12
    4. − 25 − 42
    5. 5 − 32
    6. − 15 − 12
    7. 18 − 2
    8. 25 − 22
    9. − 45 − 32
    10. − 35 − 37
    11. 14 − 32
    12. 15 − 44
    13. − 41 − 12
    14. − 18 − 13
    15. 7 − 92

    Review (Answers) 
    ::回顾(答复)