Section outline

  • lesson content

    Robin learned how to build arrows and a bow with a 50 lb draw out of PVC pipe and other cheap materials at her summer camp. She made 3 for her best friends, and had orders for another 8. Then, she discovered that business was more complicated than she'd hoped. In the same day, her best friends' mothers all made them return the bows, and she got an  order  for 32 from a PE teacher. How many more will she need to make to fill the demand?
    ::Robin在夏令营学了如何用聚氯乙烯管和其他廉价材料的50磅抽取法来造箭和弓。她为最好的朋友做了3个,并订了8个。然后,她发现生意比她所希望的复杂得多。同一天,她最好的朋友的母亲都让他们把弓还回去,她从一名体育教师那里拿到了32个订单。她还需要做多少才能满足需求?

    In this concept, you will learn how to take the  difference  between two integers with different signs.
    ::在此概念中, 您将学习如何使用两个有不同符号的整数之间的差 。

    Subtracting Integers with Different Signs
    ::减少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。

    There are two possibilities when subtracting numbers with different signs. Either the negative number is first or the positive number is. If the negative number is first, then add the two integers and put a negative sign in front of the answer, like this:
    ::当用不同的符号来减去数字时,有两种可能性。要么负数是第一个数字,要么正数是第一个数字。如果负数是第一个数字,那么在答案前面加上两个整数,并给答案加上一个负号,例如:

    − 5 − 10 = − 15

    If the positive number is first, then you are subtracting a negative number. Whenever you subtract a negative, you can re-write it as an addition problem, and then solve, like this:
    ::如果正数先为正数,则会减去负数。当减去负数时,可以重写为添加问题,然后解决,像这样:

    5 − − 10 = 5 + 10 = 15

    Notice that if the first number was negative in a difference between numbers with different signs, the answer will be negative. If the first number was positive, the answer will be positive.
    ::请注意, 如果第一个数字是负数, 则有不同符号的数字之间的差, 答案将是负数。 如果第一个数字是正数, 答案将是正数 。

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Robin and her entrepreneurial struggles.
    ::之前,你得到一个问题 关于Robin和她的创业斗争。

    She started a bow-making business. She had 8 orders to fill when her first 3 were returned and she got an order for 32 more. How many does she need to make total?
    ::她开始做鞠躬生意。当她头3次返回时,她有8份订单要填,她又收到32份订单。她需要总共做多少份?

    To solve this problem, first she assigns signs to each quantity and writes them as integers. 
    ::为了解决这个问题,她首先为每个数量指定符号,并将其写成整数。

    The ones that are returned, she doesn't have to make, so she calls them positive. She has +3 bows. The ones she still has to make, she assigns a negative. Those are the 8 she already owes: -8.
    ::被送回的人,她不必做,所以她称他们为肯定的。她有+3的弓。她仍然要做的是负的。这是她已经欠了的8个。 -8个。

    Next, she figures out what she'll have left once these orders are filled by adding these two numbers together:
    ::接下来,她通过把这两个数字加在一起 找出这些订单填满后 她会留下什么

      

    3 − 8 = − 5

    In filling the school order, she will already need to make 5. 
    ::在填写学校订单时,她已经需要做5个。

    Then, she sets up a new math problem as a difference of two integers with different signs:
    ::然后,她设置了一个新的数学问题, 即两个整数和不同符号的差别:

    − 5 − 32 =

    To solve this, she adds the two numbers together. 
    ::为了解决这个问题,她将两个数字加在一起。

    5 + 32 = 37

    Then, she checks the sign of the first number. It was negative. She decides, with a sigh, that the answer must be negative too.
    ::然后,她检查了第一个数字的符号。这是否定的。她以叹息决定答案必须是否定的。

    The answer is she must make 37 bows in order to stay in business.
    ::答案是她必须做37次鞠躬才能继续做生意。

    Example 2
    ::例2

    Write the following scenario as a mathematical expression and solve.
    ::以数学表达式和解析方式写入以下方案 。

    Here are a few to practice with. Choose a method and find the difference of each pair of integers. Javier owes Louisa $20 for dinner. Then she gives him $10 for the movies. How much does Javier owe Louisa total?
    ::选择一个方法, 找出每对整数的差别。 Javier欠Louisa 20美元用于晚餐。 然后她给了他10美元用于电影。 Javier一共欠了Louisa多少?

    First, write the expression.
    ::首先,写下表达方式。

    Javier starts out owing 20 which is -20. Then he subtracts 10 from that.
    ::哈维尔从20岁开始欠20岁,也就是20岁。然后他从中减去10岁。

    − 20 − 10
    Next, add the two together.
    20 + 10 = 30
    Then, check the sign of the first number.

    Since it was negative, put a negative in front of the answer. The answer is -30. This means that Javier owes Louisa $30 total.
    ::答案是 -30,这意味着Javier欠Louisa30美元

    Example 3
    ::例3

    Find the difference.
    ::找出差别

    -5 – 7 = ____

    First, add the two numbers together.
    ::首先,将两个数字加在一起。

    5+7=12

    Next, check the sign of the first number.
    ::下一位,检查第一个号码的标志

    In this case, it is negative, so the answer is negative.
    ::在这种情况下,答案是否定的,因此答案是否定的。

    The answer is -12.
    ::答案是 -12

    Example 4
    ::例4

    Find the difference.
    ::找出差别

    2 – -8 = ____

    First, re-write the double negative as a positive.
    ::首先,将双负值重写为正值。

    2+8

    Next, add the two together.
    ::接下来,将两者加在一起。

    2+8=10

    Then, check the sign of the first number in the original problem.
    ::然后,检查第一个号码的标志 在最初的问题。

    In this case, it is positive so the answer is positive.
    ::在这种情况下,答案是肯定的,因此答案是肯定的。

    The answer is 10.
    ::答案是10个

    Example 5
    ::例5

    Find the difference.
    ::找出差别

    -13 – 5 = ____

    First, add the two integers together.
    ::首先,将两个整数加在一起。

    13+5=18

    Next, check the sign of the first integer in the original problem.
    ::下一步,请检查原始问题中第一个整数的符号 。

    In this case, it is negative so the answer is negative.
    ::在这种情况下,答案是否定的,因此答案是否定的。

    The answer is -18.

    ::答案是 -18

    Review
    ::回顾

    Find the differences of the following integer pairs.
    ::查找以下整对的差别。

    1. -2 – 4 = ____
    2. -8 – 9 = ____
    3. -6 – 7 = ____
    4. -11 – 12 = ____
    5. -13 – 22 = ____
    6. -89 – 11 = ____
    7. 2 – 7 = ____
    8. 4 – 9 = ____
    9. 5 – 8 = ____
    10. 13 – 20 = ____
    11. 12 – 23 = ____
    12. 25 – 30 = ____
    13. 45 – 90 = ____
    14. 34 – 67 = ____
    15. -2 – -3 = ____
    16. -8 – -3 = ____
    17. -9 – -7 = ____
    18. -5 – -10 = ____
    19. -9 – -12 = ____
    20. -10 – -10 = ____
    21. -14 – -15 = ____
    22. 5 – -8 = ____
    23. 6 – -7 = ____
    24. 10 – -9 = ____
    25. 11 – -7 = ____
    26. 18 – -9 = ____
    27. 22 – -5 = ____
    28. 34 – -3 = ____
    29. 35 – -35 = ____
    30. 45 – -10 = ____

    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