2.3 添加整数和其他合理数字-interactive

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  添加整数和其他有理数字

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  Upvote, Downvote
  ::原投票人、下投票人

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  There are several YouTube and internet celebrities out there today. Their businesses thrive on the upvotes and downvotes on their countless videos. Their net votes on a video are calculated by adding the upvotes and downvotes as positive and negative integers . The more the upvotes, the more likely the video will be watched.  
  ::今天有好几个YouTube和互联网名人在那里。他们的企业在无数的视频上以高音和低音为生。他们在视频上的净票是用将高音和低音作为正和负整数来计算的。 高音和低音越多,视频就越有可能被观看。

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  A particular YouTuber, DIVbyZ, has a video with 24 upvotes and 31 downvotes. What is her net vote? Use the interactive to click on the thumbs up and thumbs down to determine your answer.
  ::一个特殊的YouTuber, DIVbyZ, 拥有一个有24个高音和31个低音的视频。 她的净投票率是多少? 使用互动来点击拇指上和低调的拇指上方和下方的拇指来确定您的答案 。

   

   

   

   

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  Discussion Question
  ::讨论问题

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  Think about the three cases of : when the addends (the two numbers that are being added) are both positive, both negative, or one of each. H ow would you approach an addition problem differently in each of these cases and what sign the answer has?
  ::想想这三种情况:当附加数(正在添加的两个数字)是正数(负数 ) , 或者每个数字都是正数(负数 ) 。 你如何在这些情况下以不同的方式处理一个新增问题? 答案的标志是什么?

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  As you can see from this interactive, there are three different outcomes from adding a positive and negative integer together – the answer could be positive, negative, or zero . See the table below.
  ::从这段互动中可以看到,将正整数和负整数加在一起有三种不同的结果 — — 答案可以是正、负或零。 见下表。

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  $$\begin{align*}\text{Given }p\text{ is a positive integer and }q\text{ is a negative integer:} \qquad \qquad \qquad \quad ~ \\ \begin{array}{|c|c|c c|} \hline & \text{Outcome} & \text{Example}\\ \hline \text{if } |p|>|q| & \text{then } p+q \text{ is positive} ~ & 10+(\text{-}8)=2 & ~~ \text{since }|10|>|\text{-}8|\\ \hline \text{if } |p|<|q| & \text{then } p+q \text{ is negative} & 5+(\text{-}9)=\text{-}4 & \text{since }|5|<|\text{-}9|\\ \hline \text{if } |p|=|q| & \text{then } p+q \text{ is zero } \quad ~ & 6+(\text{-}6)=0 & \text{since }|6|=|\text{-}6|\\ \hline \end{array}\end{align*}$$
  ::给定 p 是正整数, q 是负整数 : 结果Exampleif = = 10+( 8)= 2, 因为 = 10+( 8) = = 10+( 8) +( 8) = 2, 因为 p+q = 负5+( 9)= 4 因为 = 5+( 9) = = 5+( 9) = * * Q* * Q* q = p+q 是 0 6+( 6)= 0 因为 @ 6+-6 = = 0

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  To determine what the sign of the sum of a positive and negative number is, compare the absolute values of the integers being added.  
  ::为了确定正数和负数之和的符号,比较所加整数的绝对值。

   

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  Temperature
  ::温度

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  The rules for adding rational numbers  are the same as for adding integers.
  ::增加合理数字的规则与增加整数的规则相同。

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  During the day, the temperature raises 11.2 degrees. At night, it cools off and the temperature decreases by 8.3 degrees. How much does the temperature change?
  ::白天,温度会升高11.2度。在晚上,温度会冷却,温度会下降8.3度。温度会有多大变化?

   

   

   

   

   

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  Adding Decimals
  ::添加十进数

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  You may remember adding decimals and fractions from last year. Adding decimals is not that much different than adding whole numbers , just make sure you line up the decimal point . As with integers, which ever rational number has the greater absolute value, the answer will have that sign. 
  ::您可能记得添加去年的十进制和分数。 添加十进制与添加整数没有多大不同, 只需确定您在小数点上行。 与总和一样, 理性数字具有更大的绝对值, 答案将具有这个符号 。

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  You may use  the interactive below to brush up on adding decimals :
  ::您可以使用下面的交互程序来刷新添加小数位数 :

   

   

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  When adding  fractions, there are two approaches:
  ::在添加分数时,有两种办法:

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  First, you can put each mixed number into an improper fraction , then find the common denominator and add the numerators.
  ::首先,你可以将每个混合数分解成一个不适当的部分, 然后找到共同的分母, 并添加分子。

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  Or, you can separate the whole number from the fraction and add each part separately. When you do it this way, you will still need to find the common denominator for the fraction part, but it may end up being simpler arithmetic.
  ::或者,您可以将整数从分数中分离出来,然后将每个部分分别添加。当您这样做时,您仍然需要为分数部分找到共同的分母,但结果可能是简单的算术。

   

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  Stock Market
  ::股票市场

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  A particular stock started at $11.15 at the beginning of the day. After 3 hours, it was up $0.67 and at the end of the day it fell $2.25.
  ::一天开始时,特别库存开始为11.15美元,3小时后增加了0.67美元,在一天结束时跌了2.25美元。

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  What was the value of the stock at the end of the day? Use the number line interactive below to help you find the answer. 
  ::日终股票值是多少? 使用下面交互式的数字线来帮助您找到答案 。

   

   

   

   

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  Discussion Question
  ::讨论问题

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  How can knowledge of $\begin{align*}5+(−7)\end{align*}$   help you solve $\begin{align*}\frac{5}{9}+(−\frac{7}{9})?\end{align*}$
  ::5+(-7)的知识如何帮助你解决59+(--79)问题?

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     Summary
  ::摘要

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  • Adding decimals, fractions, and all rational numbers is the same process as adding integers.
    ::添加小数、分数和所有合理数字与添加整数相同。
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  • If the addends are different signs, the addend with larger absolute value will 'give' it's sign to the answer. Use the table in this lesson to help.
    ::如果添加端是不同的符号, 具有较大绝对值的添加端会“ 给” 给答案的符号。 使用此课中的表格帮助 。