12.1加减法短语作为表达式

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• 选择节加减法短语作为表达式

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  加减法短语作为表达式

  

  [Figure 1]

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  Coach Taylor is driving the middle school track team to a district competition. The 26 team members suggest that the coach allow the school’s pep squad to travel with them to the competition to cheer them on. Coach Taylor likes the idea and has to choose between two buses to transport the track team and the 27 students on the pep squad. One bus has a 58-passenger capacity and the other bus’ capacity is 42. How can Coach Taylor use this information to determine how many seats will be left on each bus for the pep squad?
  ::泰勒教练正在驾驶中学生赛车队去参加地区竞赛。 26名队员建议教练允许学校的足球队和他们一起去参加比赛,以使他们欢呼。 泰勒教练喜欢这个想法,必须在两辆公共汽车之间做出选择,运送赛车队和Pep队的27名学生。 一辆公共汽车拥有58名乘客的能力,另一辆汽车的车容量为42人。 泰勒教练如何利用这些信息确定每辆汽车上有多少座位留给Pep队?

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  In this concept, you will learn how to write  addition  and  subtraction  phrases as single  variable  expressions.
  ::在此概念中,您将学习如何将添加和减法短语作为单一变量表达式写入。

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  Writing Addition and Subtraction Phrases as Expressions
  ::以表达式形式写入添加和减法词句

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  A  variable  is a letter used to represent an unknown quality. An  expression  is a combination of variables, numbers and  operations  without an equal sign. Because expressions do not contain equal signs, they are evaluated instead of solved. When an expression contains a variable representing an unknown number, it is referred to as a  variable expression .
  ::变量是用于表示未知质量的字母。表达式是变量、数字和操作的组合,没有等号。由于表达式不包含等号,所以要对它们进行评审而不是解析。当表达式包含一个代表未知数字的变量时,它被称为变量表达式。

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  For example,  $\begin{array}{r}3x+1\end{array}$  is a  variable expression .
  ::例如, 3 x + 1 是一个变量表达式。

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  Variables in an expression can have different values. The variable in the expression,  $\begin{array}{r}3x+1\end{array}$ , is  $\begin{array}{r}x\end{array}$ . This variable expression can be evaluated for different values of  $\begin{array}{r}x\end{array}$ .
  ::表达式中的变量可能有不同的值。表达式中的变量 3 x + 1, 是 x。这个变量表达式可以对 x 的不同值进行评估。

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  Evaluate  the following expression.
  ::评估以下表述。

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  $\begin{array}{r}3x+1\end{array}$  when  $\begin{array}{r}x=4\end{array}$
  ::3 x = 4时 3 x + 1

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  First,  substitute  “4” for the variable “ $\begin{array}{r}x\end{array}$ ”.
  ::首先,将变数“x”改为“4”。

  $$\begin{array}{r}3(4)+1\end{array}$$

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  Next, follow the   and multiply 3 and 4.
  ::下一个,跟着乘以3和4

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  $\begin{array}{r}3(4)+1\end{array}$  can now be expressed as  $\begin{array}{r}12+1\end{array}$
  ::3 (4)+1现在可以表示为12+1

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  Then, add 12 and 1.
  ::然后,加上12和1。

  13

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  The answer is 13.
  ::答案是13岁

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  Here, the expression was given to you. There will be times when you may have to write an expression from a phrase or situation.
  ::这里的表达方式是给你的。有时你可能不得不从一个短语或情况中写出一个表达方式。

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  Expressions can be written to represent different situations. When writing expressions, pay attention to key words which identify different operations, unknown variables and numbers. After identifying key words, you can write an expression to symbolize the situation as a mathematical expression.
  ::表达式可以写来代表不同的情况。在写入表达式时,请注意识别不同操作、未知变量和数字的关键字。在指定关键字后,您可以写一个表达式,以表示该状态为数学表达式。

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  Here are some key words that indicate addition and subtraction.
  ::下面是一些关键字,表示增减。

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  Addition:
  ::加:

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  •  Sum
    ::总总和
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  •  Plus
    ::加加
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  • Altogether
    ::合计合计
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  •  And
    ::还有

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  Subtraction:
  ::减法 :

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  • Difference
    ::差异
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  • Less than
    ::小于
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  • Take away
    ::带走

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  Find the key words in this phrase then write the phrase as an expression.
  ::在此短语中查找关键字, 然后将该短语写成表达式 。

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  Nine less than an unknown quantity
  ::少于未知数量的九

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  First, look for the numbers in the phrase. The only number in the phrase is nine (9).
  ::首先,寻找该短语中的数字。该短语中唯一的数字是9(9)。

  9

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  Next, identify the key words in this phrase.
  ::接下来,指出这一短语中的关键词。

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  “Less than” indicates subtraction.
  ::“减”是指减去。

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  Then, there are the words “unknown quantity” which can be represented by a variable. Let‘s use the variable “ $\begin{array}{r}y\end{array}$ ”.
  ::然后是“未知数量”一词,可以用变量来表示。让我们使用变量“y”来表示。

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  $\begin{array}{r}y\end{array}$
  ::y y , y

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  Now you can rewrite the phrase.
  ::现在您可以重写该词句 。

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  9 less than  $\begin{array}{r}y\end{array}$
  ::9小于y

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  Since 9 is subtracted from  $\begin{array}{r}y\end{array}$ , the expression is written as  $\begin{array}{r}y-9\end{array}$ .
  ::由于从 y 中减去 9, 表达式为y - 9。

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  The answer is  $\begin{array}{r}y-9\end{array}$ .
  ::答案是y -9

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about the track team’s district meet.
  ::先前你曾因赛马队区会遇到问题,

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  Coach Taylor will be driving 26 members of the track team to a district meet. He has to determine which bus will have enough seats left to take the 27 students on the pep squad - the 42-passenger bus or the larger 58-passenger bus.
  ::Taylor教练将驾驶26名赛马队成员到区会。 他必须决定哪些巴士有足够的座位可以载27名学生到Pep队,即42名乘客的巴士或58名乘客的大型公共汽车。

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  How can you write an expression to expression to represent this situation?
  ::您如何在表达式中写出表达式来代表这种情况 ?

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  First, identify the key numbers.
  ::首先,确定关键数字。

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  There are 26 members on the track team and 27 students on the pep squad.
  ::赛马队有26名成员,小便队有27名学生。

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  Next, identify the key words and operations.
  ::接下来,指出关键词和行动。

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  “left” indicates “subtraction”
  ::“左”表示“减”

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  Then, identify the unknown number. The unknown is which bus the team will use, so let the total number of seats on the bus Coach Taylor chooses be represented by the variable “ $\begin{array}{r}x\end{array}$ ”.
  ::然后,确定未知的号码。未知的是该队将使用哪辆公共汽车,所以泰勒教练选择的公共汽车座席总数用变数“x”表示。

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  $\begin{array}{r}x\end{array}$
  ::x x

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  Now, write the expression.
  ::现在,写这个表达式。

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  $\begin{array}{r}x-26\end{array}$
  ::x - 26岁

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  You can evaluate the expression if the team uses the 58-passenger bus by substituting 58 for “ $\begin{array}{r}x\end{array}$ ” in the expression.
  ::如果团队使用58客车总线,用58换成“x”,您可以对表达式进行评价。

  $$\begin{array}{r}\begin{array}{rcl}& & x-26\\ & & 58-26\\ & & 32\end{array}\end{array}$$

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  There will be 32 seats left for the pep squad.
  ::将剩下32个座位 给pep队。

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  You can also evaluate the expression if the team uses the 42-passenger bus by substituting 42 for “ $\begin{array}{r}x\end{array}$ ” in the expression.
  ::如果团队使用42客车总线,用“x”取代“x”取代42,您也可以评价该表达式。

  $$\begin{array}{r}\begin{array}{rcl}& & x-26\\ & & 42-26\\ & & 16\end{array}\end{array}$$

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  There will be 16 seats left for the pep squad.
  ::将剩下16个座位 给Pep队。

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  The answer is Coach Taylor should choose the 58-passenger bus. It will have 32 seats left to take the 27 members of the pep squad.
  ::答案是泰勒教练应该选择58名乘客的公共汽车,它还有32个席位可以坐27名便便队队员。

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  Example 2
  ::例2

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  Write the phrase as an expression: an unknown number and four.
  ::将这一短语写成表达式:一个未知的数字和四个。

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  First, identify the number in the phrase.
  ::首先,在短语中标明数字。

  4

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  Next, identify the key words and operations.
  ::接下来,指出关键词和行动。

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  “and” means “add”
  ::“和”系指“添加”

  $\begin{array}{r}+\end{array}$

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  Then, substitute a variable for the “unknown number”. Let  $\begin{array}{r}x\end{array}$  represent the unknown number. 
  ::然后,用一个变量代替“未知数字”。 Let x 表示未知数字。

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  $\begin{array}{r}x\end{array}$
  ::x x

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  The answer is  $\begin{array}{r}x+4\end{array}$ .
  ::答案是 x + 4 。

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  Example 3
  ::例3

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  Write the phrase as an expression: the difference between ten and an unknown number.
  ::将这一短语写成表达式:10和未知数字的区别。

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  First, identify the number in the phrase.
  ::首先,在短语中标明数字。

  10

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  Next, identify the key words and  operation .
  ::接下来,确定关键词和操作。

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  “difference” means “subtraction”
  ::“差异”是指“减法”

  $\begin{array}{r}-\end{array}$

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  Then, substitute a variable for the “unknown number”. Let  $\begin{array}{r}x\end{array}$  represent the unknown number.
  ::然后,用一个变量代替“未知数字”。 Let x 表示未知数字。

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  $\begin{array}{r}x\end{array}$
  ::x x

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  As the phrase does not identify whether 10 is being subtracted from the unknown number or the unknown number is subtracted from ten, there are two possible expressions for this phrase.
  ::由于该短语没有说明从未知数字中减去10个,还是从10个数字中减去了10个,因此该短语有两种可能的表达方式。

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  $\begin{array}{r}10-x\end{array}$  or  $\begin{array}{r}x-10\end{array}$
  ::10 - x 或 x - 10

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  The answer is  $\begin{array}{r}10-x\end{array}$  or  $\begin{array}{r}x-10\end{array}$ .
  ::答案是 10 - x 或 x - 10 。

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  Example 4
  ::例4

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  Write the phrase as an expression: seven less than a number.
  ::将这一短语写成表达式:7比数字少7。

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  First, identify the number in the phrase.
  ::首先,在短语中标明数字。

  7

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  Next, identify the key words and operation.
  ::接下来,确定关键词和操作。

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  “less than” means “subtraction”
  ::“低于”系指“减法”

  $\begin{array}{r}-\end{array}$  

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  Then, substitute a variable for the “unknown number”. Let  $\begin{array}{r}x\end{array}$  represent the unknown number.
  ::然后,用一个变量代替“未知数字”。 Let x 表示未知数字。

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  $\begin{array}{r}x\end{array}$
  ::x x

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  In this example, the phrase specifically states that 7 is being subtracted from the unknown number.
  ::在这个例子中,这一短语具体指出,从未知数字中减去7个。

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  The answer is  $\begin{array}{r}x-7\end{array}$ .
  ::答案是 x - 7 。

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  Example 5
  ::例5

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  Write the phrase as an expression: seven less than the quantity of six and an unknown number.
  ::将这一短语写成表达式:比6个数量少7个,数字不详。

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  This phrase has both addition and subtraction in it. The key here is the word “quantity”. This lets you know that there is going to be a set of  " data-term="Parentheses" role="term" tabindex="0"> parentheses  in the expression.
  ::此短语中既增加又减去。 关键是“ 数量” 一词, 使您知道在表达式中将会有一组括号 。

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  Begin by writing the part of the phrase inside the parentheses first.
  ::首先在括号内写出该短语的部分。

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  The quantity is six and an unknown number.
  ::数量是6个 数字未知

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  First, identify the number in the parentheses.
  ::首先,在括号中标明数字。

  6

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  Next, identify the key words and operation inside the parentheses.
  ::接下来,在括号内标明关键字和操作。

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  “and” means “add”
  ::“和”系指“添加”

  $\begin{array}{r}+\end{array}$

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  Then, substitute a variable for the unknown number. Let  $\begin{array}{r}x\end{array}$  represent the unknown number.
  ::然后,将变量替换为未知数字。让 x 代表未知数字。

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  $\begin{array}{r}x\end{array}$
  ::x x

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  Now, rewrite the original phrase with the expression inside the parentheses and follow the same steps.
  ::现在,用括号内的表达式重写原短语,并遵循同样的步骤。

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  Seven less than  $\begin{array}{r}(6+x)\end{array}$
  ::七小于( 6+xx)

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  First, identify the numbers in the phrase.
  ::首先,在短语中标明数字。

  7

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  Next, identify the key words and operation.
  ::接下来,确定关键词和操作。

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  “less than” means “subtract”
  ::“低于”系指“减”

  $\begin{array}{r}-\end{array}$

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  Then, identify the quantity that 7 is being subtracted from. 
  ::然后,标明从中减去的 7 个数量 。

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  $\begin{array}{r}(6+x)\end{array}$
  :6+x) (6+x))

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  The answer is  $\begin{array}{r}(6+x)-7\end{array}$ .
  
  ::答案是(6+x)-7。

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  Review
  ::回顾

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  Write the following addition and subtraction phrases as single-variable expressions. Use the variable x for unknown values.
  ::将以下添加和减号作为单变量表达式写入。对未知值使用变量 x 。

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  1. The sum of six and an unknown number
     ::6和6之和,数字不详
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  2. A number and seven
     ::A号和7号
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  3. Four less than a number
     ::四个小于一个数字
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  4. The sum of a number and fourteen
     ::数字和14之和
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  5. The difference between twenty and an unknown number
     ::20和未知数字之差
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  6. Twenty-five take away a number
     ::25号拿走一个号码
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  7. Ten less than a number
     ::十个小于一个数字
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  8. Thirty-seven plus an unknown quantity
     ::37加数量未知
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  9. The sum of nine and an unknown number
     ::九和九之和,数目不详
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  10. An unknown number and eight
      ::一个未知号码和八个号码
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  11. An unknown number plus the quantity six plus seven.
      ::一个未知的数字加上数量6+7
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  12. The sum of fifteen and an unknown number
      ::十五和一数字不详的十五之和
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  13. Thirty less than the quantity of twenty - five and an unknown number.
      ::数量比二五少三十个 数目不详
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  14. Twelve less than an unknown number
      ::十二个不到未知数字
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  15. Sixteen and seven plus an unknown number
      ::十六和七加一个未知号码

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  Review (Answers) 
  ::回顾(答复)

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  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 。

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  Resources
  ::资源