1.9 将方形文字转换为变量表达式

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  将方形文字转换为变量表达式

  

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  Twins Larry and Terry want to buy their dad a great gift for his upcoming birthday. Both boys have been saving all of their dimes and quarters for several months. “I count 928 dimes,” Larry announces. “Great! I count 515 quarters,” Terry says. “But how do we go from knowing the number of coins to the amount of money?” How can Larry and Terry use a mathematical expression to figure out how much money they have in total?
  ::双胞胎拉里和泰瑞都想为他即将到来的生日给父亲买一份大礼。 两位男孩都已经存了几个月的硬币和季度。 “我数了928个硬币 , ” 拉里宣布 。 “ 好!我数了515个季度 , ” 泰瑞说 。 “ 但我们如何从知道硬币的数量到钱的数额? ”拉里和泰瑞如何用数学表达来弄清楚他们有多少钱呢?

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  In this concept, you will learn to change words into variable expressions. 
  ::在此概念中,您将学会将单词修改为变量表达式。

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  Translating Phrases into Expressions
  ::将词组转换为表达式

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  Many problems can be solved using mathematical methods. In order to do this, you must be able to translate words into mathematical expressions. More often than not, the words can be expressed as a variable expression which can be evaluated to solve a problem.
  ::使用数学方法可以解决许多问题。 要做到这一点, 您必须能够将单词转换为数学表达式。 通常情况下, 单词可以表现为可变表达式, 可以被评估来解决问题 。

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  You know the symbols $\begin{array}{r}+,-,\times ,÷\end{array}$ , represent the four most commonly used mathematical operations . The operation of multiplication can be represented by the symbol $\begin{array}{r}(\times )\end{array}$ or by $\begin{array}{r}\mathrm{\#}()\end{array}$ or $\begin{array}{r}()()\end{array}$ . Division can be represented by the symbol $\begin{array}{r}(÷)\end{array}$ or $\begin{array}{r}\frac{\mathrm{\#}}{\mathrm{\#}}\end{array}$ .
  ::您知道符号+ + -, x, , 代表四种最常用的数学操作。 乘法的操作可以用符号( x) 或 # () 或 ( 表示。 分区可以用符号 或 □ 表示 。

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  In addition to the words add, subtract, multiply and divide, there is a variety of other words that also correspond to these mathematical operations.
  ::除了添加、减、乘、除等字之外,还有与这些数学操作相对应的各种其他词。

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  Let’s start by creating a list of words that could translate into each of the mathematical operations.
  ::让我们首先建立一个可以转换为每个数学操作的单词列表 。

  Mathematical Operations

  Addition	Subtraction	Multiplication	Division
  Add	Subtract	Multiply	Divide
  Increased by	Decreased by	Product	Quotient
  Plus	Minus	Times	Shared
  Sum	Difference	Twice	Split between
  Total	Reduced by	Of	Divided by
  More	Less than

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  Let’s look at an example of translating words into a variable expression.
  ::让我们看看将文字转换成变数表达式的例子。

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  Remember that a variable expression has one or more variables (letters) that represent an unknown quantity.
  ::记住变量表达式有一个或多个变量(字母),表示数量未知。

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  Write the following as a mathematical expression with one variable:
  ::以一个变量的数学表达式写入以下文字:

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  A number increased by four.
  ::数目增加了4个。

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  First, name the variable. Let  ‘ $\begin{array}{r}n\end{array}$ ’ represent the number.
  ::首先,给变量命名。让 'n' 表示数字。

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  Next, represent the mathematical operation by its symbol. $\begin{array}{r}+\end{array}$
  ::下一步,通过符号代表数学操作。+

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  Then, insert the constant after the symbol. $\begin{array}{r}4\end{array}$  
  ::然后,在符号之后插入常数。

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  The variable expression is  $\begin{array}{r}n+4\end{array}$ .
  ::变量表达式为 n+4 。

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  Let’s look at one more example.
  ::让我们再举一个例子。

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  Write the following as a mathematical expression with two variables:
  ::写入以下带有两个变量的数学表达式:

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  Twice the length less three times the width.
  ::长度比宽度少两倍。

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  First, name the variables. Let ‘ $\begin{array}{r}l\end{array}$ ’ represent length and let  ‘ $\begin{array}{r}w\end{array}$ ’ represent width.
  ::首先,给变量命名。让“l”代表长度,让“w”代表宽度。

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  Next, represent any operations performed on the variables. $\begin{array}{r}2l\end{array}$ and  $\begin{array}{r}3w\end{array}$
  ::下一步,代表根据变量 2. 陆地 3w 进行的任何操作。

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  Then, represent the mathematical operation by its symbol. $\begin{array}{r}-\end{array}$
  ::然后,用符号代表数学操作。 -

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  The variable expression is $\begin{array}{r}2l-3w\end{array}$ .
  ::变量表达式是2l-3w。

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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 Larry and Terry and all their dimes and quarters.
  ::之前,你得到一个问题 关于拉里和泰瑞 以及他们所有的钱和住处。

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  Larry and Terry need to write a variable expression to show the value of ‘ $\begin{array}{r}d\end{array}$ ’ dimes and ‘ $\begin{array}{r}q\end{array}$ ’ quarters.
  ::Larry和Terry需要写一个变量表达式, 以显示`d ' 硬币和`q ' 方块的价值。

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  First, name the variables. Let ‘ $\begin{array}{r}d\end{array}$ ’ be the number of dimes. Let ‘ $\begin{array}{r}q\end{array}$ ’ be the number of quarters.
  ::首先,列出变量。让“d”字成为硬币数。让“q”字成为季度数。

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  Next, express the value of the coins as decimals. Ten cents is $\begin{array}{r}0.10\end{array}$ and twenty-five cents is  $\begin{array}{r}0.25\end{array}$ .
  ::接下来,以小数表示硬币的值。十分是0.10,二十五分是0.25。

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  Next, represent any operation performed on the variables. $\begin{array}{r}0.10d\end{array}$  and   $\begin{array}{r}0.25q\end{array}$    
  ::下一步,代表根据变量0.10d和0.25q进行的任何操作

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  Then, represent the mathematical operation by its symbol. $\begin{array}{r}+\end{array}$
  ::然后,通过符号代表数学操作。+

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  The variable expression is $\begin{array}{r}0.10d+0.25q\end{array}$
  ::变量表达式为0.10d+0.25q

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  How can Larry and Terry use this variable expression to figure out how much money they have?
  ::Larry和Terry怎么能用这个变数表达法 来弄清楚他们有多少钱?

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  They have counted the coins and they know they have 928 dimes and 515 quarters.
  ::他们数了硬币 他们知道他们有928块钱和515个季度

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  They have to evaluate the variable expression $\begin{array}{r}0.10d+0.25q\end{array}$  when $\begin{array}{r}d=928\end{array}$  and $\begin{array}{r}q=515\end{array}$ .
  ::他们必须评估变量表达式0.10d+0.25q whend=928和q=515。

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  First, substitute the values $\begin{array}{r}d=928\end{array}$  and  $\begin{array}{r}q=515\end{array}$ into the expression.
  ::首先,将值d=928和q=515替换为表达式。

  Next, multiply to clear the parenthesis:

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  $$\begin{array}{rl}0.10(928)& +0.25(515)\\ 92.8& +128.75\end{array}$$

   Then, add:
  ::0.10(928)+0.25(515)92.8+128.75 然后,加上:

  $$\begin{array}{r}92.8+128.75=221.55\end{array}$$

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  The answer is $\begin{array}{r}\$221.55\end{array}$
  ::答案是221.55美元

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  Larry and Terry can spend $\begin{array}{r}\$221.55\end{array}$ on their dad’s gift.
  ::Larry和Terry可以花221.55美元 支付他们爸爸的礼物

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  Example 2
  ::例2

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  Write the following as a mathematical expression with one variable:
  ::以一个变量的数学表达式写入以下文字:

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  One-half of Adam’s age six years ago.
  ::亚当六年前的一半年龄。

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  First, name the variable. Let ‘ $\begin{array}{r}x\end{array}$ ’ represent Adam’s age.
  ::首先,给变量命名。让“x”代表亚当的时代。

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  Next, represent any operation performed on the variable. $\begin{array}{r}-6\end{array}$
  ::下一步,代表变量 - 6 上进行的任何操作。

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  Then, represent the mathematical operation by its symbol. $\begin{array}{r}\frac{1}{2}()\end{array}$
  ::然后,通过符号12 代表数学操作

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  The variable expression is $\begin{array}{r}\frac{1}{2}(x-6)\end{array}$ .
  ::变量表达式是 12(x-6) 。

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  Example 3
  ::例3

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  Write the following as a mathematical expression with two variables:
  ::写入以下带有两个变量的数学表达式:

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  Four times the number of dimes less twice the number of quarters.
  ::硬币的四倍 减去季度的两倍

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  First, name the variables. Let ‘ $\begin{array}{r}d\end{array}$ ’ represent the number of dimes. Let ‘ $\begin{array}{r}q\end{array}$ ’ represent the number of quarters.
  ::首先,给变量命名。让我们“d”代表硬币数量。让我们“q”代表季度数量。

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  Next, represent any operation performed on the variables.
  ::下一步,代表根据变量进行的任何操作。

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  $\begin{array}{r}4d\end{array}$ and $\begin{array}{r}2q\end{array}$
  ::4and2q

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  Then represent the mathematical operation by its symbol. $\begin{array}{r}–\end{array}$
  ::然后通过其符号代表数学操作。 -

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  The answer is $\begin{array}{r}4d-2q\end{array}$ .
  ::答案是4d-2q。

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  Example 4
  ::例4

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  Write the following as a mathematical expression with two variables:
  ::写入以下带有两个变量的数学表达式:

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  The total tax from the first purchase at 5% and the second purchase at 9%.
  ::第一次购买总税为5%,第二次购买总税为9%。

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  First, name the variables. Let ‘ $\begin{array}{r}a\end{array}$ ’ represent the first purchase. Let ‘ $\begin{array}{r}b\end{array}$ ’ represent the second purchase.
  ::首先,给变量命名。让“a”代表第一次购买。让“b”代表第二次购买。

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  Next, represent any operation performed on the variables. $\begin{array}{r}+5\mathrm{\%}a\end{array}$ and   $\begin{array}{r}9\mathrm{\%}b\end{array}$ .  
  
  ::下一步, 表示根据变量. + 5%a 和 9%b 进行的任何操作。

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  Then, represent the mathematical operation by its symbol. $\begin{array}{r}+\end{array}$
  ::然后,通过符号代表数学操作。+

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  The answer is $\begin{array}{r}+5\mathrm{\%}a\end{array}$ and $\begin{array}{r}9\mathrm{\%}b\end{array}$ .
  ::答案是+5%a和9%b。

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  This answer is incorrect. You must multiply by the percent expressed as a decimal. The total is the sum of the taxes on each of the purchases.
  ::此答案不正确 。 您必须乘以小数点表示的百分比。 总计是每件购买的税总额 。

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  The answer is $\begin{array}{r}0.05a+0.09b\end{array}$ .
  ::答案是0.05a+0.09b。

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  Review
  ::回顾

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  Write a variable expression to represent each of the following:
  ::写入一个变量表达式, 以代表以下每个表达式 :

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  1. The sum of a number and twelve.
     ::数字和12的总和。
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  2. The difference between a number and eight.
     ::一个数字和八个数字的区别。
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  3. Three times a number
     ::一个数字三次
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  4. A number squared plus five
     ::数字平方加五
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  5. A number divided by two plus seven
     ::A除以二加七除以一除以二加七
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  6. Four times the quantity of a number plus six
     ::四倍于数字加六的数量
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  7. A number times two divided by four
     ::乘以乘以乘以乘以 乘以 乘以 乘以 乘以 乘以 乘以 乘以 乘以 乘以 乘以 乘以 乘以 乘以 乘以 乘以 乘以 乘以 乘以 乘以 乘以 乘以 乘以 乘以 乘以 乘以
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  8. A number times six plus the same number times two
     ::数乘以六乘以六 加上相同数乘以二
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  9. A number squared plus seven take a way four
     ::数字方+7乘以乘以四
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  10. A number divided by three plus twelve
      ::A除以3+12除以A除以A除以3+12
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  11. A number times five and another number times six
      ::数字乘以5 数字乘以6 数字乘以5 数字乘以6
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  12. Sixteen less than a number times negative four
      ::16个不到乘以乘以xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
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  13. A number times eight divided by two
      ::数字乘以八乘以八除以二除以二
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  14. A number divided by six and another number times negative five
      ::数字除以 6 乘以 6 乘以 数乘以 负 5
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  15. A number divided by four plus another number divided by sixteen
      ::数字A除以4除以4加上其他数字除以16

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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