4.4数与和之积的表达式

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  数与和之积的表达式

  

  [Figure 1]

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  Terry is going to a friend’s house. On his way there, his friends ask him to pick up some food at the burger place nearby. They  order  4 hamburger meals and Terry just wants 2 hamburgers. A hamburger costs $2.10 and the meal costs $3.25 cents extra. What is the total cost of the meal?
  ::Terry去朋友家了。在路上,他的朋友叫他去附近的汉堡店取些食物。他们订了4个汉堡饭,Terry只想要2个汉堡。汉堡要2.10美元,餐费加3.25美分。总餐费是多少?

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  In this concept, you will learn how to write a  numerical expression  for the product of a number and a  sum .
  ::在此概念中,您将学习如何为数字和总和的产物写出数字表达式。

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  Numerical Expressions
  ::数字表达式

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  A  numerical expression  is a statement that has more than one operation in it. A numerical expression should illustrate mathematical information in a correct way. This lesson will focus on a numerical expression that involves the product of a number and a sum.
  ::数字表达式是指一个在其中有一个以上操作的语句。数字表达式应该以正确的方式说明数学信息。此课将侧重于一个数字表达式,该表达式涉及数字和总和的产物。

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  Let’s break down the phrase “the product of a number and a sum” to understand the meaning of this expression.
  ::让我们把 " 数字和总和的产物 " 分开来理解这个表达方式的含义。

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  The word  product  means the results of multiplying two or more numbers.
  ::单词产品意指乘以两个或两个以上数字的结果。

  $$\begin{array}{r}a\times b\end{array}$$

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  The word  sum  means the results of adding two or more numbers.
  ::字和意指增加两个或两个以上数字的结果。

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

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  The product of a number and a sum is a combination of these operations. The first multiplicand is a number,  $\begin{array}{r}a\end{array}$ . The second multiplicand,  $\begin{array}{r}b\end{array}$ , will be the entire sum of two or more number. Substitute  $\begin{array}{r}b\end{array}$  with the sum of two numbers  $\begin{array}{r}c+d\end{array}$ . Use parentheses to indicate grouping and also multiplication.
  ::数字和总和的产物是这些操作的组合。第一个倍数是数字,a。第二个倍数,b,将是两个或两个以上数字的整和。以两个数字c+d之和取代b。用括号表示组合和乘法。

  $$\begin{array}{r}a(c+d)\end{array}$$

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  Here is an example of an expression using numbers.
  ::下面是使用数字的表达式的例子 。

  $$\begin{array}{r}\text{the product of 5 and the sum of 4 plus 3}\end{array}$$

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  Identify the first multiplicand. It is 5. Then, identify the second multiplicand. The second will be the sum of 4 plus 3. Write is as a numerical expression.
  ::识别第一个倍数。 它是 5 。 然后, 识别第二个倍数。 第二个是 4+ 3 的和 。 写作是一个数字表达式 。

  $$\begin{array}{r}5(4+3)\end{array}$$

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  This is the numerical expression for the information.
  ::这是信息的数字表达式。

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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 Terry at the hamburger shop.
  ::早些时候,你在汉堡店 遇到Terry的问题

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  Terry is picking up 2 hamburgers that cost $2.10 each and 4 hamburger meals that cost $3.25 extra  per  meal. Multiply and add to find the total cost of the meal.
  ::泰瑞正在收集2个汉堡包,每个汉堡包2.10美元,4个汉堡餐,每餐额外3.25美元。 乘以并加以总餐成本。

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  First, think of an expression to find the total cost of the meal. You need to find the sum of the hamburgers and the hamburger meals.
  ::首先,想出一种表达方式来找出这顿饭的总成本。你需要找到汉堡和汉堡饭的总和。

  $$\begin{array}{r}\text{total cost of hamburgers}+\text{total cost of hamburger meals}\end{array}$$

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  Let’s work on the first part, the total cost of the hamburger. The total cost of the hamburgers will be the product of the number of hamburgers times the cost of the burger.
  ::让我们首先研究汉堡总成本。 汉堡总成本将是汉堡数量乘以汉堡成本的产物。

  $$\begin{array}{r}2(\mathrm{\$}2.10)+\text{total cost of the hamburger meals}\end{array}$$

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  Then, write an expression to find the second part of the expression. The total cost of the meals is the product of the number of meals times the sum of the hamburger plus the added cost.
  ::然后写一个表达式,寻找表达式的第二部分。总膳食成本是膳食数量乘以汉堡总和加上附加成本的产物。

  $$\begin{array}{r}2(\mathrm{\$}2.10)+4(\mathrm{\$}2.10+\mathrm{\$}3.25)\end{array}$$

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  Next, find the total cost of the order. Order of operations tells you to do the addition in the parentheses first; find each product; and then find the sum.
  ::接下来,请查找订单的总成本。操作顺序要求您首先在括号中添加内容,然后找到每种产品,然后找到总和。

  $$\begin{array}{r}\begin{array}{rcl}& & 2(\mathrm{\$}2.10)+4(\mathrm{\$}5.35)\\ & & \mathrm{\$}4.20+\mathrm{\$}21.40\\ & & \mathrm{\$}25.60\end{array}\end{array}$$

   

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  The total cost of the order will be $25.60.
  ::订单的总费用为25.60美元。

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  Example 2
  ::例2

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  Write a numerical expression for the product of 2 times the sum of 3 and 4.
  ::将产品总和为3和4的2倍的数值表达式写入数字表达式。

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  First, identify the first multiplicand. It is 2.
  ::首先,确定第一个倍数。它是 2 。

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  Then identify the second multiplicand. It is the sum of 3 and 4 or 3 + 4.
  ::然后标明第二个倍数。它是3和4或3+4的总和。

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  Next, write the product as a numerical expression. Use the parentheses to group the sum.
  ::下一步,将产品写成数字表达式。使用括号对总和进行分组。

  $$\begin{array}{r}2(3+4)\end{array}$$

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  Example 3
  ::例3

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  Write the expression as a numerical expression.
  ::将表达式写成数字表达式。

  $$\begin{array}{r}\text{the product of three and the sum of four plus five}\end{array}$$

   

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  First, identify the first multiplicand. It is 3.
  ::首先,确定第一个倍数。它是3。

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  Then identify the second multiplicand. It is the sum of 4 + 5.
  ::然后标明第二个倍数。它是4+5的总和。

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  Next, write the product as a numerical expression. Use the parentheses to group the sum.
  ::下一步,将产品写成数字表达式。使用括号对总和进行分组。

  $$\begin{array}{r}3(4+5)\end{array}$$

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  Example 4
  ::例4

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  Write the expression as a numerical expression.
  ::将表达式写成数字表达式。

  $$\begin{array}{r}\text{the product of four and the sum of six plus seven}\end{array}$$

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  First, identify the first multiplicand. It is 4.
  ::首先,确定第一个倍数。它是4。

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  Then identify the second multiplicand. It is the sum of 6 + 7.
  ::然后标明第二个倍数。它是6+7的总和。

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  Next, write the product as a numerical expression. Use the parentheses to group the sum.
  ::下一步,将产品写成数字表达式。使用括号对总和进行分组。

  $$\begin{array}{r}4(6+7)\end{array}$$

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  Example 5
  ::例5

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  Write the expression as a numerical expression.
  ::将表达式写成数字表达式。

  $$\begin{array}{r}\text{the product of nine and the sum of one plus eight}\end{array}$$

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  First, identify the first multiplicand. It is 9.
  ::首先,确定第一个倍数,是9个。

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  Then identify the second multiplicand. It is the sum of 1 + 8.
  ::然后标明第二个倍数。它是1+8的总和。

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  Next, write the product as a numerical expression. Use the parentheses to group the sum.
  ::下一步,将产品写成数字表达式。使用括号对总和进行分组。

  $$\begin{array}{r}9(1+8)\end{array}$$

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  Review
  ::回顾

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  Write a numerical expression for each sentence.
  ::每个句子写一个数字表达式。

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  1. The product of two and the sum of five and six.
     ::2和5和6的产物。
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  2. The product of three and the sum of three and seven.
     ::3的产物,3和7的总和。
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  3. The product of five and the sum of two and three.
     ::5的产物和2和3的总和。
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  4. The product of four and the sum of three and five.
     ::4的产物 3和5的总和。
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  5. The product of seven and the sum of four and five.
     ::7的产物,4的和5的合计。
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  6. The product of ten and the sum of five and seven.
     ::产品十,总和 五和七。
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  7. The product of six and the sum of five and two.
     ::6的产物和5的和2的合计。
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  8. The product of five and the sum of four and nine.
     ::5的产物和4的和9的合计。
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  9. The product of thirteen and the sum of five and twelve.
     ::十三 项 的 产品 、 和 五 、 十二 项 的 合计 。
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  10. The sum of six and seven all times three.
      ::6和7的总和 全部是3乘以3
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  11. The sum of eight and ten all times four.
      ::8和10总和 全部是4乘以4
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  12. The sum of six and fifteen all times eight.
      ::6和15总和 全部乘以8乘以8
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  13. The sum of four and nine all times twelve.
      ::四九总和 十二乘以四九总和
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  14. The sum of three and eight all times sixteen.
      ::总共三八次 16次
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  15. The product of eight and the sum of four and fourteen.
      ::8 和 4 和 14 之和。

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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