4.7计算小数公式的分配律

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• 选择节计算小数公式的分配律

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  计算小数公式的分配律

  
  

  

  [Figure 1]

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  Mimi is planning on landscaping her backyard. Originally the grass covered an area that was 10.5 feet long and 6.5 feet wide. She plans to extend the width of the yard by 2 feet. What is the area of the new yard? 
  ::Mimi计划对后院进行景观美化,最初草原覆盖面积为10.5英尺长,6.5英尺宽,计划将院子宽度扩大2英尺。 新院子的面积是多少?

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  In this concept, you will learn to use the   to  evaluate  formulas using decimal quantities.
  ::在此概念中,您将学会使用小数点数量来评价公式。

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  Evaluating Formulas with Decimals
  ::使用十进制评价公式

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  The distributive property can be used when working with a  formula .
  ::在使用公式时,可以使用分配财产。

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  Let’s look at the formula for the area of a rectangle.
  ::让我们看看矩形区域的公式。

  $$\begin{array}{r}A=\text{length}\times \text{width}\text{or}A=lw\end{array}$$

   

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  Here is a rectangle with the given  dimensions .
  ::这是与给定维度的矩形。

  

  [Figure 2]

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  The area of this rectangle would be 12 times 4.
  ::这个矩形的面积是12乘以4

  $$\begin{array}{r}\begin{array}{rcl}A& =& 12in.\times 4in.\\ A& =& 48in{.}^2\end{array}\end{array}$$

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  The area of this rectangle is 48 square inches. Remember that a unit is being multiplied by another unit when finding the area of an object. The area is written as the unit with an  exponent  of 2, read as “inches squared” or “square inches.”
  ::此矩形区域为 48 平方英寸。 请注意, 当找到对象区域时, 单位正乘以另一个单位。 区域以单位形式写成, 缩写为2, 缩写为“ 英寸方英寸” 或“ 平方英寸 ” 。

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  Here are two rectangles with the same width.
  ::这里有两个相同宽度的矩形。

  

  [Figure 3]

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  Find the area of both rectangles. You could find the area each rectangle and then add them together or you can think of both rectangles as one new rectangle with the width of 4.5 inches and length of  $\begin{array}{r}12+7\end{array}$  inches. Use the new dimensions to find the area of both rectangles.
  ::查找两个矩形的面积。 您可以找到每个矩形的区域, 然后把它们加在一起, 或者您可以将两个矩形想象成一个新的矩形, 宽度为4.5英寸, 长度为 12 + 7 英寸。 使用新的尺寸来找到两个矩形的面积 。

  $$\begin{array}{r}A=4.5(12+7)\end{array}$$

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  Use the distributive property to find the area of these two rectangles. Distribute 4.5 with each length and find the sum of the products.
  ::使用分配属性找到这两个矩形的区域。 分配4.5, 每长4.5, 并找到产品的总和 。

  $$\begin{array}{r}\begin{array}{rcl}A& =& 4.5(12)+4.5(7)\\ A& =& 54+31.5\\ A& =& 85.5\end{array}\end{array}$$

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  The area of both rectangles is  $\begin{array}{r}85.5in{.}^2\end{array}$ .
  ::两个矩形区域为85.5 i n. 2。

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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 Mimi landscaping her backyard.
  ::之前,你被问及 米米美美化后院的问题

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  She is going to extend her yard that is 10.5 feet by 6.5 feet by making it 2 feet wider. Use the formula for the area of a rectangle to find the area of the new yard.
  ::她将把10.5英尺的院子扩大6.5英尺,使院子宽2英尺,用矩形面积的公式找到新院子的面积。

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  First, write an  expression  to find the area of the new yard.
  ::首先,写一个表达式来寻找新院子的面积。

  $$\begin{array}{r}\begin{array}{rcl}A& =& l\times w\\ A& =& 10.5(6.5+2)\\ A& =& 10.5(6.5)+10.5(2)\\ A& =& 68.25+21\\ A& =& 89.25\end{array}\end{array}$$

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  The area of the new yard will be 89.25 square feet.
  ::新院落面积为89.25平方英尺。

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  Example 2
  ::例2

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  Use the distributive property to find the area of the rectangles.
  ::使用分配属性查找矩形区域。

  

  [Figure 4]

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  First, write the formula to find the areas.
  ::首先,写出公式以查找区域。

  $$\begin{array}{r}A=2.5(10+4)\end{array}$$

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  Then, use the distributive property to evaluate.
  ::然后,利用分配财产进行评估。

  $$\begin{array}{r}\begin{array}{rcl}A& =& 2.5(10)+2.5(4)\\ A& =& 25+10\\ A& =& 35\end{array}\end{array}$$

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  The area of the two rectangles is  $\begin{array}{r}35m{m}^2\end{array}$ .
  ::两个矩形的面积是35米2米。

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  Example 3
  ::例3

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  What is the formula for finding the area of a rectangle?
  ::寻找矩形区域的公式是什么?

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  The formula for the area of a rectangle is  $\begin{array}{r}A=\text{length}\times \text{width}\end{array}$ .
  ::矩形区域的公式为 A = 长度 × 宽度。

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  Example 4
  ::例4

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  Which  property  is being illustrated:  $\begin{array}{r}4(a+b)=4a+4b\end{array}$
  ::说明哪些财产:4(a+b)=4a+4b

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  This is the distributive property.
  ::这是分配财产。

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  Example 5
  ::例5

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  What is the formula for finding the area of a square?
  ::找到方块面积的公式是什么?

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  A square is similar to a rectangle. Since a square has equal sides, the area for a square is  $\begin{array}{r}A=\text{side}\times \text{side}\end{array}$  or  $\begin{array}{r}A=s^2\end{array}$ .
  ::方形与矩形相似。既然一个方形具有等边,则方形的面积为 A = 侧 × 侧 或 A = s 2。

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  Review
  ::回顾

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  Practice using the distributive property to solve each problem.
  ::使用分配财产解决每个问题的做法。

  1. $\begin{array}{r}3.2(4+7)\end{array}$
  2. $\begin{array}{r}2.5(6+8)\end{array}$
  3. $\begin{array}{r}1.5(2+3)\end{array}$
  4. $\begin{array}{r}3.1(4+15)\end{array}$
  5. $\begin{array}{r}6.5(2+9)\end{array}$
  6. $\begin{array}{r}7.5(2+3)\end{array}$
  7. $\begin{array}{r}8.2(9+3)\end{array}$
  8. $\begin{array}{r}4(5.5+9)\end{array}$
  9. $\begin{array}{r}5(3.5+7)\end{array}$
  10. $\begin{array}{r}2(4.5+5)\end{array}$
  11. $\begin{array}{r}3.5(2.5+3)\end{array}$
  12. $\begin{array}{r}2.5(9+1.5)\end{array}$
  13. $\begin{array}{r}3.2(7+8.3)\end{array}$
  14. $\begin{array}{r}1.5(8.9+2.5)\end{array}$
  15. $\begin{array}{r}3.5(2.5+8.2)\end{array}$

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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