4.5分配律

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  分配律

  

  [Figure 1]

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  Josh is at the yarn store for their annual sale. Each bundle of yarn is on sale for $3.49. He buys 10 bundles of red yarn, 8 bundles of green, 6 bundles of blue, and another 6 bundles of yellow. How much did Josh spend on yarn?
  ::Josh在书店做年销售。每包纱都卖349美元。他买了10包红纱,8包绿色,6包蓝色,6包黄色。乔什花了多少钱在书上?

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  In this concept, you will learn to use the distributive property to  evaluate  numerical expressions.
  ::在此概念中,您将学会使用分配属性来评价数字表达式。

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  Distributive Property
  ::分配财产

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  To  evaluate  an  expression  means to simplify an expression to find the value or quantity. Expressions of the product of a number and a sum can be evaluated using the distributive property.
  ::用于评价表达式的手段是简化表达式以找到价值或数量。 数字和数字的产物的表示式可以用分配属性来评价。

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  Distributive Property
  ::分配财产

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  The  distributive property  is a  property  that allows you to multiply a number and a sum by  distributing  the multiplier outside the  " data-term="Parentheses" role="term" tabindex="0"> parentheses  with each addend inside the parentheses.
  ::分配财产是一种允许您乘以数字和总和的财产,在括号内以每个增编在括号内分配括号外的乘数。

  $$\begin{array}{r}a(b+c)=ab+ac\end{array}$$

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  Then you can evaluate the expression by finding the sum of the products.
  ::然后,您可以通过找到产品的总和来评估表达式。

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  Here an expression of the product of a number and a sum.
  ::这里表达一个数字和一个数字的产物。

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

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  To use the distributive property, take the 4 and distribute the multiplier to the addends inside the parentheses.
  ::使用分配财产时,取4,并将乘数分配给括号内的加号。

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

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  Then, find the sum of the products.
  ::然后,找到产品的总和。

  $$\begin{array}{r}\begin{array}{rcl}& & 4(3)+4(2)\\ & & 12+8\\ & & 20\end{array}\end{array}$$

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  Therefore , the value of the product of 4 times the sum of 3 plus 2 is 20.
  ::因此,产品价值是3+2总和的4倍,为20。

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  Here is another example, this time with a  variable .
  ::下面是另一个例子, 这次有一个变量 。

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

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  Evaluate the expression using the distributive property. First, distribute the 8 to each addend inside the parentheses.
  ::使用分配属性评价表达式。 首先, 在括号内将 8 分发到每个增编 。

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

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  Then, find the sum of the products.
  ::然后,找到产品的总和。

  $$\begin{array}{r}\begin{array}{rcl}& & 8(9)+8(a)\\ & & 72+8a\end{array}\end{array}$$

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  This is as far as this expression can be evaluated. If there is a known value for  $\begin{array}{r}a\end{array}$ , you can  substitute   $\begin{array}{r}a\end{array}$  with the value to continue evaluating the expression.
  ::这是该表达式可以被评估的范围。 如果一个表达式有一个已知的值, 您可以用该值替换该值, 以继续评估该表达式 。

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  Evaluate the expression if  $\begin{array}{r}a=4\end{array}$ .
  ::如果a=4,评价表达式。

  $$\begin{array}{rl}& 72+8(4)\\ & 72+32\\ & 104\end{array}$$

  
  
  The value of the product of 8 times the sum of 9 plus  $\begin{array}{r}a\end{array}$ , when  $\begin{array}{r}a\end{array}$  equals 4, is 104.

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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 Josh at the yarn store.
  ::早些时候,你得到一个问题 关于乔希在书店。

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  Josh buys 10 bundles of red yarn, 8 bundles of green, 6 bundles of blue, and another 6 bundles of yellow for $3.49 each. Multiply the sum of bundles of yarn by $3.49 to find the total cost of the yarn.
  ::Josh购买了10捆红纱、8捆绿纱、6捆蓝纱和6捆黄纱,每人3.49美元。将木纱的总量乘以3.49美元,以寻找毛纱的总成本。

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  First, write an expression to find the total cost of the yarn.
  ::首先,写一个表达式 来寻找毛线的总成本。

  $$\begin{array}{r}\mathrm{\$}3.49(10+8+6+6)\end{array}$$

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  Then, distribute the multiplier to each value in the parentheses.
  ::然后,将乘数分配到括号中的每个值。

  $$\begin{array}{r}\mathrm{\$}3.49(10+8+6+6)=\mathrm{\$}3.49(10)+\mathrm{\$}3.49(8)+\mathrm{\$}3.49(6)+\mathrm{\$}3.49(6)\end{array}$$

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  Then, find the sum of the products.
  ::然后,找到产品的总和。

  $$\begin{array}{r}\begin{array}{rcl}& & \mathrm{\$}3.49(10)+\mathrm{\$}3.49(8)+\mathrm{\$}3.49(6)+\mathrm{\$}3.49(6)\\ & & \mathrm{\$}34.90+\mathrm{\$}27.92+\mathrm{\$}20.94+\mathrm{\$}20.94\\ & & \mathrm{\$}104.70\end{array}\end{array}$$

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  Josh spent $104.70 on yarn.
  ::Josh花了104.70美元在缝线上

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  Use the distributive property to evaluate the following expressions.
  ::使用分配财产来评价以下表达式。

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  Example 2
  ::例2

  $$\begin{array}{r}4(9+2)\end{array}$$

   

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  First, distribute the 4 and multiply it by each value in the parentheses.
  ::首先,在括号中按每个值分配 4 并乘以乘以 4。

  $$\begin{array}{r}4(9+2)=4(9)+4(2)\end{array}$$

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  Then, find the sum of the products.
  ::然后,找到产品的总和。

  $$\begin{array}{r}\begin{array}{rcl}& & 4(9)+4(2)\\ & & 36+8\\ & & 44\end{array}\end{array}$$

   

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  The value of the product of 4 times the sum of 9 plus 2 is 44.
  ::产品价值是9+2总和的4倍,为44。

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  Example 3
  ::例3

  $$\begin{array}{r}5(6+3)\end{array}$$

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  First, distribute the multiplier to each value in the parentheses.
  ::首先,将乘数分配到括号中的每个值。

  $$\begin{array}{r}5(6+3)=5(6)+5(3)\end{array}$$

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  Then, find the sum of the products.
  ::然后,找到产品的总和。

  $$\begin{array}{r}\begin{array}{rcl}& & 5(6)+5(3)\\ & & 30+15\\ & & 45\end{array}\end{array}$$

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  The value of the product of 5 times the sum of 6 plus 3 is 45.
  ::产品价值是6+3总和的5倍,即45倍。

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  Example 4
  ::例4

  $$\begin{array}{r}2(8+1)\end{array}$$

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  First, distribute the multiplier to each value in the parentheses.
  ::首先,将乘数分配到括号中的每个值。

  $$\begin{array}{r}2(8+1)=2(8)+2(1)\end{array}$$

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  Then, find the sum of the products.
  ::然后,找到产品的总和。

  $$\begin{array}{r}\begin{array}{rcl}& & 2(8)+2(1)\\ & & 16+2\\ & & 18\end{array}\end{array}$$

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  The value of the product of 2 times the sum of 8 plus 1 is 18.
  ::产品价值是8加1之和的2倍,而18是8加1之和的2倍。

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  Example 5
  ::例5

  $$\begin{array}{r}12(3+2)\end{array}$$

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  First, distribute the multiplier to each value in the parentheses.
  ::首先,将乘数分配到括号中的每个值。

  $$\begin{array}{r}12(3+2)=12(3)+12(2)\end{array}$$

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  Then, find the sum of the products.
  ::然后,找到产品的总和。

  $$\begin{array}{r}\begin{array}{rcl}& & 12(3)+12(2)\\ & & 36+24\\ & & 60\end{array}\end{array}$$

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  The value of the product of 12 times the sum of 3 plus 2 is 60.
  ::产品价值是3+2总和的12倍,为60。

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  Review
  ::回顾

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  Evaluate each expression using the distributive property.
  ::使用分配财产评价每个表达式。

  1. $\begin{array}{r}4(3+6)\end{array}$
  2. $\begin{array}{r}5(2+8)\end{array}$
  3. $\begin{array}{r}9(12+11)\end{array}$
  4. $\begin{array}{r}7(8+9)\end{array}$
  5. $\begin{array}{r}8(7+6)\end{array}$
  6. $\begin{array}{r}5(12+8)\end{array}$
  7. $\begin{array}{r}7(9+4)\end{array}$
  8. $\begin{array}{r}11(2+9)\end{array}$
  9. $\begin{array}{r}12(12+4)\end{array}$
  10. $\begin{array}{r}12(9+8)\end{array}$  
  11. $\begin{array}{r}10(9+7)\end{array}$
  12. $\begin{array}{r}13(2+3)\end{array}$
  13. $\begin{array}{r}14(8+6)\end{array}$
  14. $\begin{array}{r}14(9+4)\end{array}$
  15. $\begin{array}{r}15(5+7)\end{array}$

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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