维恩图

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Mr. Tristany counts all of the boys and girls in the 7th grade at his school. Field Day is quickly approaching and Mr. Tristany is in charge of dividing some of the students into teams that are equally matched. All of the students will not be on teams, but for those that are, each team must have the same number of boys and the same number of girls as all the other teams. Mr. Tristany wants to make sure that there are enough students to make at least 10 teams so he decides to calculate the greatest number of teams that can be formed. He uses a   to make his calculation. The diagram that he used is below.
::崔斯坦尼先生在七年级的学校里清点了所有男女生人数。田间日即将到来,崔斯坦尼先生负责将一些学生分成同等人数的队,所有学生将不参加队,但对于那些参加队的学生,每个队的男生人数和女生人数必须与其他队的男生人数相同。崔斯坦尼先生希望确保有足够的学生组成至少10个队,以便他决定计算能够组建的队伍最多。他用一个队来计算。他使用的图表如下:

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What is the greatest number of teams that can be formed with the given number of boys and girls? 
::与特定人数的男女儿童相比,最多能够组建的队伍是什么?

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In this concept, you will learn how to draw a Venn diagram to organize materials.

::在这个概念中,你将学会如何绘制文恩图来组织材料。

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Venn Diagrams
::文文图

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A  Venn diagram  shows the common numbers in two sets of objects or numbers by using overlapping circles. A Venn diagram helps you to organize data in a visual way to notice patterns and solve for the answer.
::Venn 图表通过使用重叠圆来显示两组对象或数字的共同数字。 Venn 图有助于您以直观的方式组织数据,以发现模式和解答答案。

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There are 280 girls and 260 boys playing on soccer teams this fall. If each team has the same number of girls and the same number of boys, what is the greatest number of teams that can be formed?
::今年秋天,有280名女孩和260名男孩参加足球队,如果每个球队的女生人数相同,男生人数相同,那么能够组建的球队最多是多少?

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A Venn diagram is used to show things that are common and things that are different. For this example, you can write the prime factors of 280 in one circle, the prime factors of 260 in the other circle and the common factors in the part of the circle that overlaps.
::文恩图用于显示共同的事物和不同事物。例如,您可以在一个圆圈中写出280的质因数,在另一个圆圈中写出260的质因数,在重叠的圆段里写出共同因数。

 

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By looking at this diagram, you can see that the common factors between 280 and 260 are 5, 2 and 2. If you multiply these together, you will have the total number of groups possible.
::通过查看这个图表,你可以看到280到260之间的共同因素是5、2和2。如果将这两个因素乘在一起,你将拥有可能的组数总数。

$\begin{array}{r}5\times 2\times 2=20\end{array}$

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There are 20 possible groups.
::有20个可能的群体。

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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 Mr. Tristany and his plans for Field Day.
::早些时候,你被问及 特里斯坦尼先生和他的 野外日计划的问题。

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He counts all of the boys and girls in the 7th grade at his school. He wants the same number of boys and girls on each team and he wants to make sure that there are enough students to make at least 10 teams so he decides to calculate the greatest number of teams that can be formed. He uses a Venn diagram to make his calculation. The diagram that he used is below.
::他在学校的七年级里计算了所有男女生人数,他要求每个队伍的男女生人数相同,他想确保学生人数至少达到10个队伍,因此他决定计算最多可以组建的队伍。他用文恩图进行计算。他使用的图表如下。

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What is the greatest number of teams that can be formed with the given number of boys and girls?
::与特定人数的男女儿童相比,最多能够组建的队伍是什么?

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First, identify the common factors of 105 and 120.
::首先,确定105和120的共同因素。

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5 and 3
::5和3

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Then, multiply those numbers to calculate the greatest common multiple. 
::然后,乘以这些数字来计算最大的共同数倍数。

$\begin{array}{r}5\times 3=15\end{array}$

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The answer is 15. Mr. Tristany has enough students to fill 15 teams, which is greater than the 10 teams that he wants to build.
::答案是15。 崔斯坦尼先生有足够的学生 来填满15支队伍, 这比他想要建的10支队伍还要多。

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Example 2
::例2

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What is the greatest common factor of 66 and 72?
::66和72这两个最大的共同因素是什么?

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First, identify the common factors of 72 and 66.
::首先,确定72和66的共同因素。

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3 and 2
::3和2

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Then, multiply those numbers to calculate the greatest common multiple.
::然后,乘以这些数字来计算最大的共同数倍数。

  $\begin{array}{r}3\times 2=6\end{array}$

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The answer is 6.
::答案是6个

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Example 3
::例3

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Use the Venn diagram to write the greatest common multiple of 225 and 90.
::使用 Venn 图表写出最大常见的乘数 225 和 90。

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First, identify the common factors of 225 and 90.
::首先,确定225和90的共同因素。

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5, 3 and 3
::5、3和3

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Then, multiply those numbers to calculate the greatest common multiple.
::然后,乘以这些数字来计算最大的共同数倍数。

  $\begin{array}{r}5\times 3\times 3=45\end{array}$

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The answer is 45.
::答案是45岁

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Example 4
::例4

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What is the greatest common factor of 98 and 44?
::最大的共同因素是98和44?

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First, identify the common factors.
::首先,确定共同因素。

2

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Then, identify the greatest common factor.
::然后找出最大的共同因素。

2

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The answer is 2.
::答案是2。

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Example 5
::例5

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What values should be listed in the middle section of the Venn diagram below?
::在下文文恩图的中间部分应列出哪些值?

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First, identify the  value  of the factors on one of the sides.
::首先,确定其中一方因素的价值。

  $\begin{array}{r}7\times 2\times 2=28\end{array}$

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Next, identify the factors that are missing from the 112 side.
::接下来,找出112侧缺失的因素。

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2 and 2
::2和2

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Then, write those factors in the middle section.
::然后把这些因素写在中间部分。

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2 and 2
::2和2

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The answer is 2 and 2.

::答案是2和2。

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Review
::回顾

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Create a Venn diagram for the following data.
::为以下数据创建 Venn 图表 。

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1. The factors of 20 and 30.
   ::因素20和30。
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2. The factors of 45 and 55
   ::45和55的因素
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3. The factors of 67 and 17
   ::系数67和17
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4. The factors of 54 and 18
   ::系数54和18
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5. The factors of 27 and 81
   ::系数27和系数81
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6. The factors of 9 and 18
   ::9 和 18 系数
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7. The factors of 100 and 200
   ::系数100和200
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8. The factors of 8 and 80
   ::系数8和系数80
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9. The factors of 120 and 144
   ::120和144系数
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10. The factors of 120 and 140
    ::120和140系数
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11. The factors of 80 and 100
    ::系数80和100
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12. The factors of 10 and 60
    ::10和60的因素
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13. The factors of 70 and 140
    ::70和140系数
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14. The factors of 6 and 60
    ::6和60的因素
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15. The factors of 330 and 900
    ::330和900因数

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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