Of the 82 pupils in grade 9, 73 take mathematics 56 take science, all those who take science take mathematics. Show the information on the venn diagram.
How many take neither mathematics nor science?
draw the science circle totally within the math circle
enter 56 in the science circle, put 17 in the science only circle
82-73 or 9 take neither science nor math.
To solve this problem, we can use a Venn diagram to visualize the information provided. Here are the steps to construct the Venn diagram and find the number of students who take neither mathematics nor science:
1. Draw two overlapping circles to represent mathematics and science.
2. Label one circle as "Mathematics" and the other as "Science."
3. Write the given numbers inside the respective circles:
- The number of students taking mathematics is 73, so write 73 inside the Mathematics circle.
- The number of students taking science is 56, so write 56 inside the Science circle.
4. Since all those who take science also take mathematics, write 56 in the overlapping region of the two circles to represent the students taking both subjects.
Now, let's find the number of students who take neither mathematics nor science.
5. To do this, calculate the total number of students who take either mathematics or science. To find the total, add the number in the Mathematics circle (73) to the number in the Science circle (56), and then subtract the number in the overlapping region (56). The equation would be:
Total = Students taking Mathematics + Students taking Science - Students taking both
Total = 73 + 56 - 56
Total = 73
So, the total number of students taking either mathematics or science is 73.
6. Finally, subtract the total number of students taking either mathematics or science (73) from the total number of students in the grade, which is given as 82. The equation would be:
Number of students taking neither Mathematics nor Science = Total number of students in Grade 9 - Total number of students taking either Mathematics or Science
Number of students taking neither Mathematics nor Science = 82 - 73
Number of students taking neither Mathematics nor Science = 9
Therefore, 9 students take neither mathematics nor science.