## Math test on the first day

Tanya had enjoyed the summer vacation. She had gone to a summer camp with several of her friends. She also went with her parents on holidays to a hill station. There she enjoyed the scenery and the hikes in the wilderness. She loved to see the birds sitting on the trees around their cottage. Well, the vacation finally ended and it was school time again – back to books and the friends in the school.

On the first day, the classes seemed to be going well and she also enjoyed the recess. But then Ms. Chan, the teacher decided to give the class a math test to see how much they remembered from the previous year. There were six questions in all. The first two questions were very easy addition of two digit numbers. Next two questions related to multiplication and division and the last two to fractions. The questions were worth 5 marks each.

**Tanya’s marks**

Tanya, like everyone in her class wrote the test. The next day she got her test paper back. She had received full marks for the first five questions but only 3 out of 5 in the sixth question. She added her marks for the 6 questions and came up with 5 + 5 + 5 + 5 + 5 + 3 which was 28. She also figured that the maximum marks one could get would be 30, that would be if they 5 marks for each of the 6 questions. So she figured that her mark should be 28 out of 30. Surprisingly, Ms. Chan had written 93.3% as her total mark. She looked around. All the other kids also got a mark which was a number followed by the symbol %. They all looked lost just like she was.

Then Ms. Chan addressed the class: Hello, every one, today’s lesson is about the concept of percent which has the symbol % (she wrote on the board) written on the test papers I returned to you. Tanya, what mark did you get?

Tanya: I figured that I mark added to 28 out of a maximum of 30 but my test paper says 93.3%.

**What is a century?**

Ms. Chan: Thank you Tanya. Before We go further, does anyone know what century it is now?

Many students raised hands and said twenty first century.

Ms. Chan: What is a century?

Tinku raise hands and said one hundred years.

Ms. Chan: Very good Tinku but century just means 100, it can be 100 years like you said and used to mean 100 soldiers in the Roman Empire. What we are going to do is pretend that your test was worth a century. Then Tanya, what will your mark of 28/30 mean?

Tanya: So you mean, the denominator will become 100 instead of 30 for my mark of 28/30. Then my mark will be 100 x 28/30 which comes out to 93.3.

Ms. Chan: Very good Tanya. When we change a fraction to an equal value fraction such that its denominator is 100 (century), the numerator of this fraction is called percent. So you got 93.3% mark in your test. Now I want everyone in class to add their mark, multiply it by 100 and divide it by 30. That will give you the percent mark I wrote on your test. Yes, Tinku. It seems like you are done already

Tinku: Yes, Ms. Chan I am done. I had 24/30 which comes out to 80/100. So my mark was 80% as you wrote on my test.

**What is the point of using percent values?**

Kate: Ms. Chan, I learned how to get a percent value but what is the point of making the all the extra effort to do the conversion. We could have said Tanya got 28 marks out of 30 and Tinku got 24.

Ms. Chan: I am going to tell you about a student in my class two years ago. I am going to change the name of the student to keep it confidential. Let’s call her Sophie Lamours.

I gave 6 tests to the class. Some tests had 5 questions, others had six or seven or eight. Each question was always worth 5 marks. Here are Sophie’s marks in all the tests.

Test numbers from beginning of the semester to the end | Sophie’s marks/Maximum marks | Sophie’s marks as percent |

1 | 12/30 | 40 |

2 | 18/35 | 51.4 |

3 | 20/40 | 50 |

4 | 25/35 | 71.4 |

5 | 28/35 | 80 |

6 | 33/40 | 82.5 |

Peter: Ms. Chan, based on the percent marks, I can clearly see that Sophie went from a failing student to a very good one with marks above 80%. I could perhaps see the same thing by comparing the values of each fraction but it is much easier with the percent value.

Ms. Chan: Thank you Peter for answering Kate’s question about the advantage of converting fractions to percent values. There are many more applications of percent values and we will talk about some of them in the coming classes.

*Challenge*

*Challenge*

Tanya’s mom invited many of her friends to her place. She gave them some other refreshments but also had a large 24 slice pizza. She told them that they could share the pizza equally such that each person gets 12.5% of the pizza. How many slices did each person get? If the all the pizza was finished by this sharing, how many people were there at the party?

* Solution*: Each person got 12.5% of 24 slices =24 x 12.5/100 = 300/100 = 3 slices.

Because all 24 slices were distributed equally and each person got 3 slices, there must have been 24/3 = 8 persons to share the pizza.

### Supplementary

Johnny plays junior basketball and practices hard to make good free throws. He says that a month ago, his free throw success was 30% of the time and now it is 75%. Suppose, he threw the ball 20 times in each of the trials. How many shots did he make a month ago and this time ?

**Answer:** The number of successful shots = total attempts x percent success /100

A month ago: 20 x 30/100 = 6, this time 20 x 75 /100 = 15.