Mathematical+Reflections,+p.+36+0910

__S**Date:**__Tuesday, December 1st, 2009

__**N.A**__


 * __Big Idea:__** Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them.


 * __Essential Questions:__** What methods are there for comparing things?

__Mathematical Reflection:__

 * 1). Expain how to form a ratio and how ratios can be used to compare two numbers. Use examples to help explain your thinking.**

To form a ratio a ratio I need two information, either the total and one part of the data, or two parts of the data. So I can make a part to whole ratio with the total and one part of the data, or I can make a part to part ratio with the two parts of the data. Ratios can be used to compare two numbers by using the part to part ratio, or the part to whole ratio. A part to part ratio consists of two parts of the data. And a part to whole ratio consists of one of the parts of the data, and the whole.

Total:** 20 people**, Data:** 12 Males**, Data:** 8 Females**:
 * Example:

Part to part ratio:** 12:8 (Males:Females)
 * Part to whole ratio:** 12:20 (Males:Total)


 * 2). What strategy can you use to compare two ratios? Be very specific. Your strategy should allow you to tell whether the two ratios are the same or different. Make up a problem that can be solved by using your strategy.**

A strategy to compare ratios could be to change the ratios to percents, then compare it. This allowes me to see wheather the ratios are the same or different because both the ratios are going to be based one 100, and what ever percent of 100 is, I can still compare it.

3 to 2 is the ratio of boys to girls in the 7th grade class in a school, and 160 to 80 is the ratio of boys to girls in the whole school. Compare this two ratios to find if the ratio of the 7th graders are same is the whole school.
 * Problem:**

3+2= 5, 3/5=.6x100= 60%(boys), 2/5=.4x100= 40%(girls). 160+80= 240, 160/240= .6666x100~67%, 80/240=.3333x100~ 33%
 * Solving:**

So, as you can see in the solving section, the percentage of boys to girls in the 7th grade is 60% to 40%, and the whole school the the percentage is 67% to 33%, so no, the 7th grade percentage, and the whole school percentage isn't the same.
 * Answer:**


 * 3). The percent of orange concentrate in a juice mix is 60%. What is the ratio of concentrate to water in the mix?**

The Ratio of orange concentrate to water in a mix is: 6 to 4


 * 4). The ratio of concentrate to water in a juice mix is 3 to 5. What percent of the mix is concentrate?**

If the ratio of concentrate to water is 3 to 5, there would be 37.5 % of concentrate in the mix.


 * Think about your answers to these questions, discuss your ideas with other students and your teacher, and then write a summary of your findings in your journal.

Summery:**

In this investigation, I have learned about ratios and about using ratios to make comparisons. There are two different types of ratios: Part to part, and part to whole, there are also many different ways to express ratios we can express them as quotients, fractions, decimals, percents, or as the form a:b. We use ratios in many different ways in our daily lives, one examples would be when we cook, everytime we use a reciepy, we are using ratios.