Mathematical+Reflections,+p.+36+0910

K.D 11/22/09 **Big Idea: Many important practical and mathematical applications involve comparing quantities of one kind of another; it is important to know which method to use and how we should use them. Essential Question: What methods are there for comparing things?** You form a ratio by finding part to part information and it’s usually simplified. Ratios can be used to compare two (or more) numbers. Say your making a class of lemonade (from concentrate) and 2 out of 4 out it is water that’s a ratio.
 * 1. Explain how to form a ratio and how ratios can be used to compare two numbers. Use examples to help explain your thinking.**

One way is to find the least common multiple. To do this say you had two ratios which are: Ms. K’s class has 3 people who run track and 5 who prefer soccer, then Mr. Lillard has 4 people who prefer track and 4 who prefer soccer. All you do is find the LCM for 5 and 4 (20). 5 goes into 20 4 times so 3 x 4= 12 and 4 goes into 20 5 times. 4x5=20. So Mr. Lillard’s class has a ratio of 20/20 and Ms.K’s has a ration of 12/20.
 * 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.**


 * 3. The percent of orange concentrate in a juice mix is 60%. What is the ratio of concentrate to water in mix?**
 * The ratio is 6 to 4 or if you want to reduce it 3 to 2. I found it by doing: **100-60= 40 ÷ 100 = 0.4 = 4 water.


 * 4. The ratio of concentrate to water in a juice mix is 3 to 5. What percent of the mix is concentrate?**
 * Concentrate is 3 and water is 5. Then 3 divided by 5 = .40 x 100= 40= 40%. Therefore 40%**** of the juice is concentrate and 60% is water. **


 * Summary:**
 * In this unit the main thing was: ratios. In 3.1 we learned how to convert them and compare them to others. You can find the least Common Multiple or convert them into percentages. Then in 3.2 we got introduced to part to part and part to whole rations. In 3.3 we used part to part and part to whole ratios. It was a fairly short unit but we learned all about ratios and the three ways the can be written. ||