Session 7

You are researching how to do the perfect chocolate drink. For that, you try different drinks: 1) First, you try two mixes: - In the first mix, you put 100 ml of milk, and 200 ml of cocoa. - In the second mix, you put 200 ml of milk, and 400 ml of cocoa. In each case, how much drink do you get in total? Which drink tastes more like cocoa? Why? 2) Then, you try two mixes: - In the first mix, you put 200 ml of milk, and 450 ml of cocoa. - In the second one, you put 300 ml of milk, and 400 ml of cocoa. In each case, how much drink do you get in total? Which drink tastes more like cocoa? Why? 3) Finally, you try two new drinks: - In the first mix, you put 100 ml of milk, and 300 ml of cocoa. - In the second mix, you put 200 ml of milk, and 400 ml of cocoa. In each case, how much drink do you get in total? Which drink has more cocoa? Which mix tastes more like cocoa? Why? In each case, how can you make the drinks taste the same? Tip: Are there any fractions in this problem? Do we have any techniques to solve this?

Using the applet, try to find as many equivalent fractions as you can: a) b) c)  d) e) What can you say about the numerators and denominators?

When we combine pieces to obtain equivalent fractions, we obtain smaller numbers. We call this simplifying the fraction. When a fraction cannot be simplified, we say that it is irreducible. a) In activity 2, did you simplify any fractions? b) Using the applet, simplify the following fractions and find the irreducible fraction: a) b) c) c) d) e)