You are researching how to do the perfect chocolate drink. For that, you try different drinks:[br][br]1) First, you try two mixes:[br]- In the first mix, you put 100 ml of milk, and 200 ml of cocoa.[br]- In the second mix, you put 200 ml of milk, and 400 ml of cocoa.[br][b]In each case, how much drink do you get in total? [br]Which drink tastes more like cocoa? Why?[/b][br][br]2) Then, you try two mixes:[br]- In the first mix, you put 200 ml of milk, and 450 ml of [b]cocoa. [br][/b]- In the second one, you put 300 ml of milk, and 400 ml of cocoa.[br][b]In each case, how much drink do you get in total?[br]Which drink tastes more like cocoa? Why? [/b][br][br]3) Finally, you try two new drinks: [br]- In the first mix, you put 100 ml of milk, and 300 ml of cocoa.[br]- In the second mix, you put 200 ml of milk, and 400 ml of cocoa.[br][b]In each case, how much drink do you get in total?[br]Which drink has more cocoa? [br]Which mix tastes more like cocoa? Why? [br][/b][br][b]In each case, how can you make the drinks taste the same? [br][/b][i]Tip: Are there any fractions in this problem? Do we have any techniques to solve this? [/i]
Using the applet, try to find as many equivalent fractions as you can: [br][br]a) [math]\text{\frac{2}{4}}[/math] b) [math]\text{\frac{1}{2}}[/math] c) [math]\text{\frac{4}{6}}[/math] d) [math]\text{\frac{1}{5}}[/math] e) [math]\text{\frac{2}{3}}[/math][br][br][b]What can you say about the numerators and denominators?[/b]
To find equivalent fractions, we can do three things: [br][br]1) Break each portion into equal parts.[br][br]2) Combine several portions in groups of the same size.[br][br]3) Do both![br][br][i]How does this affect the numerator and denominator?[/i]
When we combine pieces to obtain equivalent fractions, we obtain smaller numbers.[br]We call this [b]simplifying [/b]the fraction.[br][br]When a fraction cannot be simplified, we say that it is [b]irreducible.[/b][br][br]a) In activity 2, did you simplify any fractions? [br][br]b) Using the applet, simplify the following fractions and find the irreducible fraction:[br][br]a) [math]\text{\frac{7}{14}}[/math] b) [math]\text{\frac{2}{6}}[/math] c) [math]\text{\frac{22}{8}}[/math] c) [math]\text{\frac{8}{6}}[/math] d) [math]\text{\frac{14}{8}}[/math] e) [math]\text{\frac{16}{10}}[/math]