Activity 2 Multiplying Fractions Math 33. Is it important to have common denominators when we multiply fraction? Why or why not?


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1 Activity Multiplying Fractions Math Your Name: Partners Names:.. (.) Essential Question: Think about the question, but don t answer it. You will have an opportunity to answer this question at the end of the lecture. Is it important to have common denominators when we multiply fraction? Why or why not? Task : a) What is the area of the following rectangle? inches inches b) How did you come up with your answer? The product of two numbers, call them x and y, can be represented by the area of a rectangle with length x and width y. Let us use the same idea to understand how to multiply fractions. Task : Consider the square with length equal to inch and width equal to inch on page. Follow the following steps: a) Separate the width of the square in to thirds and separate the length of the square in half. b) You have separated the square in to equal pieces. How many equal pieces is the square separated in to?
2 c) Shade of the square. d) Shade of the square. e) Is the product represented by.. i. All shaded parts, those in blue, in yellow, and in yellow and blue. ii. The common area. The area that is shaded in blue and yellow. iii. The nonshaded area. f) Give a brief explanation how you made your decision. inch inch g) What is the product equal to? Explain how you made your decision. Your explanation should not include RULES on how to multiply fractions. Task : Let us imagine you had a pie saved in the fridge and your roommate (without asking you ) decided to eat a twothirds of it. a) Make a sketch of the remaining pie you have. Use a circle to represent the pie and make sure to include as many labels as possible. b) How much pie do you have left?
3 NOTE: When you are multiplying, you can say "of" or "groups of" instead of "times"  that may make more sense to you. / * 4/ is the same as "twothirds of fourfifths" or "fourfifths of twothirds." c) Suppose that you decided to save fourfifths of what you have for tomorrow. To take fourfifths of onethirds of the pie, you'd basically chop each of the slices in to slices. (Fill in the blank). d) How many of the slices you ve created will you be saving? What do you call these slices? We can't keep calling them fifths, because "fifths" really means "fifths of a whole." And they aren't fifths of a whole, they are fifths of a third. e) You cut a third into fifths which gave you slices altogether, right? But these slices are actually of a third. f) So to make a whole, you'd need three groups of those five pieces, giving you a total of. g) Therefore, when you chop the thirds in to fifths, although each of those pieces is a fifth of a third, they are each a of a. 4 4 h) So, going back to the problem, you saved of which is the same as which equals.
4 Task 4 So far we have seen two explanations of what multiplying fraction means. Let s look at one more. a) Remember that multiplication is a short hand notation for addition. can be thought as + + which equals b) Remember that the order on which we multiply numbers doesn t matter. So = = 6, what property is this? c) We can do something similar when multiplying fractions with whole numbers. Consider the product. We can think of this product as a short hand notation for adding times. d) Write the sum. e) Illustrate this sum using the circles provided. f) What did you find to be the total? g) So we have just found that = h) What kind of fraction is this? Why? i) Locate the fraction you found on the number line. Make sure you put all appropriate labels. In your own words, how do you multiply fractions? 4
5 Task : 0 Consider the following product. 9 We have just learned that to multiply fractions we simply multiply the numerators together and the denominators together, so the product 0 = = 0 9 = a) Can you simplify? If so, simplify the fraction. (KEEP IT AS AN IMPROPER 4 FRACTION) b) Complete the table below. STATEMENT 0 EQUALS Is the statement TRUE or FALSE? EXPLANATION (Please be as clear as possible) EQUALS 4 What we just performed is sometimes referred as cross canceling. We can cancel any numerator with any denominator with common factors. Task 6 Answer the following question Is it important to have common denominators when we multiply fraction? Why or why not?
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