CLASS ACTIVITY: 2N SOLVING PROBLEMS BY CHANGING DENOMINATORS By: Amanda comer, Amanda perez, and patricia shady Math 105

Question #1

We know this to be correct because if the imagined large piece of paper is divided into 6 equal parts, than 2/3 of the large piece would be 4 parts of the whole 6 parts, which is 4/6, and 4/6 = 2/3. Additionally, it is evident that 6 of these 1/6 pieces that we created by folding on the previous slide, do fit together to make the imagined whole large piece of paper. 2/3 appears in a different form: 4/6, when the numerator and denominator are both multiplied by 2. But there are many other acceptable solutions too (i.e. 6/9 when the numerator and denominator are both multiplied by 3), so yes, two people could have different solutions (fractions) that are both correct forms of 2/3. According to our text on p. 61, “every fraction is equal to infinitely many other fractions.” 2/3 = 4/6 = 6/9

Question #2

When we divide a cup of butter into 6 equal parts, a 1/2 cup of butter = 3 parts (of 6 parts) of butter, and 1/3 cup of butter = 2 parts (of 6 parts) of butter. Since 3 parts of butter are actually needed to make the casserole, and Jean only has 2 parts of the butter needed, she can only make 2/3 of the casserole recipe, because she only has 2 out of 3 parts of butter. In solving the problem, 1/2 becomes 3/6 when the numerator and denominator are both multiplied by 3. And 1/3 becomes 2/6 when the numerator and denominator are both multiplied by 2. Important to note: when the numerator and denominator of a fraction are multiplied by a number, such as 2 or 3, this means that the fraction gets further divided into 2 or 3 parts, respectively.

Question #3

If we divide the cup of cereal into 8 equal parts, then 3/4 cup of cereal = 6 parts (of 8 parts) of cereal. So if Joey wants half of a serving, then he can eat 3 parts (of 8 parts) of cereal, or 3/8 cup. In solving the problem, 3/4 becomes 6/8 when the numerator and denominator are both multiplied by 2, what this means is that each ¼ of a cup has been divided into 2 parts.

THE BOTTOM LINE: In all of these exercises, the most important thing we did was to change the denominators of each fraction in the drawings, so that a common denominator could be found, which would then create like parts between the two fractions. The bottom line is that a problem is a lot easier to solve if we are working with like parts. Our information is justified by section 2.3 of our text. THANK YOU FOR WATCHING!