Finding The Common Denominator

In everyday life, we interact with fractions multiple times throughout the day. Whether it is the amount of gas left in a tank, how much flour we need to measure out in a recipe or even how much money we have used up. There is a major importance for students to have the ability to understand and compare fractions. The lesson I have developed will help students be able to convert and compare fractions that have different denominators. I included three separate methods that will help students do so: Finding the common denominator, cross-multiplying, and finding the exact percentages. Finding the common denominator will help the students examine which fraction is the greater fraction since both fractions will be altered to share the same denominator. Cross multiplying the fractions will provide a simplified equation, thus allowing students to compare the results. Last, finding the percentages will further assist student’s comprehension of the exact amount of each fraction. I began leading the lesson by asking Linda which amount is greater: 3/5 or 3/7? I wanted to hear her initial reactions to the fractions before actually finding the truth of which is greater. First, she stated that 3/5 is greater since “there are only two numbers missing” and 2/7 is

When I explained to her that we had to make the denominator the same, her reply was “So it would be 12? Or are we supposed to multiply it?” This was a great discovery since most students have the misconception that adding the denominators is how you would find a common! But after clarifying that multiplication was the method of finding the common denominator, she then understood. As well, whatever you multiply to the bottom, you have to multiply to the top. Thus, leaving us the two fractions 21/35 and 20/35. With these two fractions now converted into the same type of fraction with equal denominators, she could easily comprehend that 21/35 is in fact, greater than