We can use these proportions to compare two ratios with different denominators by finding a denominator that their proportions have in common. Thus the common denominator of 2/3 and 3/4 is 12. We then can use the common denominator to add/subtract and divide common ratios (fractions). This approach to division is quite different from the traditional approach and does not rely on the mechanical process of inverting the divisor and multiplying which most students find difficult to understand. Using common denominators means that to divide two fractions we simply divide the numerators of their common denominators, because when we divide common denominators they =1 since both have the same value.
Tag: ratios and proportions
Ratio and Proportion
We think about ratio tables in terms of motion. Move up 2 and over 1, or move up 1 and over 2. In this way we build proportional patterns. By coloring the cells we land on like knights in a chess table, we can see the proportions of different ratios. These proportions build linear patterns on the ratio table and introduce us to the very important concept of slope
Division and Ratio
We can make a division table just like we made a multiplication table. Division is surprisingly our most important operation in terms of most of the problems we solve in our daily lives. Division produces numbers we call fractions or rationals and functions we call ratios. With spreadsheets we concentrate on ratios and on the patterns of ratios.