Ratio

A ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient. The ratio of quantities A and B can be expressed as: the ratio of A to B (fractional notation) A is to B A:B For example, the "ratio of men to women" in the group. if there are 50 people, 20 are men. Then the ratio of men to women is 20 to 30.Notice that, in the expression "the ratio of men to women","men" came first. This order is very important, and must be respected: whichever word came first, its number must come first. If the expression had been "the ratio of women to men", then it will be "30 to 20".Expressing the ratio of men to women as "20 to 30" is expressing the ratio in words. There are two other notations for this "20 to 30" ratio: Odds notation:  20 : 30 Fractional notation:  20/30 You should be able to recognize all three notations; you will probably be expected to know them for your test.Given a pair of numbers, you should be able to write down the ratios. For example: There are 25 goats and11 chicken in a certain park. Express the ratio of goats to chicken in all three formats. 25:11,    25/11,    "25 to11" Consider the above park. Express the ratio of chicken to goats in all three formats.         11:25,    11/25,    "11 to 25" The numbers were the same in each of the above exercises, but the order is different. In ratios, order is very important. Let's return to the15 men and 20 women in our original group. I had expressed the ratio as a fraction, namely, 15/20. This fraction reduces to 3/4. This means that you can also express the ratio of men to women as 3/4, 3 : 4, or "3 to 4". This points out something important about ratios: the numbers used in the ratio might not be the absolute measured values. The ratio "15 to 20" refers to the absolute numbers of men and women, respectively, in the group of thirty-five people. The simplified or reduced ratio "3 to 4" tells you only that, for every three men, there are four women. The simplified ratio also tells you that, in any representative set of seven people (3 + 4 = 7) from this group, three will be men. In other words, the men comprise 3/7 of the people in the group. These relationships and reasoning are what you use to solve many word problems: In a certain class, the ratio of passing grades to failing grades is 7 to 5. How many of the 36 students failed the course?zabeth St The ratio, "7 to 5" (or 7 : 5 or 7/5 ), tells me that, of every (7 + 5 = 12 )students, five failed. That is, 5/12  of the class . Then ( 5/12 )(36) = 15 students failed. In the park mentioned above, the ratio of goats to chicken is 25 to 11. How many of the 360 animals are chicken? The ratio tells me that, of every 25 + 11 = 36 animals, 11 are chicken. That is, 11/36 of the animals are chicken. So there are ( 11/36 )(360) = 110 chicken. Generally, ratio problems will just be a matter of stating ratios or simplifying them. For example: Express the ratio in simplest form:  $10 to $45 This exercise wants me to write the ratio as a reduced fraction: .10/45 = 2/9. This reduced fraction is the ratio's expression in simplest fractional form. Note that the units (the "dollar" signs) "cancelled" on the fraction, since the units,"$", were the same on both values. When both values in a ratio have the same unit, there should be no unit on the reduced form. Express the ratio in simplest form: 240 km to 80 minutes When I simplify, I get (240 km) / (80 min) = (3 km) / (1 min), or 3 km per minute. In this exercise the answer did need to have units on it, since the units on both parts of the ratio, the "km" and the "minutes", do not "cancel" with each other. Ratios are the comparison of one thing to another (meter to centimeter, km to minutes, goats to chicken, etc). But this is  useful in the setting up and solving of proportions.