Proportions play an important part in recipe conversions.
Mathematics concepts appear in many forms and apply in many fields. Use the concepts of proportion, percentage and ratio in chemistry, cooking and architecture, among others. All three ideas deal with parts of a whole and how they are related to each other. Understand the basic meanings and you'll find that the concepts occur in nearly every part of life.
The Sample
A group of people bring their pets to a special event at the zoo. As each party registers, the pet is identified as to gender and classified as canine, feline, avian or amphibian. Canines make up 10 of the animals, with six females and four males. The eight felines contain two females and six males. The avian group totals five, two females and three males. The four amphibians consist of one female and three males. The registrars could not identify gender in the 13 "other" specimens, consisting of insects and fish.
Proportion
Proportion identifies the relationship of a part to the whole or parts to parts. Use the proportion to assist in calculating larger or smaller groups. The proportion of canines in the sample is 10 of the total 40 animals or 10-in-40. Simplify the numbers to 1-in-4. The simplified number allows easy multiplication but obscures the total in the sample. A typical problem might read, "Ten animals in a group of 40 are dogs. If the same proportion of dogs exists in a group of 96 animals, how many dogs are there?"
Ratio
Ratio reflects how parts of a whole relate to each other. Express the ratio as number-to-number or number:number. The ratio of female-to-male amphibians is 1-to-3 or 1:3 in the total group of four. Ratios frequently show up in recipes for bulk products: mix 1 part water to 1 and 1/2 cups baking mix. Whether the baker needs 10 pancakes or 200, the recipe adjusts easily. A sample problem might read, "If there are 10 dogs, eight cats and five birds in a group of pets, what is the ratio of dogs to cats?"
Percentage
Percentages can be expressed on a pie chart for a visual report.
Divide the second number of a ratio into the first to convert it to a percentage. In the sample, calculate the percentage of mammals in the group by adding the canine and feline counts: 10+8=18. Express the ratio of mammals to the total of the group as 18-to-40 or 18:40. Calculate the percentage by dividing 18 by 40, for a value of 0.45 or 45 percent. A typical problem might ask, "In a group of 40 animals, 8 are cats. What percent of the group is made up of cats?"
Comparison
Proportion, percentage and ratio express similar ideas in slightly different formats. In the sample, there are 10 dogs. The dogs make up a 1-in-4 proportion of the group when the value of 10-in-40 is simplified. The ratio of dogs to the whole group is 1:4. The percentage of dogs in the group is 25 percent or .25, based on dividing 10 by 40. When any part is given, the others can be calculated. For example, "In a group of 40 animals, 25 percent are dogs. How many dogs are there?" "Dogs make up 1-in-4 animals in a group. If there are 10 dogs, what is the total number of animals?" "The ratio of dogs to cats in a group of animals is 5:4. If there are eight cats, how many dogs are there?"
