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Math 300 Basic College Mathematics Chapter 5 Ratio and Proportion Math 300 M-G Chapter 5; Rev: Jan 2009 Page 1 of 8 5.1 Ratios Ratios A ratio is the quotient of two quantities. Ratio Notation as a Fraction The ratio of a to b is given by the fraction notation a , where a b is the numerator and b is the denominator. Example: Write each ratio using fractional notation. Do not simplify. 1. 7 to 12 2. 14 to 5 Example: Write each ratio as a ratio of whole numbers using fractional notation. Write the fraction in simplest form. 3. 25 to 150 4. 18 quarts to 30 quarts Math 300 M-G Chapter 5; Rev: Jan 2009 Page 2 of 8 5.2 Rates Rates When a ratio is used to compare different kinds of quantities. Example: Write each rate as a fraction in simplest form. 1. 14 lab tables for 28 students Writing a Rate as a Unit Rate To write a rate as a unit rate, divide the numerator of the rate by the denominator. Example: Write the rate as a unit rate. 2. 275 miles in 11 hours Unit Price The unit price is the ratio of price to the number of units. Formula for unit price: unit price price number of units Example: Find the unit price. 3. $0.87 for 3 apples Math 300 M-G Chapter 5; Rev: Jan 2009 Page 3 of 8 5.2 Rates (cont) Example: Find the unit price and decide which is the better buy. Round 3 decimal places. Assume that we are comparing different sizes of the same brand. 4. Pickles: $1.89 for 32 ounces $0.89 for 18 ounces Math 300 M-G Chapter 5; Rev: Jan 2009 Page 4 of 8 5.3 Proportions When 2 ratios or rates are equal. For example: a proportion. We sometimes read 3 6 2 4 3 6 2 4 is called as “3 is to 2” as “6 is to 4.” Example: Write this sentence as a proportion. 1. 4 hit songs is to 16 releases as 1 hit song is to 4 releases. 2. 1 1 cups milk is to 10 bagels as 2 Math 300 M-G Chapter 5; Rev: Jan 2009 3 4 cup milk is to 5 bagels. Page 5 of 8 5.3 Proportions (cont) Determining Whether Proportions Are True If the cross products are equal, then the proportion is true. If the cross products are not equal, then the proportion is false. Example: Determine whether the proportion is a true proportion. 3. 8 20 6 15 4. 7 4 12 7 Finding an Unknown Value n in a Proportion Method 1: Simple Proportion Method 1. Multiply the two number values which are diagonal to one another. 2. Divide the product above by the third (unused) number in the proportion Method 2: Algebra Method 1. Set the cross products equal to each other. 2. Divide both sides of the equation by the number that is multiplied by n. Math 300 M-G Chapter 5; Rev: Jan 2009 Page 6 of 8 5.3 Proportions (cont) Example: For each proportion, find the unknown number n. 1. n 12 3 9 2. 25 7 100 n 3. 12 n 10 16 Math 300 M-G Chapter 5; Rev: Jan 2009 Page 7 of 8 Math 300 Chapter 5 Glossary Ratio – a quotient of two quantities. It is exactly like a fraction. Rate – are used to compare different kinds of quantities. For example, miles/minute. Proportion - a statement that 2 ratios or rates are equal. For example, 3/4 = 6/8. Properties Use cross products to determine whether proportions are true or false. Finding an unknown value “n” in a proportions 1) Set the cross products equal to each other. 2) Divide the number not multiplied by “n” by the number that is multiplied by “n”. Hints Be careful when writing ratios. A ratio of 12/7 is not the same as 7/12. Ratios are not written as mixed numbers. Always write them as proper or improper fractions. In the context of ratios, the word “per” means division. For example, miles per hour. When you properly set up your proportions, you should check that the numerators all have the same units. Also check the denominators to ensure that they have the same units as well. Math 300 M-G Chapter 5; Rev: Jan 2009 Page 8 of 8