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Math 64 6.1 "Ratios and Rates" Bibiana Lopez Riverside City College July 2010 (RCC) 6.1 July 2010 1 / 14 Objectives: * Write ratios and rates as fractions. * Find unit rates and unit prices. (RCC) 6.1 July 2010 2 / 14 Writing Ratios as Fractions A ratio is the quotient of two quantities. A ratio, in fact, is no di¤erent from a fraction, except that a ratio is sometimes written using notation other than fractional notation. For example, the ratio of 2 to 3 can be written as 1 to 2 or 12 (fractional notation) or 1 : 2 (colon notation) (RCC) 6.1 July 2010 3 / 14 Writing Ratios as Fractions A ratio is the quotient of two quantities. A ratio, in fact, is no di¤erent from a fraction, except that a ratio is sometimes written using notation other than fractional notation. For example, the ratio of 2 to 3 can be written as 1 to 2 or 12 (fractional notation) or 1 : 2 (colon notation) In this section, we write ratios using fractional notation. If the fraction happens to be an improper fraction, do not write the fraction as a mixed number. Why? The mixed number form is not a ratio or quotient of two quantities. (RCC) 6.1 July 2010 3 / 14 Writing Ratios as Fractions A ratio is the quotient of two quantities. A ratio, in fact, is no di¤erent from a fraction, except that a ratio is sometimes written using notation other than fractional notation. For example, the ratio of 2 to 3 can be written as 1 to 2 or 12 (fractional notation) or 1 : 2 (colon notation) In this section, we write ratios using fractional notation. If the fraction happens to be an improper fraction, do not write the fraction as a mixed number. Why? The mixed number form is not a ratio or quotient of two quantities. If a ratio contains decimal numbers or mixed numbers, we simplify by writing the ratio as a ratio of whole numbers. (RCC) 6.1 July 2010 3 / 14 Writing Ratios as Fractions Writing a Ratio as a Fraction: The order of the quantities is important when writing ratios. To write a ratio as a fraction, write the …rst number of the ratio as the numerator of the fraction and the second number as the denominator. (RCC) 6.1 July 2010 4 / 14 Writing Ratios as Fractions Example 1: (Writing ratios as fractions) Write each ratio as a ratio of whole numbers using fractional notation. Write the fraction in simplest form. a) 4.63 to 8.21 b) 8.1 to 10 (RCC) 6.1 July 2010 5 / 14 Writing Ratios as Fractions d) 3 13 days to 4 16 days c) 120 miles to 80 miles (RCC) 6.1 July 2010 6 / 14 Writing Ratios as Fractions Example 2: (Application) Find the ratio of the length to the width of a regulation size basketball court. (RCC) 6.1 July 2010 7 / 14 Writing Ratios as Fractions Example 3: (Application) Find the ratio of the longest side to the perimeter of the right-triangularshaped billboard. (RCC) 6.1 July 2010 8 / 14 Writing Rates as Fractions A special type of ratio is a rate. Rates are used to compare di¤erent kinds of quantities. For example, 3 miles 1 mile = (In simplest form) 33 minutes 11 minutes (RCC) 6.1 July 2010 9 / 14 Writing Ratios as Fractions Example 4: (Writing rates as fractions) Write each rate as a fraction in simplest form. a) 4 inches of rain in 18 hours b) 295 miles on 15 gallons of gasoline (RCC) 6.1 July 2010 10 / 14 Finding Unit Rates A unit rate is a rate with a denominator of 1. Writing a Rate as a Unit Rate: To write a rate as a unit rate, divide the numerator of the rate by the denominator. (RCC) 6.1 July 2010 11 / 14 Finding Unit Rates Example 5: (Finding unit rates) Write each rate as a unit rate. a) A hummingbird moves its wings at a rate of 5400 wingbeats a minute. Write this rate in wingbeats per second. b) 400,000 library books for 8000 students. (RCC) 6.1 July 2010 12 / 14 Finding Unit Prices Rate are used extensively in sports, business, medicine, and science. One of the most common uses of rates is in consumer economics. When a unit rate is "money per item," it is also called a unit price. unit price = (RCC) price number of units 6.1 July 2010 13 / 14 Finding Unit Prices Example 6: (Finding unit price) Find each unit price. a) $57.50 for 5 compact disks (RCC) b) $0.87 for 3 apples 6.1 July 2010 14 / 14