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Adv. Math Chapter 6 Review 6-1 Ratios • Ratio: a comparison of two numbers by division. Each number in a ratio is called a term. Example: 6 cups party mix to 2 cups pretzels • 3 ways to write a Ratio: in words- 6 to 2 with a symbol- 6:2 as a fraction- 6/2 6-1 Ratios: written in 3 ways A drama club sells 35 student tickets, 24 adult tickets, and 11 senior citizen tickets. Write each ratio in three ways. 1. Students to adults 35 to 24, 35:24, 35/24 2. Adults to senior citizen 24 to 11, 24:11, 24/11 3. Senior citizen to total number of tickets 11 to 70, 11:70, 11/70 6-1 Ratios: Writing Equal Ratios • Divide or multiply each term by the same number. 1. 6 to 18 sample: 3 to 9, 12 to 36, 1 to 3, etc. 2. 4/14 sample: 2/7, 8/28, 12/42, etc. 3. 8:10 sample: 4:5, 16:20, 80:100, etc. 6-1 Ratios in Simplest Form • To find simplest form divide by the GCF 1. 6/15 2/5 2. 40:30 4:3 3. 42 to 50 21 to 25 6-1 Ratios: Find the Value Complete to make ratios equal: 1. 6 to 9, ___ to 3 2 2. 18/3, 54/___ 9 3. ___:96, 4:6 64 6-2 Unit Rates • A rate is a ratio that compares two quantities measured in different units. Example: the rate 150 heartbeats/2minutes compares heartbeats to minutes • A unit rate is the rate for one unit of a given quantity. Denominator is always 1! • Example: 150 heartbeats/2 minutes 150÷2= 75 So the unit rate is 75 heartbeats per minute 6-2 Unit Rates Find the unit rate for the following: 1. 210 heartbeats in 3 minutes 70 heartbeats per minutes 2. $19.50 for 3 T-shirts $6.50 3. 45 miles in 5 hours 9 mph 6-2 Unit Rates Write the unit rate as a ratio. Then find an equal ratio: 1. The cost is $6.75 for 1 t-shirt. Find the cost of 8 t-shirts. $6.75/1t-shirt = $54/8t-shirts 2. There are 3 feet in 1 yard. Find the number of feet in 15 yards. 3ft/1yd = 45ft/15yd 6-2 Unit Rates • Tell which unit rate is greater: 1. Krysta earns $44.55 in 9 hours. Megan earns $51 in 12 hours. Answer: $44.55 in 9 hours 2. Austin reads 60 pages in 2 hours. Tony reads 99 pages in 3 hours. Answer: 99 pages in 3 hours Proportions 6-3 • A proportion is an equation stating that two ratios are equal. • Example: ½ = 4/8 • Example: 27/18 = 9/6 Proportions 6-3 Do the ratios in each pair form a proportion? 1. 4/12 = 6/8 NO 2. 42/6 = 504/72 YES 3. 10/20 = 30/40 NO Proportions 6-3 • Find the value that completes each proportion. 1. 7/35 = 21/___ 105 2. 12/4 = ___/28 84 3. ___/190 = 3/114 5 • Using Cross Products 6-4 You can find the Cross Products of two ratios by multiplying the denominator of each ratio by the numerator of the other ratio • The . 1. 7/35 = 21/ n n = 105 2. 12/4 = r /28 r = 84 3. m /190 = 3/114 m=5