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Adv. Math Chapter 6 Review

This chapter review covers the basics of ratios, writing ratios in different forms, finding unit rates, solving proportions, and using cross products. Learn how to compare quantities, express ratios in simplest form, and find missing values in proportions.

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Adv. Math Chapter 6 Review

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  1. Adv. Math Chapter 6 Review

  2. 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

  3. 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. • 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

  4. 6-1 Ratios: Writing Equal Ratios • Divide or multiply each term by the same number. • 6 to 18 sample: 3 to 9, 12 to 36, 1 to 3, etc. • 4/14 sample: 2/7, 8/28, 12/42, etc. • 8:10 sample: 4:5, 16:20, 80:100, etc.

  5. 6-1 Ratios in Simplest Form • To find simplest form divide by the GCF • 6/15 2/5 • 40:30 4:3 • 42 to 50 21 to 25

  6. 6-1 Ratios: Find the Value Complete to make ratios equal: • 6 to 9, ___ to 3 2 • 18/3, 54/___ 9 • ___:96, 4:6 64

  7. 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

  8. 6-2 Unit Rates Find the unit rate for the following: • 210 heartbeats in 3 minutes 70 heartbeats per minutes • $19.50 for 3 T-shirts $6.50 • 45 miles in 5 hours 9 mph

  9. 6-2 Unit Rates Write the unit rate as a ratio. Then find an equal ratio: • The cost is $6.75 for 1 t-shirt. Find the cost of 8 t-shirts. $6.75/1t-shirt = $54/8t-shirts • There are 3 feet in 1 yard. Find the number of feet in 15 yards. 3ft/1yd = 45ft/15yd

  10. 6-2 Unit Rates • Tell which unit rate is greater: • Krysta earns $44.55 in 9 hours. Megan earns $51 in 12 hours. Answer: $44.55 in 9 hours • Austin reads 60 pages in 2 hours. Tony reads 99 pages in 3 hours. Answer: 99 pages in 3 hours

  11. Proportions 6-3 • A proportion is an equation stating that two ratios are equal. • Example: ½ = 4/8 • Example: 27/18 = 9/6

  12. Proportions 6-3 Do the ratios in each pair form a proportion? • 4/12 = 6/8 NO • 42/6 = 504/72 YES • 10/20 = 30/40 NO

  13. Proportions 6-3 • Find the value that completes each proportion. • 7/35 = 21/___ 105 • 12/4 = ___/28 84 • ___/190 = 3/114 5

  14. 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 . • 7/35 = 21/ n n =105 • 12/4 = r /28 r =84 • m /190 = 3/114 m = 5

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