advertisement

Lesson 7-1: Ratios and Proportions Learning Goal: Write and solve basic and extended ratios Wastepaper Basketball • 2 volunteers shoot 10 times • 1 volunteer to record successes and failures Analysis of basketball stats • Write ratio of successes : failures • If the ratio stays true and 50 shots are made, how many successes and failures can be expected? Analysis of basketball stats cont. • Write ratio of successes : attempts • How many attempts should it take you to make 12 shots? Notes: Ratios and Proportions • Ratio – a comparison of two quantities by division – Can be written a : b, a to b, or a/b – Usually write a and b with the same units so you can simplify Example 1 A bonsai tree is 18in wide and stands 2 ft tall. What is the ratio of the width of the bonsai to its height? Example 2 Members of the school band are buying pots of tulips and pots of daffodils to sell at their fundraiser. They plan to buy 120 pots of flowers. The ratio of tulips to daffodils will be 2 : 3. How many pots of each type of flower should they buy? Notes: Extended Ratios • Extended Ratio – compares 3 or more numbers – a:b:c • Example 3: The lengths of the sides of a triangle are in the extended ratio 4 : 7 : 9. The perimeter is 60cm. What are the lengths of the sides? Proportions • Proportion – an equation that sets 2 ratios equal to each other • Extremes– first and last numbers • Means – middle 2 numbers Example 4: Solve each proportion 9=a 2 14 15 = 3 m+1 m Does order matter? • If you flip a proportion (the reciprocal) is it still true? Yes! • If you switch the means is the proportion still true? Yes! • If you add one to both sides of the proportion is the proportion still true? Yes! Equivalent Proportions 7-1 Homework • Heading: 7-1 pg 459 #13, 14, 16, 19, 20, 22, 23, 32, 38, 39 • Work must be shown to receive credit • Due Tuesday, February 10th