That’s Not Fair!!! Or, 7.5.2 Proportions

Is it fair? Basically, proportions tell us if rates or ratios are equal, fair Rate example: One day in gym you have to run 2 laps in 5 minutes. The next day you have to run 3 laps in 7 minutes. Are the rates for the 2 days equal? Ratio example: One day your mom says your brother can have 3 mini cookies for every 2 scoops of vegetables he eats. The next day she says you can have 4 mini cookies for every 3 scoops of vegetables you eat. Is this ratio between you and your brother fair?

Give it a try Do 6/4 and 8/12 make a proportion? In other words, are these fractions proportional? Compare them in simplest form: 6/4 = 3/2 and 8/12 = 2/3 3/2 is NOT proportional with 2/3; the two fractions do NOT make a proportion

One more time Compare each ratio X to Y in simplest form. 1/2 1 3/2 2 Y 3 6 9 12 Compare each ratio X to Y in simplest form. ½ / 3 = 1/6 1 / 6 = 1/6 3/2 / 9 = 1/6 2 / 12 = 1/6 The ratios ARE equivalent

Do these ratios form a proportion? 1/2 and 5/10 YES 4/6 and 18/24 NO 10/3 and 5/6 NO 25/20 and 15/12 YES

Cross Products Pretend A/B represents 2/3 and C/D represents 6/9 2/3 = 6/9 A/B = C/D 2 x 9 =18 3 x 6 = 18 AD = BC Cross Products = the products of AD and BC Cross Products Property = the cross products of a proportion are equal Psst…this is a SHORT CUT to find out if ratios are equal

Suggested Practice 7.5.2 Proportions Pg. 174 - 175