8.3 SOLVING PROBLEMS WITH PROPORTIONS Essential Question: When should I reason proportionally?

EQUIVALENT RATIOS Using the ratio 16 : 20, write four equivalent ratios (two scaling up, two scaling down )

PROPORTION  In a proportion the units must be in the same order in both ratios!  A proportion is a statement that two ratios or rates are equivalent.

USING PROPORTIONS TO SOLVE PROBLEMS 1.Write the given rate or ratio (using labels) 2.Set up a proportion (using the same order) 3.Solve for x (the missing piece of information) 4.Check your answer for reasonableness

EXAMPLE: USING PROPORTIONS TO PREDICT The PTA is ordering pizza for their next meeting. They plan to order 2 cheese pizzas for every 3 pepperoni pizzas they order. How many cheese pizzas will they order if they order 15 pepperoni pizzas?

EXAMPLE: USING UNIT RATES TO SOLVE You can also use equivalent rates to solve proportions. Finding a unit rate may help you write equivalent rates. Ms. Reinhold's sprinkler system has 9 stations that water all the parts of her front and back lawn. Each station runs for an equal amount of time. If it takes 48 minutes for the first 4 stations to water, how long does it take to water all parts of her lawn?

USING PROPORTIONAL RELATIONSHIPS TO FIND DISTANCE ON A MAP  A scale drawing is a drawing of a real object that is proportionally smaller or larger than the real object.  A scale factor is a ratio that describes how much smaller or larger the scale drawing is than the real object. A map is a scale drawing. The measurements on a map are in proportion to the actual distance. If 1 inch on a map equals 2 miles actual distance, the scale factor is 2 miles/1 inch

EXAMPLE: DISTANCE ON A MAP The distance between Sandville and Lewiston is shown on the map. What is the actual distance between the towns? SCALE REAL =