Using Unit Rates Conversions Solving Proportions Applying Similarity

Using Unit Rates Price of Apple Juice Price Volume Cost/Oz $.72 16 oz $1.20 32 oz ????¢/oz $1.60 64 oz The table at the right gives prices for different sizes of the same brand of apple juice. Find the unit rate (cost/oz) for the 32 oz and the 64 oz size. How?: divide cost by oz, and move the decimal to the right 2 places cost Now….What size is best economical choice? Unit Rates: a rate with a denominator of 1) Ratio: a comparison of two numbers by division. Rate: the ratio of a to b if a and b are measured in different units. $.72 = $.045 =4.5¢ ounces 16 oz

Unit Rates and Conversions…. When converting from one unit to another, as in hours to minutes or minutes to hours, you must decide which conversion factor will produce the appropriate unit. This process is called unit analysis. To change one unit of measure to another, you can use rates that equal 1. For Example: 7 h 60 min Divide the common unit, which is hours (h), The result is minutes. = 420 min 7 h= 1 1 h Try: You and your friends go on a road trip and drive for 5 Hours. How many minutes were you driving? Bonus: If you were driving at an average speed of 63 MPH, How many miles did you travel?

Converting Rates….. A cheetah ran 300 feet in 2.92 seconds. What was the cheetah’s speed in MPH? You need to convert feet to miles, and seconds to hours…… Try: A sloth travels at 0.15 MPH. Convert this speed into Feet-Per-Minute.

Using the Multiplication Property of Equality: Solving Proportions…. A proportion is an equation that states two rations are equal. a c For this proportion, a and d are the extremes of the proportion, and b and c are the means of the proportion. = b d Proportions may also be written like this: a : b = c : d Using the Multiplication Property of Equality: t 5 = 9 6 Try: 18 m = 50 15

Using Cross Products… a c = b d The products of ad and bc are the cross products of the proportion a c = b d

Solving Multi-Step Proportions To solve a proportion with variable expressions with more than one term, you will use cross products and the Distributive Property.

Finding the Length of a Side In the Figure below, ABC ~ DFE. Find DE. E C x 18 cm 21 cm D F 10 cm A B 15 cm

Applying Similarity You can use proportions to find dimensions of objects that are difficult to measure directly… EX: A tree Casts a shadow 7.5 feet long. A woman 5ft tall casts a shadow 3 feet long. How tall is the tree?

Finding Distances on Maps The scale of a map is 1 inch = 10 miles. Aprx How far is it from Valkaria to Wabasso if the two cities are 1.75 inches apart on the map? A scale drawing is similar to an actual object or place. The ratio of a distance in the drawing to the corresponding actual distance is the scale of the drawing.