Using Unit Rates <ul><li>Unit Rates : a rate with a denominator of 1) </li></ul><ul><li>Ratio : a comparison of two numbers by division. </li></ul><ul><li>Rate : the ratio of a to b if a and b are measured in different units. </li></ul>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? $.72 ounces 16 oz = $.045 =4.5 ¢ ????¢/oz 64 oz $1.60 ???? ¢/oz 32 oz $1.20 4.5 ¢/oz 16 oz $.72 Cost/Oz Volume Price Price of Apple Juice
Unit Rates and Conversions…. <ul><li>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 . </li></ul><ul><li>To change one unit of measure to another, you can use rates that equal 1. For Example: </li></ul>7 h= 7 h 1 60 min 1 h = 420 min Divide the common unit, which is hours (h), The result is minutes. 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….. <ul><li>Try: A sloth travels at 0.15 MPH. Convert this speed into Feet-Per-Minute. </li></ul>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……
Solving Proportions…. <ul><li>A proportion is an equation that states two rations are equal. </li></ul>a c = b d For this proportion, a and d are the extremes of the proportion , and b and c are the means of the proportion . 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… The products of ad and bc are the cross products of the proportion a c b d =
Solving Multi-Step Proportions <ul><li>To solve a proportion with variable expressions with more than one term, you will use cross products and the Distributive Property. </li></ul>
Chapter 4, Section 2 Proportions and Similar Figures.
Finding the Length of a Side <ul><li>In the Figure below, ABC ~ DFE . Find DE . </li></ul>C A B 21 cm 18 cm 15 cm E D F x 10 cm
Applying Similarity <ul><li>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? </li></ul>You can use proportions to find dimensions of objects that are difficult to measure directly…
Finding Distances on Maps <ul><li>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. </li></ul>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?
Chapter 4, Section 3 Proportions and Percent Equations
Finding the Percent… <ul><li>Remember: a percent is a ratio that compares a number to 100. </li></ul>What percent of 80 is 18?
Finding the Part… <ul><li>You can use a proportion to find the part (is) or the whole (of) in a percent problem… </li></ul>Find 75% of 320.
Finding the Whole…. <ul><li>Surface water accounts for 77.6% of our countries total water supply. The surface water supply is about 264.4 billion gallons per day. Find the total water supply. </li></ul>
Finding the Whole… <ul><li>Try: Carlos worked 31.5 hours at a hospital as a volunteer. This represents 87.5% of his school’s requirement for community service. How many hours does his school require for community service? </li></ul>
Using a Percent Equation… <ul><li>What percent of 170 is 68? </li></ul>You can also solve a percent problem by translating the words into an equation.
Percents Greater than 100% and Less than 1% <ul><li>a. What percent of 90 is 135? </li></ul><ul><li>b. What is .48% of 250? </li></ul>
Using Estimation… <ul><li>You can estimate some percents using fractions. For example, if you wanted to find 26.1% of a number, you could multiply ¼ times the number to estimate the answer. </li></ul>Percents and Fractional Equivalents. 33.3 Percent 1/4 1/5 1/10 1/20 Fraction 25% 20% 10% 5% Percent