5-1 Objective: Solving proportions

A ratio is the comparison of two numbers written as a fraction. An equation in which two ratios are equal is called a proportion. A proportion can be written using colon notation like this a:b::c:d Or as the more recognizable (and useable) equivalence of two fractions.

Proportions To set up a proportion think part/whole part ______ part = whole whole If you can travel 120 miles on 6 gallons of gas, how far can you drive on 8 gallons of gas? (6)gas (8)gas ______ ______ 6x=960 x=160 = 120miles (x) miles

RATIOS & PROPORTIONS Are the following proportions? FALSE – Not a proportion FALSE – Not a proportion TRUE – this is a proportion TRUE – this is a proportion

RATIOS & PROPORTIONS Find the missing numbers to make the following proportions. 10 10 9 9

5-2 Objective: Solve proportions involving scale drawings and models

SCALE DRAWINGS A scale drawing is a drawing of an object with dimensions proportional to those of the actual object. To find lengths from scale drawings, set up and solve proportions.

SCALE DRAWINGS USING PROPORTIONS EXAMPLE#1: ¼ in = 5 ft is a scale for a rock band’s concert stage. A. The scale length of the drum stand is 1 in. What is the actual length of the drum stand? Cross multiply. Divide by .25 .25 .25

SCALE DRAWINGS USING PROPORTIONS Given a scale of .5 in = 4 ft, find the actual length for each scale length given. .5 .5 .5 .5

5-3 Objective: Solve problems by using the percent equations

PERCENTS & DECIMALS Percent (%) means per hundred. To change a decimal to a percent Multiply the decimal by 100 Write a percent sign after it Multiply the decimal by 100 (move the decimal point 2 places to the right) Write a percent sign after it

To change a percent to a decimal Divide the percent by 100 Omit the percent sign Divide the percent by 100 (move decimal 2 places to the left) Omit the percent sign

PERCENTS AND DECIMALS Convert the following decimals to percents: 44.5% A. 0.15 15% 1.5% F. 0.1111 11.11% B. 0.015 0.5% 62.5% G. 0.005 C. 0.625 104.2% H. 1.042 D. 0.9 90%

PERCENTS AND DECIMALS Convert the following percents to decimals: 0.015 A. 23.45% 0.2345 0.25 F. 35% 0.35 B. 25% 0.00005 0.125 G. 0.005% C. 12.5% 3.1 H. 310% D. 45% 0.45

The percent equation P r = 100 B Percent r (percentage) = 100 Base

Figuring out what goes where? Remember is/of “is” will always be “P” “of” will always be “B” What number is 15% of 10 What percent of 60 is 3 P 3 r r = = 100 100 10 60