Ratio and Proportion Ms. Crusenberry 9-2013

Vocabulary Ratio – comparison of two numbers using division Comparison – examining two numbers to see which is larger Fractional Form – expressed as a fraction

A Ratio as a Fraction Example: 9 to 12 9 3 12 = 4 **always simplify

Practice 12 to 20 18 to 21 8 to 19 125 to 250

Answers 3/5 6/7 8/19 1/2

Writing a Ratio from Words Example: 15 minutes to 1 hour 15 to 60 = 5 to 12 15/60 = 5/12

Practice 150 miles to 4 hours 4 hits for 6 times at bat 1 year to 8 months 1 fifty-cent piece to 1 dime

Answers 75/2 2/3 3/2 5/1

Identifying Proportions A proportion is two equal ratios Example: 5 10 80 8 16 80 **cross multiply first numerator by the second denominator and put that answer on the left side – then multiply the first denominator by the second numerator and put that answer on the right side. If they equal, then they are proportionate.

Practice 10/16 5/8 4/8 2/3 5/9 15/27 **1 1/2/3 3/6

Answers =

Solving Proportions Example: 8 = 4 n 6 Cross multiply to get: 48 = 4n Divide each side by 4 4 4 12 = n

Practice 12/n = 20/25 2/3 = 16/n 5/n = 10/16 **12/8 = 4 ½ /n

Answers N = 15 N = 24 N = 8 N = 3

Problem Solving Gorp is 5 parts peanuts and 2 parts raisins. How many pounds of peanuts should be mixed with one-half pound of raisins? Peach paint is 1 part yellow to 3 parts red. How much yellow should be mixed with 4 quarts of red?

Continued On a map, 1 inch equals 15 miles. How many miles apart are two towns that are 6.4 inches apart on the map? Your car gets 32 miles to one gallon of gas. How much gas will you use on a 475 mile trip?

Answers p/r = p/r; 5/2 = .5/x; 5x = 1; x = .2 y/r = y/r; 1/3 = x/4; 4 = 3x; x = 1 1/3 or 1.33 i/m = i/m; 1/15 = 6.4/x; 96 = x m/g = m/g; 32/1 = 475/x; 32x = 475; x = 14.84