5 It’s Friday night and your friends are having a party…… The ratio of girls to guys is 2 to 12.Would you want to attend the party?
6 How many basketballs to footballs are there? For every 4 basketballs there are 6 footballs.The ratio is 4 to 6.
7 What are some other ways we can write the ratio of basketball to footballs? Every ratio can be written in 3 ways:4 to 64 : 646First quantity to Second quantityCareful!!Order matters in a ratio.4 to 6Is NOT the same as6 to 4First quantity : Second quantityFirst quantity divided by the second quantity (as a fraction).
8 Write the ratio of sandwiches to coke bottles 3 different ways. 6:8 , 6 to 8, and 68Since a fraction can be simplified, We can simplify the ratio 6/8 to 3/4. The ratio of sandwiches to coke bottles can also be expressed as 3 : 4 or 3 to 4.In other words, ratios can be simplified to form equivalent ratios.
9 Equivalent Ratios Simplify the following ratios: 4 to 8 10 to 8 /GCF = 4Step 1 – Write the ratio as a fractionStep 2 – Simplify the fraction (Find the greatest common factor (GCF) of both numbers and divide the numerator and denominator by the GCF).Step 3 – Write the equivalent ratio in the same form as the question
10 The ratio 2 : 3 can be expressed as Equivalent Ratios can be formed by multiplying the ratio by any number.For example, the ratio 2 : 3 can also be written as4 : 6 (multiply original ratio by by 2)6 : 9 (multiply original ratio by by 3)8 : 12 (multiply original ratio by by 4)The ratio 2 : 3 can be expressed as2x to 3x (multiply the original ratio by any number x)
11 Compound RatiosA ratio that compares more than 2 quantities is called a compound ratio.Example:A cake recipe says the ratio of cups of milk, sugar, and batter are 1:2:4.This means that there is one cup of milk for every two cups of sugar and four cups of batter.
12 A bag contains 18 yellow, blue, and red marbles A bag contains 18 yellow, blue, and red marbles. The ratio of yellow to blue to red marbles is 4 : 2 : 3.Write the ratio of yellow to blue marbles in simplest form.What is the ratio of yellow to red marbles?How many yellow marbles are there?Yellow : Blue : Red is 4 : 2 : 3Since any multiple of this is an equivalent ratio, this can also be written as 4x : 2x: 3xLet 4x = yellow, 2x = blue , 3x = red4x + 2x+ 3x = 189x = 18X= 2Since the question asks for yellow marbles,there are 4x or 4 (2) = 8 yellow marbles.4 : 2 can be simplified to 2 : 14 : 3
13 Practice problem # 1(1) You have 100 different shirts. The ratio of blue to black shirts is30a) Write the ratio of blue to black shirts 3 different ways.b) Write the ratio in simplest form.c) Explain what this ratio tells us.d) How many black shirts do you have?
14 There are 2x black shirts so 2 (20) = 40 black shirts Solution - # You have 100 different shirts. The ratio of blue to black shirts is 20 / 30a) Write the ratio of blue to black shirts 3 different ways.20 to 30 , 20 : 30, 2030b) Write the ratio in simplest form. 23c) Explain what this ratio tells us. For every two blue shirts, there are 3 black shirts.d) How many black shirts do you have?2x + 3x = 1005x = 100x = 20There are 2x black shirts so 2 (20) = 40 black shirts
15 Practice Word Problems You go to a party where the ratio of boys to girls is 28 to 56. Express the ratio of boys to girls in simplest form.Explain what this ratio tells us.28 / 56 = 1 / 2The ratio of boys to girls is 1 to 2(2) For every 1 boy there are 2 girls at the party.
16 Practice Word Problems Mindy has 72 candy bars. If the ratio of Mars to Snickers is 8:4, Find the number of each type of candy.Explain what this ratio tell us.
17 Challenge QuestionThe perimeter of a rectangle is 500 feet. The ratio of the base and height is 3:2. What is the measure of the height?