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DO NOW (not later): <ul><li>Compare the number of boys to girls in the class. </li></ul>
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<ul><li>The number of boys = </li></ul><ul><li>The number of girls = </li></ul><ul><li>If we compare boys to girls we get </li></ul><ul><li>___ boys to _____ girls. </li></ul>
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What do we call a comparison between two or more quantities? RATIO We just found the RATIO of boys to girls. Is the ratio of girls to boys the same ? No, when writing a ratio, ORDER matters.
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It’s Friday night and your friends are having a party…… <ul><li>The ratio of girls to guys is 2 to 12. </li></ul>Would you want to attend the party?
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How many basketballs to footballs are there? <ul><li>For every 4 basketballs there are 6 footballs. </li></ul><ul><li>The ratio is 4 to 6. </li></ul>
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What are some other ways we can write the ratio of basketball to footballs? <ul><li>4 to 6 </li></ul><ul><li>4 : 6 </li></ul><ul><li>4 </li></ul><ul><li>6 </li></ul>First quantity to Second quantity First quantity : Second quantity First quantity divided by the second quantity (as a fraction ). Every ratio can be written in 3 ways: Careful!! Order matters in a ratio. 4 to 6 Is NOT the same as 6 to 4
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Write the ratio of sandwiches to coke bottles 3 different ways. <ul><li>6:8 , 6 to 8, and 6 </li></ul><ul><ul><ul><ul><ul><li>8 </li></ul></ul></ul></ul></ul>Since 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.
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Equivalent Ratios <ul><li>Simplify the following ratios: </li></ul><ul><ul><li>4 to 8 </li></ul></ul><ul><ul><li>10 to 8 </li></ul></ul><ul><ul><li>8 to 10 </li></ul></ul>Step 1 – Write the ratio as a fraction Step 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 <ul><li>= 4 / 4 = 1 = 1 to 2 </li></ul><ul><li>8 8 / 4 2 </li></ul>GCF = 4
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Equivalent Ratios can be formed by multiplying the ratio by any number. <ul><li>For example, the ratio 2 : 3 can also be written as </li></ul><ul><ul><li>4 : 6 (multiply original ratio by by 2) </li></ul></ul><ul><ul><li>6 : 9 (multiply original ratio by by 3) </li></ul></ul><ul><ul><li>8 : 12 (multiply original ratio by by 4) </li></ul></ul><ul><ul><li>The ratio 2 : 3 can be expressed as </li></ul></ul><ul><ul><li>2x to 3x (multiply the original ratio by any number x ) </li></ul></ul>
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Compound Ratios <ul><li>A ratio that compares more than 2 quantities is called a compound ratio. </li></ul><ul><li>Example: </li></ul><ul><ul><li>A cake recipe says the ratio of cups of milk , sugar , and batter are 1 : 2 : 4 . </li></ul></ul><ul><ul><ul><li>This means that there is one cup of milk for every two cups of sugar and four cups of batter. </li></ul></ul></ul>
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A bag contains 18 yellow, blue, and red marbles. The ratio of yellow to blue to red marbles is 4 : 2 : 3 . <ul><li>Write the ratio of yellow to blue marbles in simplest form. </li></ul><ul><li>What is the ratio of yellow to red marbles? </li></ul><ul><li>How many yellow marbles are there? </li></ul>4 : 2 can be simplified to 2 : 1 4 : 3 Yellow : Blue : Red is 4 : 2 : 3 Since any multiple of this is an equivalent ratio, this can also be written as 4x : 2x: 3x Let 4x = yellow, 2x = blue , 3x = red 4x + 2x+ 3x = 18 9x = 18 X= 2 Since the question asks for yellow marbles, there are 4 x or 4 ( 2 ) = 8 yellow marbles.
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Practice problem # 1 <ul><li>(1) You have 100 different shirts. The ratio of blue to black shirts is 20 . </li></ul><ul><li>30 </li></ul><ul><li>a) Write the ratio of blue to black shirts 3 different ways. </li></ul><ul><li>b) Write the ratio in simplest form. </li></ul><ul><li>c) Explain what this ratio tells us. </li></ul><ul><li> d) How many black shirts do you have? </li></ul>
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Solution - # 1 <ul><li>You have 100 different shirts. The ratio of blue to black shirts is 20 / 30 </li></ul><ul><li>a) Write the ratio of blue to black shirts 3 different ways. </li></ul><ul><li>20 to 30 , 20 : 30, 20 </li></ul><ul><li> 30 </li></ul><ul><li>b) Write the ratio in simplest form. 2 </li></ul><ul><li> 3 </li></ul><ul><li>c) Explain what this ratio tells us. For every two blue shirts, there are 3 black shirts. </li></ul><ul><li>d) How many black shirts do you have? </li></ul><ul><li>2x + 3x = 100 </li></ul><ul><li>5x = 100 </li></ul><ul><li>x = 20 </li></ul><ul><li>There are 2 x black shirts so 2 ( 20 ) = 40 black shirts </li></ul>
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Practice Word Problems <ul><li>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. </li></ul><ul><li>Explain what this ratio tells us. </li></ul><ul><li>28 / 56 = 1 / 2 </li></ul><ul><li>The ratio of boys to girls is 1 to 2 </li></ul><ul><li>(2) For every 1 boy there are 2 girls at the party. </li></ul>
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Practice Word Problems <ul><li>Mindy has 72 candy bars. If the ratio of Mars to Snickers is 8:4, Find the number of each type of candy. </li></ul><ul><li>Explain what this ratio tell us. </li></ul>
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Challenge Question <ul><li>The perimeter of a rectangle is 500 feet. The ratio of the base and height is 3:2. What is the measure of the height? </li></ul>
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