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# Algebraic Ratios

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### Algebraic Ratios

1. 1. ALGEBRAIC RATIOS
2. 2. <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>
3. 3. 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.
4. 4. AIM: <ul><li>What is a ratio? </li></ul>
5. 5. 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?
6. 6. 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>
7. 7. 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
8. 8. 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.
9. 9. 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
10. 10. 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>
11. 11. 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>
12. 12. 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.
13. 13. PRACTICE PROBLEM # 1 <ul><li>It takes Max ¼ of an hour to ride his bike to school, and it takes Riley 21 minutes to walk to school. </li></ul><ul><li>Write a ratio comparing Max’s time to Riley’s time. </li></ul>
14. 14. PRACTICE PROBLEM #2 <ul><li>A TV normally sells for \$400 is on sale for \$340. The tax on the reduced price is \$23.80, so the total cost with tax is \$363.80. </li></ul><ul><li>What is the discount rate? </li></ul><ul><li>What is the tax rate? </li></ul><ul><li>Including tax, how much would a customer save by buying the TV on sale? </li></ul>
15. 15. 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>
16. 16. 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>
17. 17. CHALLENGE QUESTION <ul><li>Suppose a team has won 15 of it’s first 38 games. How many games must it win in a row to bring its winning percentage to at least .500? </li></ul>