2. Ratios II Adding to what we know…………

3. Previously

4. Today? We will use bar diagrams to compare and analyze data. We will learn identify equivalent ratios and equivalent ratio pairs.

5. Karla wants to divide her 30 flowers into two groups, so that the ratio is 2 to 3. Let’s use bar diagrams to illustrate the parts of this ratio. part2 3 whole30 5 ??? There are 5 groups of 6 in the total, so there are 6 in each of the parts, too! 6 12 18 6 6 6 Discuss this within your group. Compare each illustration for a thorough understanding of how these values come together in different illustrations!

6. You have 28 cans of soda that you will distribute in a ratio of 3 to 4. Complete this section on your own. Discuss this with your group as you work. We will check this together in a few minutes. part 3 4 whole 28 7 There are 7 groups of 4 in the total, so there are 4 in each of the parts, too! 12 16 4 4 4 4 4 Does anyone prefer one representation over the other? If so, why????

7. Equivalent Ratios In our previous lesson, we used scaling to write equivalent ratios. We divided by common factors, or multiplied values by the same number. In some cases you could even scale down before scaling forward! The fact that these were equal was obvious. This is not always the case.

8. Checking for equal ratios You can easily check to see if two ratios are equal by multiplying and comparing the cross-products. We will use this process to see if these ratios are equivalent. 24 = 20 = 24 25 ≠ 12 = 36 32 ≠ 2 x 7 ends in a 4. 1 x 8 ends in an 8. NO ≠

9. Challenge: Use Ratio Reasoning to Solve A fruit basket contains four kinds of fruit, totaling 3 dozen pieces. The basket has 7 bananas, 11 oranges, and 12 apples. The rest are pears. How many are pears? If you want to duplicate this basket how many of each type of fruit would you need if you have 44 oranges? bananas 7 oranges 11 apples 12 pears total 36 7 + 11 + 12 + n = 36 30 + n = 36 6 44 28 48 24 144

10. Warm Up: As pictures appear, you will be asked to write a specific type of ratio. Jot them down somewhere in your notes……. Part to part cylinders:triangles 4 to 5 9:5 whole to part shapes:triangles Part to whole Cylinders to total 4:9 If two more cylinders were added, what would be the ratio of triangles to total shapes? 5:11

11. 7 525 35 = As you can see, ratios are similar to fractions. 7 5 We walk like Fractions. We can multiply or divide them to create equivalent ratios. 7 525 35 We talk like fractions 25 35 We even Taste like fractions.... but we are NOT fractions! 7 5 2 5 1

12. We Are Ratios! Comparison of numbers by division!!