1. Ratios and Proportions
2-6 Notes for Algebra 1
Ratios and Proportions

2. Ratio
A comparison of 2 numbers by division. 𝑎 𝑏 , 𝑎 to 𝑏 𝑎:𝑏

3. Proportion
An equation stating that 2 ratios are equal. 𝑎 𝑏 = 𝑐 𝑑 a:b=c:d 𝑎𝑑=𝑏𝑐 Extremes equals means First term times last term equals product of the middle terms

4. Example 1 pg. 111 Determine whether ratios are Equivalent
1.) Determine whether and are equivalent ratios. Write yes or no. Justify your answer.

5. Example 1 pg. 111 Determine whether ratios are Equivalent
1.) Determine whether 7 8 and are equivalent ratios. Write yes or no. Justify your answer. Yes the ratios are equivalent when expressed in simplest form.

6. Example 2 pg. 112 Cross Products
Use cross products to determine whether each pair of ratios forms a proportion. 1.) = ) = 16 20

7. Example 2 pg. 112 Cross Products
Use cross products to determine whether each pair of ratios forms a proportion. 1.) = Not a proportion 2.) = Yes a proportion

8. Example 3 pg. 113 Solve a Proportion
Solve each proportion. If necessary, round to the nearest hundredth. 1.) 𝑛 12 = ) 𝑥+4 12 = 3 4

9. Example 3 pg. 113 Solve a Proportion
Solve each proportion. If necessary, round to the nearest hundredth. 1.) 𝑛 12 = 3 8 𝑛=4.5 2.) 𝑥+4 12 = 3 4 𝑥=5

10. Rate
A ratio of two measurements having different units of measure.

11. Unit rate
A rate that tells how many of one item is being compared to 1 of another item.

12. Example 4 pg. 113 Real World example
1.) BICYCLING The gear on a bicycle is 8:5. This means that for every 8 turns of the pedals, the wheel turns 5 times. Suppose the bicycle wheel turns about 2435 times during a trip. How many times would you have to crank the pedals during the trip?

13. Example 4 pg. 113 Real World example
1.) BICYCLING The gear on a bicycle is 8:5. This means that for every 8 turns of the pedals, the wheel turns 5 times. Suppose the bicycle wheel turns about 2435 times during a trip. How many times would you have to crank the pedals during the trip? About 3896 times.

14. Scale/Scale Model
A rate called a scale is used to make a Scale Model of something too large or too small to be convenient at actual size.

15. Example 5 pg. 114 Real World Example
1.) MAP In a road atlas, the scale for the map of Connecticut is 5 𝑖𝑛𝑐ℎ𝑒𝑠=41 𝑚𝑖𝑙𝑒𝑠. What is the distance in miles represented by 𝑖𝑛𝑐ℎ𝑒𝑠 on the map?

16. Example 5 pg. 114 Real World Example
1.) MAP In a road atlas, the scale for the map of Connecticut is 5 𝑖𝑛𝑐ℎ𝑒𝑠=41 𝑚𝑖𝑙𝑒𝑠. What is the distance in miles represented by 𝑖𝑛𝑐ℎ𝑒𝑠 on the map? 𝑚𝑖𝑙𝑒𝑠.

17. 2-6 pg o, 40-44, 51-69(x3)