In this lesson, let’s learn about equivalent ratios and rates. We’ll do three problems. The first one wants us to write three equivalent ratios to compare the number of red stars to the number of orange stars. A ratio to compare the number of red stars would be, well if I counted the number of red stars and divided it or compared it to the number of oranges stars, what do we have? Number of red stars is four; number of orange stars is two, so the ratio is 4/2 or 4:2. What I could do is draw or bring out equivalent ratios. The way we bring out equivalent ratios is I can multiply the numerator and the denominator by the same number, 4×2 gives me 8, 2×2 gives me 4. I could also divide the numerator and denominator by the same number. 4÷2 gives me 2, 2÷2 gives me one. The equivalent ratios are, 4/2 is the original, 8/4 2/1 are all equivalent ratios. Remember the key thing, if you take a ratio and multiply or divide by the same number as long as we apply to top and the bottom. Let’s use a table to do the second problem which is use a table to find three equivalent ratios of 3/5. What I am going to do is draw a table right and for each value of the table, let’s multiply it by a number. I can multiply it by any number. 3×2=6, 3×3=9, 3×4=12, 3×5=15, similarly denominator 5×2 10, 5×3=15, 5×4=20, 5×5=25, the equivalent ratios of 3/5 are 6/10, 9/15, 12/20, 15/25, each one of these is an equivalent ratio. Third problem, Leo runs laps around the track. The table shows how long it takes him to run the different number of laps. Three laps in 15 minutes, nine laps in 45 minutes etcetera. Predict how long it will take for him to 11 laps. We have two things. Let’s put 11 here. We know the answer should be between 45 and 60. Here is how we solve it. We know that the ratio of number of laps to the time taken is 3/15 or 9/45, any of the values. What we can do is figure out the rate which is for one lap. If three laps in 15 minutes right, if I divide both top and bottom by three, what do I get? One lap in 5 minutes or the ratio is 1/5. Once we have the rate for one lap, the amount of time taken for 11 laps is I can take the rate and multiply it by the number of laps that gives me 1/5×11, top and bottom, so 11 laps will take me 5×11 is 55 minutes. How long will it take to run 11 laps? 55 minutes.