Determining Equivalent Ratios 04:19 minutes

Video Transcript

Transcript Determining Equivalent Ratios

While playing around with some weird science stuff in his dad’s home laboratory, Junior Moranis sort of...might have...maybe...shrunk his little sister. With his mom coming home soon, Junior Moranis notices a growth ray conveniently hanging on the wall . But before he fires it at his sister, he decides to try it out to determine if it maintains equivalent ratios. You already know that a ratio is the relationship between two quantities, which we can call 'a' and 'b'. And you also know there are three ways to write a ratio: as a fraction with a colon or as numbers separated by the word “to.” We can also put this information in a table of equivalent ratios. Let's take this cereal bowl as an example. It has a diameter of 8 inches and a height of 3 inches. So we can say the diameter to height ratio is 8 to 3. If the growth ray maintains equivalent ratios, no matter how big we increase the size of the cereal bowl, this ratio will stay the same. Let's put the cereal bowl dimensions in a table so we can see which other ratios are equivalent to 8 to 3. Just like with equivalent fractions, equivalent ratios can be found by multiplying both numbers by the same value. So, if we double the diameter and height, we get a ratio of 16 to 6. We know the ratios are consistent because 8 thirds and 16 sixths are equivalent fractions. Let’s fill in the rest of the table with a few more ratios. Multiply both 8 and 3 by 3 to get the equivalent ratio 24 to 9. Multiply by 4 to get 32 to 12, and so on. No matter how big we make the cereal bowl, the diameter to height ratio can be simplified to 8 to 3. We can also use equivalent ratios to find missing information. This hair dryer has a 9-inch nozzle and a 5-inch handle. If we use the growth ray to increase the size of the nozzle to 36-inches, how long will the handle be? Just like before, we can use equivalent fractions to fill in the ratio table. Multiply both 9 and 5 by a value of 2 to get the equivalent ratio 18 to 10, then multiply 9 and 5 by a value of 3 to get the equivalent ratio of 27 to 15. We can fill in the final row of the table by multiplying the original ratio of 9 to 5 by a value of 4, which gives us the equivalent ratio of 36 to 20. If we look here, we can see that when the nozzle is 36-inches long, the handle will be 20-inches long. This humongous hair dryer is much bigger than before, but the ratio of the nozzle to the handle has stayed the same. To review... A ratio is a comparison of two different quantities. A table can be used to list pairs of numbers that form equivalent ratios. You can tell that two ratios are equivalent if they also are equal fractions. You can use equivalent ratios to solve real-world (and not so real-world) problems. Now that Junior Moranis is sure the growth ray works, he’s ready to try it out on his sister. Oh no! Look out! It may be fun to play around with math, but that's why you don’t mess with science.