Comparing Ratios with Rates and Prices
Video Lessons > Comparing Ratios with Rates and Prices
In this video lesson, we're going to learn about comparing ratios with rates and prices. This skill is particularly useful when making purchasing decisions, as it helps in comparing prices to find the better deal. By understanding how to set up ratios and convert them into unit rates or unit prices, we can make informed decisions in many real-life scenarios and word problems.
Let's look at the details of the lesson using examples of comparing prices and determining the faster runner.
Let's start by looking at a word problem that involves comparing prices to determine the better deal when shopping. At Super Shopper, you can buy six cans of soup for $5.40, while at All-mart, you can buy four cans for $3. To figure out which store offers the better deal, we'll compare the unit price at each store.
Now, let's consider another example involving comparing running speeds. Jalen can run 60 meters in 9 seconds, and Kayla can run 80 meters in 12 seconds. We'll use ratios and unit rates to compare their speeds and determine the faster runner.
In this video lesson, we learned that when comparing values, setting up ratios as fractions and converting them to unit rates or unit prices is a valuable method. This approach enables us to make informed decisions when determining the better deal, faster runner, or any other comparative scenario presented in word problems. By understanding the concept of ratios and their application in rates and prices, we can enhance our problem-solving skills and make more informed decisions in various real-life situations.
Try this practice activity to see what you learned. Click on the correct answer.
In this video lesson, we're going to learn how to compare ratios that have rates and prices. And this actually comes in handy a lot when you're going out shopping and you want to compare prices to see which deal is better.
First we're going to look at a word problem that helps us to figure out the best deal when we're shopping. At Super Shopper, you can buy six cans of soup for $5.40. You can buy the same kind of soup at All-mart for $3 for four cans. Which is the better deal?
Well, to compare these prices and see which one is the better deal, it would be helpful to break it down and see the cost for one can. In other words, if we can figure out the unit price at each store, we'll be able to tell which store has the better deal.
So let's look at the information that we have, we know that Super Shopper has six cans of soup for $5.40, All-mart has $3 for four cans. So we'll need to set those up as ratios in order for us to find the unit price. So at Super Shopper, we can set that up as a fraction as $5.40 over six cans.
And remember, when we're working with money and we set up a ratio, we want it to be in the numerator. And now we can use division to figure out the unit rate. So we'll do five dollars forty cents divided by six, which equals zero point 90 or $0.90. So that tells us that at Super Shopper it's ninety cents per can.
And at All-mart we have $3 for four cans. So as a fraction, that's $3 over four cans keeping the money at the numerator. And we can use division. Three divided by four will equal zero point 75 or seventy five cents per can.
And of course, when we're shopping, the better deal means the lower price. So since All-mart is 0.75 per can, that means that All-mart is the better deal because it has a lower unit price.
And here's our second example. Jalen can run 60 meters in 9 seconds, and Kayla can run 80 meters in 12 seconds. Who is the faster runner? If we set up a ratio using how far they run for how many seconds, we can convert that to a unit rate to compare their speeds and see who runs faster.
So for Jalen, we have 60 meters in 9 seconds, and for Kayla we have 80 meters in 12 seconds. And when we set up these ratios, since one of our values involves time, we want that value to be in the denominator. So for Jalen, we'll have 60 meters over 9 seconds, keeping the seconds in the denominator. And we can convert this to a unit rate using division. 60 divided by nine gives us 6.67 when we round it off. So we can say the Jalen runs 6.67 meters/second.
For Kayla we have 80 meters over 12 seconds. 80 divided by twelve equals 6.67. So Kayla also runs at 6.7 meters/second. So we have the same speed for both runners. So we will say that neither runner is faster because Jalen and Kayla run at the same rate.
So remember, when you want to compare values, you can set up a ratio as a fraction and then convert them to a unit rate or a unit price if you're dealing with money. And then you can compare those two unit rates or unit prices to see which one is the better deal or faster runner or whatever you're looking for, depending on the word problem.
Related Standard: Common Core 7.RP.A.2
Hi, I'm Mia!
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