Get ready for 7th grade
Ratios represent the relationship between two quantities and can be visualized on a graph. When the ratio is constant, the points form a straight line, illustrating the connection between the quantities. Examples include bakers using flour, car wash charges, and earnings from shoveling snow.
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Let's look carefully at an example. Suppose a group of kids is invited to a party. Every kid is supposed to get two cookies each at the party. If four kids get invited, how many cookies would you have to make so that there are just enough cookies to give each child his or her two cookies? If you reply with the answer we can keep working through this.(13 votes)
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- [Instructor] We are told that a baker uses eight cups of flour to make one batch of muffins for his bakery. Complete the table for the given ratio. So they're saying that for every batch, he needs eight cups of flour or he needs eight cups of flour for every batch. So if you have two batches how many cups of flour would that be? Pause the video and try to figure it out. Well if he has twice as many batches, he's gonna have twice the number of cups of flour. So instead of eight, it would be 16 cups of flour. And if he had three times the number of batches, it would be three times the number of cups of flour. So instead of eight, it would be eight times three, or 24. Now down here, they say plot the ordered pairs x comma y from the table on the following graph. So we wanna graph one batch, eight cups, two batches, 16 cups, three batches, 24 cups. So let's do that. Let's see if we can, okay. So right here, I'm assuming on the horizontal axis that is our batches, and then our vertical axis is cups of flour. So for every batch, we need eight cups of flour. So one batch, this is eight right over here, five, six, seven, eight, and then for two batches, we're going to need 16 cups of flour so that puts us right over there, that's 16. And then for three batches, we are going to need 24 cups of flour, and that actually goes slightly off of our screen here, let me scroll up a little bit. So for three batches, we're going to have to bring that to 24 which is right here and I can see the 25 right above that. And what you'll see, because the ratio between our batches and our cups of flour are constant, that all of these points, you could connect them all with one straight line because we have a fixed ratio. Every time we move one to the right, we're gonna move eight up. Every time we add another batch, we're gonna have eight more cups of flour, every time we add a batch, eight more cups of flour. Lets do another example. Here we're told Drew earns money washing cars for his neighbors on the weekends. Drew charges a set rate for each car he washes. The points on the following coordinate plane show how much Drew charges for two, five, and eight cars. So let's see what's going on over here. So when he washes two cars, he looks like he charges $15. When he washes five cars, it looks like he's charging, well it looks like some place between 35 and $40, and he charges eight cars, it looks like he's charging $60. So one way to think about it is the ratio between the number of cars he's washing and the dollars, it stays at two to 15, notice two cars, for every $15. I guess I could say $15 for every two cars. And so, when you go to eight cars, you're multiplying by four the number of cars and you're also multiplying by four the number of dollars. And so once again, since we have a fixed ratio here, all three of these points sit on the same line. But then they ask us down here, they say how much does Drew charge for four cars? Well if it's $15 for two cars, well then four cars would be twice as much. So it would be $30 for four cars. We have the same ratio. Let's do one more example. Here we're told McKenna earns money each time she shovels snow for her neighbors, as she should. McKenna plots points on the coordinate plane below to show how much she earns for different numbers of times she shovels snow. Alright. So let's see, when she shovels snow three times, looks like she gets, halfway between 16 and 20, looks like she gets $18, four times, looks like it's $24, so looks like the ratio is staying constant at three to 18. The ratio of three to 18 is the same thing as, one way to think about it is $18 for every three times she shovels snow, that would be equivalent of six dollars for every time she shovels snow. So let's go down here to see what they're asking us. They say which of the following ordered pairs could McKenna add to the graph? So this would be one times she shoveling snow, would she get $10 for it. So does she get $10 for every time she shovels snow? No, that wouldn't be consistent with the data here. She got $18 for shoveling snow three times. So that looks like she's getting six dollars for every time she shovels snow. So I would rule out choice A, choice B, shoveling snow twice, she gets $12. Well that makes sense, if she gets six dollars every time she shovels snow. If the ratio of shoveling of the times to the dollars is three to 18 or one to six, that would be equivalent to two to 12 and we would pick that choice.