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# Comparing with multiplication and addition: money

CCSS.Math:

## Video transcript

so we're told that Minli has five more dollars than James Minli has 33 dollars how much does James have so let's do some letters to represent the amount of money Minli has in the amount of money James has so let's say that M is the is represents the amount of money that Minli has and J represents the amount that James has so we're told that Minli has five more dollars in James so men Lee's money or the amount of money Minli has is going to be equal to the amount of money James has plus 5 so plus plus 5 start with the amount James has add 5 you have min Lee's Minli has five more dollars than James now they tell us min Lee has 33 dollars so let me write this down so we know that M M is equal to so this this sentence right here tells us this right here tells us that M is equal to 33 dollars so instead of an M here we could say well 33 dollars is equal to is equal to the amount of money James has plus plus five and so now we just need to think about how much money does James have it I encourage you to pause the video and think about it on your own well one way to visualize this is maybe on a number line so let me draw a number line right over here and let's say this is 0 this is the amount that Minli has right up here so min Lee has 33 dollars that represents that point right over here and J is the amount that James has so let's say that this is J right over here and we know that if we add five to J if you take J add five you get 233 so you start at J if you add five you get you get 233 well how can I go to 33 - how can I start with M or how can I start with the amount min Lee has and then end up with the amount James has well I could just go the other way around I could start with M and I could subtract five I could subtract five so we could say at 33 which is M the amount of money Minli has -5 minus 5 is equal to the amount of money that James has so how much money does James have well 33 minus 5 is going to be 28 so we can say that James James has 28 is equal to J or James has 28 dollars so this right over here is 28 and you see that 28 plus 5 is 33 33 is 5 more than 28 so this all works out now let's think about this next question Jessica's house is five times as far from school as Paulette's house Jessica's house is 15 miles from school how far is Paulette's house from the school so just like we did let's just look at each of these sentences and see what they're telling us and encourage you to define use some letters to represent the distance Jessica's house from school and Paulette's house from school and try to figure this out on your own pause the video right now and try to figure out on your own so you could imagine Jamie might be a good letter for Jessica's the distance from Jessica's house to school and let's say that P it will use for Paulette's house from school so we're told that however far Paulette's house is from school you take five times that to see how far Jessica's house is from school so we could write that P which is how far Paulette's house is from school times 5 times 5 times 5 is equal to how far Jessica's house is from school Jessica's house is five times as far from school as Paulette's house P is Paulette's houses distance from school J is Jessica's houses distance from school they then tell us that Jessica's house is 15 miles from school so that they're essentially telling us the sentence right over here they're telling us that J is equal to 15 J is equal to 15 so we can rewrite this as the distance Paulette's houses from school times 5 which we know to be Jessica's distance from school or Jessica's houses distance from school which we now know to be 15 is going to be equal to 15 so what would P be some number times five is going to be equal to 15 some number of miles times five is equal to 15 miles well you might already be able to think about this in your head but we could also visualize it so let's draw a number line again let's draw a number line again and if you start with that number P so let's this is Paulette's distance from school so P and you multiply it by five something so that's x 1 x 2 x 3 x 4 x 5 so notice this is p this distance is p right over here this is another p right over here this is another p right over a year that's another p right over there and another p right over there or another way of thinking about it this whole distance right over here is going to be P plus P plus P plus P plus P or P times 5 P times 5 and that's equal to how far jessica is from school or Jessica's house is from school so this right over here is equal to 15 which is the same thing which is the same thing as J so how would you figure it out well if five times P is equal to 15 if I want to figure out what P is I could just divide 15 into five equal groups so we could say that P P is equal to 15 is equal to 15 divided into five equal groups if you take 15 miles and divide it into five equal groups that's going to you're going to end up with P so what is this well we get P 15 divided by three is I'm sorry 15 divided by 5 is 3 so Paulette Paulette lives 3 miles from school and you see that if this is a 3 another 3 another 3 plus another 3 in another 3 3 times 5 is 15 Jessica's house which is 15 miles from school is 5 times as far from school as Paulette's house which is 3 miles from school so it all makes sense