Writing and Evaluating Expressions with Multiplication and Division 04:52 minutes

Video Transcript

Transcript Writing and Evaluating Expressions with Multiplication and Division

It’s December 1st, and the neighbors on Winter Way have started decorating for the holidays. Everyone on the block is very excited. Especially the Smith family. Will this finally be the year the Smiths win for best neighborhood decorations? For ten years running, the Joneses have had the best decorations on the block. This year, the Smiths don't want to simply keep up with the Joneses, they want to beat them. To do that, the Smiths will need to know about Writing and Evaluating Expressions with Multiplication and Division. So, what’s their big plan? The Smith's daughter, Polly the Problem Solver, has made a list of steps. Step 1 on the list is to buy a Christmas tree. The Smiths think bigger is better, so they plan to get a tree that is 2 times the size of the Jones’s tree. But, there's a problem, the Smiths don’t know the size of the Jones’s tree. Let's make a table to help Polly. We already know that we can use a variable to represent an unknown quantity. Since our unknown quantity is the height of the Jones's tree, let's let 'h' represent the height, in feet, of the Jones's tree. The Smiths want a tree that is 2 times ‘h’. We can write this quantity in algebraic terms as: 2h. Notice how we dropped the multiplication sign? If you have a coefficient in front of a variable it already means times, so when writing algebraic terms, we won’t write the multiplication symbol, but we still know we're multiplying. If 'h' is equal to 1, then 2h is equal to 2. If 'h' is equal to 2, then 2h is equal to 4, and so on, and so on and so on. Will you look at the Jones’s tree!? It must be 11 feet tall! If we fill out the chart until 'h' equals 11. 2h would equal 22. To have a tree that will be two times the size of the Jones’s tree, the Smiths will need to buy a tree that is 22 feet tall. 22 feet tall!!! Oh boy! Now the Smiths need to get started on the next item on Polly's list: to have 4 times as many twinkling lights as the Joneses, plus 200 special snowflake-shaped lights. There is a slight problem with Polly's list. Just like with the tree, the Smiths don’t know how many twinkling lights the Joneses will have. Let's make another table to help Polly. Polly picks the variable ‘L' to represent the unknown number of lights displayed on the Jones' house. 4L represents part of Polly's wish: to have 4 times the number of lights on the Jones's house, and don't forget to add the 200 snowflake shaped lights. So, the expression to describe the total number of lights on the Jones's house is 4L + 200. Polly counts the twinkling lights on the Jones’s house. There are exactly 1,000 lights! Instead of filling out the table until 'L' equals 1,000, we can save time and let L equal 1,000 in the expression 4L+200. If we plug this in to our equation, we see that her family will need 4,200 lights altogether to best the Joneses. 4,200 lights? That’s a lot of lights. Oh look, it’s snowing! But there's no time to play because we still have one more decoration to put up. Polly's list includes candle lights for the windows. As far as they know, the Joneses don't have any candles for their windows. The Smith's have 5 windows in their house and want to know how many candles they can put in each window. Using another table, let 'c' represent the number of candles they have, so 'c' divided by 5 represents how many candles per window. If they have 5 candles, the Smiths can put one candle in each window. If they have 10 candles, they can put 2 in each window. If they have 15 candles, they can put 3 in each window. If they have 20 candles, they can put 4 in each window, and so on. Let's drop in on the Smiths to look at the finished product. Oh no! Looks like it's lights out on Polly's idea!