TenMarks teaches you how to write and evaluate multiplication and division expressions
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Learn about Expressions with Multiplication and Division In this problem, the first one states that a town will purchase 4 acres of lands every year. How many acres of land will the town will purchase after each of the first 4 years. So in this problem, let us write an expression for the number of acres of land purchased over period of time. The expression for the total land purchased will be such. The number of acres of land purchased every year times the number of years. We’re going to let A represents the number of acres that will be purchased every year. So A is going to be the number of acres purchased every year. And then we’re going to let Y represent the number of years. Our equation now will be the total land purchased by the town is given in the expression A×Y. Now, we know the number of acres that we purchased every year and so we know that that is 4. That means that we can substitute A for 4. So to find the total land that we purchased after 4 years we’re going to put a Y, so we know A is going to equal 4 because that’s the 4 acres of land that’s purchased every year. So we know that the total land purchased in this problem, the acres purchased every year is A, and we know that A is 4. We’re going to do 4×Y, now we also the number of years. They tell us that the number of years is the first 4 years, so that means the number of years which is Y is going to equal 4. So we’re going to plug in 4 for Y, so now we have 4×4 which we get 16. So the town will have purchase 16 acres of land for every year. Here we just solved this problem using expressions. Another way to solve it is using models. So we can represent the above situation using our models. Each counter represents 1 acre of land that would be purchased by the town. So after 4 years, there will be 16 counters. In the first year, there’s 4 acres of land. The number of acres purchased after 2 years, we just double it, 3 years and then 4 years. So in 4 years, there will 16 acres of land. Let’s move on to the second problem. In this problem, it states that the town has A acres of land. We need to write in expression to represent half the total amount of land own by the town and then we evaluate the expression for A, where A=40. In this problem, we know the town owns A acres of land. So to find half the value of the number, we’re going to divide the number by 2. Because we know we need to represent half the total amount of land owned by the town. Since we know it’s half, that’s means we’re going to divide the number by 2. So half the total amount of land will equal the total land divided by 2. We know that the town had A acres of land, so we’re going to put A in for 2. We also know that A tells us to valid expression where A=40, for A=40 half the total amount of land will equal A which is 40 so it would be 40÷2 and 40÷2 is 20. It would be 20 acres, so half the total amount of land owned by the town is 20 acres. All right, things to remember and to keep in mind is that an algebraic expression can be use to describe situations and unknown quantity can be represented using a variable in the expression. The value of the expression changes but the change of the value of the variable.