In our last lesson, we looked at translating some of the most common math words. Now we're going to look at translating those math words into expressions that will have numbers and variables in them. First, we have the sum of five and a number. Sum of refers to addition. So we know we're going to be adding something together. We're going to add five and some unknown number and that unknown number will be represented by a variable. And you can use whatever letter you want to represent that variable. Here I used x, so I have five plus x. This represents the sum of five and a number. Now remember, with addition the order does not matter. That's because of the commutative property of addition. So we could write this the other way around as x plus five. Either way it still represents the same expression. Next, we have eight less than, a number less than refers to subtraction. So we know we have some subtraction involving that number eight and also some unknown number which we will represent with a variable. Now remember, less than is the same as taking away from something. So if we have eight less than a number, then we're starting with some number and taking eight away from it. So we'll represent that as n or whatever variable you'd like to use minus eight to show that we're taking eight away from that number. Because with subtraction the order does matter. So if we wrote this as eight minus N, it would not be correct. So be very careful with that. Next, we have the product of 15 and a number. Product of refers to multiplication. And once again we have an unknown number that will represent with a variable. So we can show 15 times m to represent the product of 15 and our variable with multiplication, you can also use parentheses around the number or the variable. So you could also represent it as 15 parentheses and then the variable inside the parentheses. Either way it's perfectly fine. Or if you want to represent it with the number right next to the variable as a coefficient, that's perfectly fine as well. And the order does not matter in multiplication, but we normally do write the number first. Next we have the quotient of a number and three. Quotient of refers to division and we have some unknown number that will represent with a variable. So we need to show that we're taking that variable and dividing it by three. We can represent it like this y divided by three. Now, as we're working our way into algebra, most likely we're going to see division represented as fractions. So another way to write this is y over three. As a fraction, it still represents y being divided by three. And just like the order matters with subtraction, it also matters with division. So if you wrote this as three divided by y, it would not be correct. And lastly, we have half of a number. Now, half of can be represented two different ways. We can either multiply by one half or divide by two. And we also have an unknown number that will represent with a variable. So I can represent half of a number as multiplying one half times our variable, which I used y for this example. Or I can show that I'm dividing by two and represent it as Y divided by two. And here I set it up as a fraction to show that division either way represents the same value. So both ways are perfectly fine. So when you are translating math into expressions, just make sure that you're reading the words very carefully and you understand what operation you're working with. And if that operation is addition or multiplication, the order does not matter because of the commutative property. However, if you're working with subtraction or division, the order does matter. So just make sure that you understand that expression and that you're setting it up in the proper order.