Combining Rational Number Like Terms 04:10 minutes

Video Transcript

Transcript Combining Rational Number Like Terms

We're in Cambodia, located in Southeast Asia, to check in with our friend Laura. Laura’s an archaeologist and she's busy excavating a site that hasn't been touched in hundreds of years. While digging, Laura's discovered lots of interesting artifacts. Unfortunately they are all broken, so she has to put the pieces back together correctly. Just like putting together pieces of broken artifacts, combining rational number like terms works similarly by piecing parts of an expression together. Here's the first expression that we need to simplify: First, let's find the like terms and use the Commutative Property of Addition to reorder the expression writing the x’s together and the y’s together. Next, combine the like terms giving us 15x plus 2y. Let’s try another problem with rational numbers. Because the coefficients for this problem are fractions, we may have a few more steps but the strategy to simplify the expression is the same. First, use the Commutative Property of Addition to reorder the terms. Next, we want to combine the like terms but we can't add the coefficients of 'h' just yet. First, we'll have to find a common denominator and modify the expression. Nine works. Now, use the Multiplicative Identity Property of 1 to modify the expression so both coefficients have 9 as the denominator. To do this, we multiply three thirds by two thirds giving us six ninths. Now that both coefficients of 'h' have the same denominator we can combine the like terms and simplify the fractions.

Notice, the expression contains terms that are not multiplied with a variable. These terms are called constants.
Constants are numbers that are multiplied by a variable raised to the zero power which is always equal to 1. Even though the variable raised to the zero power is not written we know it's there. In other words, a constant is simply a number by itself. And just in time to try another problem. To make the problem easier to solve first change the mixed number into an improper fraction. Next, use the Distributive Property to get rid of the parentheses. Now, reorder the terms into Standard Form using the Commutative Property. If we want to combine like terms, we have to first find a common denominator for the constant terms. In this case, it's 18.

Now, we can combine the like terms. The last step, as always, make sure all the fractions are written in lowest terms and that the expression is written in standard form. Looks like we're good to go! So, how's Laura doing putting together all of the broken pieces? How about that? She's put together enough pieces to host a tea party with her new pal.