Lesson Two - Simplifying Expressions
The focus of this lesson will involve simplifying expressions. This will include using the distributive property including combining like terms within or without grouping symbols eliminating parentheses as much as possible. The order of operations will be reviewed.
Problem 1
Robert has 6 bags of red beads and 9 bags of green beads. How many beads are there in all the bags?
Here we assume that all the bags contain the same number of beads, which we will indicate by the unknown x. Then we may say that
Number of red beads = 6x
Number of green beads = 9x
Total number of beads = 6x + 9x = (6+9)x
= 15x
6x + 9x = x+x+x+x+x+x + x+x+x+x+x+x+x+x+x =15x
The terms 6x and 9x are called like terms because their variable portions are the same.
How many more green beads than red beads are there? 9x - 6x = (9 - 6)x = 3x
What factors do the addends have in common? Rewrite each sum.
2x + 7x = (2 + 7)x
= (9)x
= 9x
16x + 5x = (16 +5)x
= (21)x
=21x
12x - 30x = (12 -30)x
= (-18)x
=-18x
Note that these examples of "combining like terms" are all applications of the distributive property.
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