Lesson 15: Simplify Algebraic Expressions6.AT.7

I can…

I can simplify algebraic expressions by combining like terms.

Key words

• Simplify Algebraic Expressions — Rewrite an expression in a shorter equivalent form by combining like terms and using properties.
• Like Terms — Terms with the same variable raised to the same exponent, like 2x and 5x.
• Combine — To add or subtract terms with the same variable and exponent into one.
• Simplify — To rewrite an expression in a shorter form that is still equal to the original.
• Coefficient — The number in front of a letter, like the 3 in 3x.
• Term — A single number, variable, or product of them, separated by + or − signs.
• Distributive property — Multiplying a number by everything inside the parentheses: a(b + c) = ab + ac.

Steps

1. The rooms need microphones and stands: (4 + 2 + 6) microphones and (3 + 5 + 1) stands.
2. Microphones are like items, so I add: 4 + 2 + 6 = 12 microphones.
3. Stands are like items, so I add: 3 + 5 + 1 = 9 stands.
4. In algebra this is the same as 4m + 2m + 6m + 3s + 5s + 1s = 12m + 9s.

Try it

Dad writes 4y + 2 + 5y + 6 for the cost of his grocery list. Simplify 4y + 2 + 5y + 6.

Check your answer

9y + 8

4y + 5y = 9y and 2 + 6 = 8, so the simplified expression is 9y + 8.

Sentence starter

I know ___ because ___.

Goal: I can explain my steps using the words like terms, combine, simplify, and coefficient.