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# Module 1 Topic 2 Notes

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### Module 1 Topic 2 Notes

1. 1. Module 1 Topic 2 Variables and Expressions Variable: an unknown that is usually represented by a letter; used in writing expressions Expressions are different from equations because expressions do not have an “equals” sign
2. 2. Writing an Algebraic Expression <ul><li>EX: Write the algebraic expression that represents the sum of a number and 3 </li></ul>X + 3 Write this down: sum + difference – product x quotient /
3. 3. Writing an Algebraic Expression <ul><li>EX: Juan has 40 different plants that he wants to plant into r rows. Write an algebraic expression that represents how many plants will be in each row. </li></ul>40/r
4. 4. Order of Operations <ul><li>Never goes away!  </li></ul><ul><li>Parenthesis and Exponents </li></ul><ul><li>Multiplication and Division </li></ul><ul><li>Addition and Subtraction </li></ul>
5. 5. Order of Operations <ul><li>EX: 2 3 – 4(-7 + 10) + 6 </li></ul><ul><li>8 – 4(3) + 6 </li></ul><ul><li>8 – 12 + 6 </li></ul><ul><li>-4 + 6 </li></ul><ul><li>2 </li></ul>
6. 6. Simplifying Algebraic Expressions <ul><li>EX: Simplify 3x*2 2 + 5x – 8/2 </li></ul><ul><li>3x*4 + 5x – 8/2 </li></ul><ul><li>12x + 5x – 4 </li></ul><ul><li>17x - 4 </li></ul>EX: Simplify (-3) 2 – 6y + 2y(5) -10 YOU TRY! 9 – 6y + 2y(5) – 10 9 – 6y + 10y – 10 4y – 1 (Did you get it?  )
7. 7. The Distributive Property <ul><li>Allows us to simplify expressions when you can’t use order of operations. </li></ul>EX: Distribute the expression 5(r + 12) 5r + 5*12 5r + 60
8. 8. Let’s Put it All Together! <ul><li>EX: Simplify 2 – 3(t + 5) + 4 3 - 60t/5 </li></ul><ul><li>2 – 3(t + 5) + 64 – 60t/5 </li></ul><ul><li>2 – 3t – 15 + 64 – 12t </li></ul><ul><li>-15t + 51 </li></ul>
9. 9. Let’s Try a Word Problem <ul><li>Sharon has \$125 in a savings account and is spending \$8 each week on lunch at school. </li></ul><ul><li>How much will she have left after w weeks? A: \$125 - \$8w </li></ul><ul><li>How much will she have after 5 weeks? </li></ul><ul><ul><li>A: \$125 - \$8(5) = \$125 - \$40 = \$85 </li></ul></ul><ul><li>What equation can be written to find out how many weeks it will take for her to have \$45 left? </li></ul><ul><ul><li>A: \$45 = \$125 - \$8w </li></ul></ul>