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Algebraic Expressions with Addition and Subtraction

Learn to write and simplify algebraic expressions using addition and subtraction with the distributive property. Identify terms, coefficients, and constants.

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Algebraic Expressions with Addition and Subtraction

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  1. Splash Screen

  2. Five-Minute Check (over Chapter 7) Main Idea and Vocabulary Example 1: Write Expressions With Addition Example 2: Write Expressions With Addition Example 3: Write Expressions with Subtraction Example 4: Write Expressions with Subtraction Example 5: Identify Parts of an Expression Example 6: Simplify Algebraic Expressions Example 7: Simplify Algebraic Expressions Example 8: Real-World Example Lesson Menu

  3. Use the Distributive Property to simplify algebraic expressions. • equivalent expressions • constant • simplest form • simplifying the expression • term • coefficient • like terms Main Idea/Vocabulary

  4. Write Expressions With Addition Use the Distributive Property to rewrite 3(x + 5). 3(x + 5) = 3(x) + 3(5) = 3x + 15 Simplify. Answer: 3x + 15 Example 1

  5. A B C D Use the Distributive Property to rewrite 2(x + 6). Example 1

  6. Write Expressions With Addition Use the Distributive Property to rewrite (a + 4)7. (a + 4)7 = a● 7 + 4 ●7 = 7a + 28 Simplify. Answer: 7a + 28 Example 2

  7. A B C D Use the Distributive Property to rewrite (a + 6)3. Example 2

  8. Write Expressions With Subtraction Use the Distributive Property to rewrite (q – 3)9. (q – 3)9 = [q + (–3)]9 Rewrite q – 3 as q + (–3). = (q)9 + (–3)9 Distributive Property = 9q + (–27) Simplify. = 9q – 27 Definition of subtraction Answer: 9q – 27 Example 3

  9. A B C D Use the Distributive Property to rewrite (q – 2)8. Example 3

  10. Write Expressions With Subtraction Use the Distributive Property to rewrite –3(z – 7). –3(z – 7) = –3[z + (–7)] Rewrite z – 7 as z + (–7). = –3(z) + (–3)(–7) Distributive Property = –3z + 21 Simplify. Answer: –3z + 21 Example 4

  11. A B C D Use the Distributive Property to rewrite –2(z – 4). Example 4

  12. Identify Parts of an Expression Identify the terms, like terms, coefficients, and constants in 3x – 5 + 2x – x. 3x – 5 + 2x – x = 3x + (–5) + 2x + (–x)Definition of subtraction = 3x + (–5) + 2x + (–1x)Identity Property; –x = –1x Answer: The terms are 3x, –5, 2x, and –x.The like terms are 3x, 2x, and –x.The coefficients are 3, 2, and –1.The constant is –5. Example 5

  13. A B C D Identify the terms, like terms, coefficients, and constants in 6x – 2 + x – 4x. Example 5

  14. Simplify Algebraic Expressions Simplify the expression 6n – n. 6n – n are like terms. 6n – n = 6n – 1nIdentity Property; n = 1n = (6 – 1)nDistributive Property = 5n Simplify. Answer: 5n Example 6

  15. A B C D Simplify the expression 7n + n. Example 6

  16. Simplify Algebraic Expressions Simplify 8z + z – 5 – 9z + 2. 8z, z, and –9z are like terms. –5 and 2 are also like terms. 8z + z – 5 – 9z + 2 = 8z +z + (–5) + (–9z) + 2 Definition of subtraction = 8z +z + (–9z)+ (–5) + 2 Commutative Property = [8 + 1+ (–9)]z+ [(–5) + 2] Distributive Property = 0z + (–3) or –3 Simplify. Answer: –3 Example 7

  17. A B C D Simplify 6z + z – 2 – 8z + 2. Example 7

  18. THEATERTickets for the school play cost $5 for adults and $3 for children. A family has the same number of adults as children. Write an expression in simplest form that represents the total amount of money spent on tickets. Words$5 each for adults and $3 each for the same number of children. Variable Let x represent the number of adults or children. Equation5● x + 3 ● x Example 8

  19. Simplify the expression. 5x + 3x = (5 + 3)x Distributive Property = 8x Simplify. Answer: The expression $8x represents the total amount of money spent on tickets. Example 8

  20. A B C D MUSEUMTickets for the museum cost $10 for adults and $7.50 for children. A group of people have the same number of adults as children. Write an expression in simplest form that represents the total amount of money spent on tickets to the museum. A. $2.50x B. $7.50x C. $15.50x D. $17.50x Example 8

  21. End of the Lesson End of the Lesson

  22. Five-Minute Check (over Chapter 7) Image Bank Math Tools Graphing Equations with Two Variables Two-Step Equations Resources

  23. A B C D (over Chapter 7) Find the area of a triangle with base 10 in. and height 15 in. Find the area of a circle with diameter 14 m. Five Minute Check 1

  24. End of Custom Shows

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