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Variables and Expressions - PreAlgebra Teachers

Learn about variables, numerical and variable expressions, substitution property of equality, order of operations, and properties of numbers in this comprehensive lesson.

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Variables and Expressions - PreAlgebra Teachers

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  1. Unit 1 Chapter 1-1 Variables and expressions PreAlgebrateachers.com www.prealgebrateachers.com

  2. Vocabulary: Expression-mathematical phrase that contains operations, numbers, AND/OR variables. ***Does not have an equal sign (=) Variable – A letter that represents a value that can change or vary 2 types of expression: • Numerical Expression: Does not contain variables • Variable Expression: Contains one or more variables. www.prealgebrateachers.com

  3. Writing Variable Expression Key Words: Total (+) Difference (-) Product (X) (•) () Quotient (÷) (-) (/) More Than (+) Fewer Than (-) Times (X) (•) () Divided By (÷) (-) (/) Increased By (+) Less Than (-) Decreased By (-) www.prealgebrateachers.com

  4. Write the algebraic expression for the given verbal expression: Ex 1: Nine more than a number Y Ex 2: Four less than a number N Ex 3: Five times the quantity four plus a number C (See next slide for answers) www.prealgebrateachers.com

  5. Write the algebraic expression for the given verbal expression: Ex 1: Nine more than a number Y 9 + Y Ex 2: Four less than a number N N - 4 Ex 3: Five times the quantity four plus a number C 5 X (4+C) or 5(4+C) www.prealgebrateachers.com

  6. Substitution Property of Equality • If two quantities are equal, then one quantity can be replaced by the other in a mathematical expression • “Plug it in Plug it in!” Evaluate each expression if K = 2, m=7, and X = 4. Ex 1: 6M-2K 6(7) – 2 (2) (replace m with 7 and K with 2) 42 - 4 Multiply 38 Subtract www.prealgebrateachers.com

  7. Substitution Property of Equality Example 2: • Evaluate each expression if K = 2, m=7, and X = 4. • Example 2: = (Replace k with 2 and m with 7) = (Multiply numerator) = =7 Example 3: • Evaluate each expression if K = 2, m=7, and X = 4. • Example 3: =3X + 7 (Replace x with 4 ) =3(4) +7 (Multiply 3 and 4) =12 +7 (Add) =19 www.prealgebrateachers.com

  8. Let’s do some practice Evaluate: • 3a – 5, A=10 2) Y=2 3) 2X + 3Y + 4Z, X=4, Y=3, Z=2 (answers on next slide) www.prealgebrateachers.com

  9. Let’s check our answers! Evaluate: • 3a – 5, A=10 3 (10) – 5 30 – 5 = 25 2) Y=2 = = 6 3) 2X + 3Y + 4Z, X=4, Y=3, Z=2 2 (4) + 3 (3) +4 (2) 8 + 9 + 8 =25 www.prealgebrateachers.com

  10. UNIT 1 Chapter 1-2 Order of Operations www.prealgebrateachers.com

  11. Vocabulary: • Evaluate an expression: find the numerical value Order of Operations Rules: • Simplify expressions inside parenthesis ( ) • Simplify any exponents • Do all multiplication and/or division from left to right • Do all addition and/or subtraction from left to right www.prealgebrateachers.com

  12. Find the value of each expression: Ex 1) 4 + 15 ÷ 3 4 + 5 (divide) 9 (simplify) EX 2) 4 (5) – 3 20 – 3 (complete parenthesis) 17 (simplify) www.prealgebrateachers.com

  13. Find the value of each expression Ex 3: [2 + (6 • 8)] – 1 [ 2 + 48] – 1 (complete parenthesis) [50] - 1 (Add) 49 (Simplify) Ex 4: 10 ÷ [9 – (2 • 2)] 10 ÷ [9 – ( 4)] (complete parenthesis) 10 ÷ [5] (complete parenthesis) 2 (simplify by dividing) www.prealgebrateachers.com

  14. Let’s Practice! Find the value of each expression: • 3 + 4 x 5 • 6 (2+9) – 3 • 8 www.prealgebrateachers.com

  15. Let’s check our answers! Find the value of each expression: • 3 + 4 x 5 3 + 20 (multiply) 23 (simplify) 2) 6 (2+9) – 3 • 8 6 (11) – 3 • 8 (complete parenthesis) 66 – 24 (complete each multiplication) 42 (simplify) • = (53 +15) ÷ (17-13) (rewrite as division problem) (68) ÷ (4) (simplify each parenthesis) 17 (divide) www.prealgebrateachers.com

  16. UNIT 1 Chapter 1 – 2 Properties www.prealgebrateachers.com

  17. Vocabulary and Properties: • Properties: statements that are true for any numbers www.prealgebrateachers.com

  18. Vocabulary and Properties www.prealgebrateachers.com

  19. Vocabulary and Properties www.prealgebrateachers.com

  20. Name the property shown by each statement: • EX 1) 3 + 5 + 9 = 9 + 5 +3 • EX 2) A • (9 • 7) = (A•9) • 9 • EX 3) 0 + 15 = 15 Check answers next! www.prealgebrateachers.com

  21. Name the property shown by each statement: EX 1) 3 + 5 + 9 = 9 + 5 +3 Commutative Property of Addition EX 2) A • (9 • 7) = (A•9) • 9 Associative Property of Multiplication EX 3) 0 + 15 = 15 Additive Identity www.prealgebrateachers.com

  22. You can use what you’ve learned about properties of numbers to find sums and products mentally. Group numbers mentally so that sums or products end in a zero. Ex 1: 4 + 5 + 6 (4+6) + 5 (group the 4 and 6) 10 + 5 (simplify) 15 (Add mentally) EX 2: 5 • 7 • 8 (5•8) • 7 (group the 5 and 8) (40) • 7 (simplify) 280 (multiply mentally) www.prealgebrateachers.com

  23. Unit 1 Chapter 1 – 4 Ordered Pairs www.prealgebrateachers.com

  24. Vocabulary: Coordinate System - used to locate points and is formed by the intersection of two numbers that meet at a right angle at their zero points (also called a coordinate plane) Y-axis – Vertical number line Origin- is at (0,0), the point at which X-Axis - the horizontal number line the number lines intersect www.prealgebrateachers.com

  25. Vocabulary: An ordered pair of numbers is used to locate a point on a coordinate plane. The first number is called is the X-coordinate. The second number is called the Y-coordinate. (3, 2) The x-coordinate corresponds to a The y-coordinate corresponds to a number Number on the x-axis on the y-axis www.prealgebrateachers.com

  26. To graph an ordered pair, draw a dot at the point that corresponds to the ordered pair. The coordinates are your direction to locate the point. Example 1: Graph each ordered pair on a coordinate system (4, 2) Step 1: Start at origin Step 2: Since the x-coordinate is at 4, move 4 units to the right Step 3: Since the y-coordinate is 2, move 1 unit up. Draw a dot. www.prealgebrateachers.com

  27. Example 2: Grade the ordered pair on a coordinate system (5,0) Step 1: Start at the origin Step 2: The x-coordinate is 5. So, move 5 units to the right Step 3: Since the y-coordinate is 0, you will not need to move up. Place your dot directly on the x-axis www.prealgebrateachers.com

  28. Sometimes a point on a graph is named by using a letter. To identify its location, you can write the ordered pair that represents the point. Write the ordered pair that names each point Ex. 1) Point C Step 1: Start at the origin Step 2: Move right on the x-axis to find the X-coordinate of point C, which is 3. Step 3: Move up the y-axis to find the y-coordinate, Which is 4. The ordered pair for point C is (3,4) Ex 2) Point G The x-coordinate of G is 4, and the y-coordinate is 5. The ordered pair for point G is (4,5) www.prealgebrateachers.com

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