UNIT 1 Chapter 1 1 Variables and expressions
UNIT 1 Chapter 1 -1 Variables and expressions Pre. Algebrateachers. com www. prealgebrateachers. com
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
Writing Variable Expression Key Words: Total (+) Quotient (÷) (-) (/) More Than (+) (/) Difference (-) Fewer Than (-) Increased By (+) Less Than (-) Decreased By (-) www. prealgebrateachers. com Product (X) ( • ) () Times (X) ( • ) () Divided By (÷) (-)
■ 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
■ 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
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!” Evaluate each expression if K = 2, m=7, and X = 4. Ex 1: 6 M-2 K 6(7) – 2 (2) (replace m with 7 and K with 2) 42 - 4 Multiply 38 Subtract www. prealgebrateachers. com
Substitution Property of Equality ■ Example 3: ■ Evaluate each expression if K = 2, m=7, and X = 4. ■ Example 3: =3 X + 7 (Replace x with 4 ) =3(4) +7 (Multiply 3 and 4) =12 +7 (Add) =19 www. prealgebrateachers. com
Let’s do some practice ■ www. prealgebrateachers. com
Let’s check our answers! ■ www. prealgebrateachers. com
UNIT 1 Chapter 1 -2 Order of Operations www. prealgebrateachers. com
■ Vocabulary: – Evaluate an expression: find the numerical value Order of Operations Rules: 1) Simplify expressions inside parenthesis ( ) 2) Simplify any exponents 3) Do all multiplication and/or division from left to right 4) Do all addition and/or subtraction from left to right www. prealgebrateachers. com
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
Find the value of each expression Ex 3: Ex 4: [2 + (6 • 8)] – 1 10 ÷ [9 – (2 • 2)] [ 2 + 48] – 1 (complete parenthesis) 10 ÷ [9 – ( 4)] (complete parenthesis) [50] - 1 (Add) 10 ÷ [5] (complete parenthesis) 49 (Simplify) 2 (simplify by dividing) www. prealgebrateachers. com
Let’s Practice! ■ www. prealgebrateachers. com
Let’s check our answers! ■ www. prealgebrateachers. com
UNIT 1 Chapter 1 – 2 Properties www. prealgebrateachers. com
Vocabulary and Properties: ■ Properties: statements that are true for any numbers www. prealgebrateachers. com
■ Vocabulary and Properties www. prealgebrateachers. com
■ Vocabulary and Properties www. prealgebrateachers. com
■ 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
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
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
UNIT 1 Chapter 1 – 4 Ordered Pairs www. prealgebrateachers. com
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 the number lines intersect www. prealgebrateachers. com X-Axis - the horizontal number line
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 Number on the x-axis www. prealgebrateachers. com The y-coordinate corresponds to a number on the y-axis
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
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
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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