Copyright © Ed2Net Learning, Inc.1 Properties of Numbers Grade 7 Pre-Algebra

Copyright © Ed2Net Learning, Inc.2 Warm-Up  Find the LCM of 24,  Compare; Use, or = 7/8 __ 7/9 > __ -7/8 >  Add 1/8 + ¾ 7/8  Multiply 3/5 x ½ 3/10

Copyright © Ed2Net Learning, Inc.3 Identifying Properties  Commutative Properties of Addition and Multiplication Changing the order of the values you are adding or multiplying does not change the sum or product.  =  9 x 5 = 5 x 9  a + b = b + a  a x b = b x a

Copyright © Ed2Net Learning, Inc.4 Identifying Properties  Associative Properties of Addition and Multiplication Changing the grouping of the values you are adding or multiplying does not change the sum or product.  (2 + 7) + 3 = 2 + (7 + 3)  (9 x 4) x 5 = 9 x (4 x 5)  (a + b) + c = a + (b + c)  (ab)c = a (bc)

Copyright © Ed2Net Learning, Inc.5 Identifying Properties  Identity Properties of Addition and Multiplication The sum of any number and zero is the original number. This is the additive identity of 0. The product of any number and 1 is the original number. This is the multiplicative identity of 1.  = 12  10 x 1 = 10  a + 0 = a  a x 1 = a In mathematics, an identity leaves the value of other numbers unchanged.

Copyright © Ed2Net Learning, Inc.6 Try This!  Name each property shown. 5 x 7 = 7 x 5 Commutative Property of Multiplication c x 1 = c Identity Property of Multiplication 7 + a = a + 7 Commutative Property of Addition 5(xy) = (5x)y Associative Property of Multiplication

Copyright © Ed2Net Learning, Inc.7 Using Properties  When numbers are easy to compute mentally, you can use properties and mental math to fin sums. Simplify (81 + 6) + 9  = (6 + 81) + 9-> Use commutative property  = 6 + (81 + 9)-> Use associative property  =  = 96 Look for combinations that equal 10 or a multiple of 10, since they are easier to use in calculating mentally.

Copyright © Ed2Net Learning, Inc.8 Try It!  Use mental math to simplify the expression = (6 + 14) + 7 = = 27

Copyright © Ed2Net Learning, Inc.9 Using Properties  Simplify (4 x 9) x 5 = (9 x 4) x 5 -> Use commutative property = 9 x (4 x 5)-> Use associative property = 9 x 20 = 180

Copyright © Ed2Net Learning, Inc.10 Try It!  Use mental math to simplify the expression 25 x (3 x 4) = (25 x 4) x 3 = 300

Copyright © Ed2Net Learning, Inc.11 Distributive Property  You can find the total are of two rectangles by two methods:  Method 1: Find the area of each rectangle. Then find the sum of the areas.  Method 2: Combine the area of two rectangles into one large rectangle. Find its length. Find its width. Then find its area.  It suggests the Distributive Property, which combines multiplication with addition and subtraction

Copyright © Ed2Net Learning, Inc.12 Distributive Property  To multiply a sum or difference, multiply each number within the parentheses by the number outside the parentheses.  3(2 +6) = 3(2) + 3(6)  a(b + c) = ab + ac  (2 + 6)3 = 2(3) + 6(3)  (b + c)a = ba + ca  6(7 – 4) = 6(7) – 6(4)  a(b – c) = ab – ac  (7 – 4)6 = 7(6) – 4(6)  (b – c)a = ba - ca

Copyright © Ed2Net Learning, Inc.13 Using the Distributive Property  Find 20(102) mentally  20 (102) = 20 ( ) = 20 x x 2 = 2, = 2,040

Copyright © Ed2Net Learning, Inc.14 Try It!  Find the product 9 x 199 mentally.  9 x 199 = 9 x (200 -1) = 1800 – 9 = 1791

Copyright © Ed2Net Learning, Inc.15 Using the Distributive Property  Simplify 8(15) – 8(5) = 8(15 – 5) = 8(10) = 80

Copyright © Ed2Net Learning, Inc.16 Try It!  Simplify 7(21) + 7(9) = 7 (21 + 9) = 7 x 30 = 210

Copyright © Ed2Net Learning, Inc.17 Variable Expressions  Use of algebra tiles to model the Distributive Property with variable expressions 3(2x + 5) Model three groups of 2x + 5. Group like tiles. So, 3(2x + 5) = 6x + 15 represents x represents 1

Copyright © Ed2Net Learning, Inc.18 Try it!  Use algebra tiles to multiply 4(2x -3) represents x represents -1 So, 4(2x -3) = 8x - 12

Copyright © Ed2Net Learning, Inc.19 Using the Distributive Property  Multiply -5(4x -3) = -5(4x) – (-5)(3) = -20x – (-15) = -20x + 15

Copyright © Ed2Net Learning, Inc.20 Try It!  Multiply 2(7 -3d) = 14 -6d

Copyright © Ed2Net Learning, Inc.21 Identifying parts of a Variable Expression  A term is a number or the product of a number and variable(s).  A constant is a term that has no variable.  Like Terms have identical variables.  A coefficient is a number that multiplies a variable. 7a + 4a + 3b - 6

Copyright © Ed2Net Learning, Inc.22 Identifying parts of a Variable Expression  When you have a variable expression that includes subtraction, you can rewrite the expression using only addition.  5x – 3y + z – 2 = 5x + (-3y) + z + (-2) = 5x + (-3y) + 1z + (-2)-> Identity property  The coefficients are 5, -3, and 1  The constant is -2

Copyright © Ed2Net Learning, Inc.23 Try It!  Name the coefficients, the like terms, and the constants in 3m -2n + n – 4  Coefficients: 3, -2, 1  Like terms: -2n and n  Constant: -4

Copyright © Ed2Net Learning, Inc.24 Simplifying Variable Expressions  Using Tiles to simplify Simplify 2x x 2x4 3x 5x+ 4 ++

Copyright © Ed2Net Learning, Inc.25 Try It!  Use tiles to simplify 3a a – 1. 3a2 4a 7a

Copyright © Ed2Net Learning, Inc.26 Simplifying Variable Expressions  Combining Like Terms  Simplify 5y + y = 5y + 1y-> Identity property = (5 + 1)y-> Distributive property = 6y

Copyright © Ed2Net Learning, Inc.27 Try It!  Simplify 3b – b = (3 -1)b = 2b

Copyright © Ed2Net Learning, Inc.28 Simplifying Variable Expressions  Using Deductive Reasoning  Simplify 4g + 3(3 + g) = 4g g-> Distributive property = 4g + 3g + 9-> Commutative property = (4 + 3)g + 9-> Distributive property = 7g + 9

Copyright © Ed2Net Learning, Inc.29 Try It!  Simplify 6y + 4m -7y + m.  6y -7y + 4m + m  6y – 7y + 4m + 1m  (6 – 7)y + (4 + 1)m  -1y + 5m  5m -y

Copyright © Ed2Net Learning, Inc.30 Break!!!

Copyright © Ed2Net Learning, Inc.31

Copyright © Ed2Net Learning, Inc.32 Variables & Equations  Classifying Equations  An equation is a mathematical sentence with an equal sign = 11: a numerical expression equal to a numerical expression x + 7 = 37: a variable expression equal to a numerical expression a + (-3) = 2a + 5: a variable expression equal to a variable expression  An equation with a numerical expression equal to another numerical expression is either true or false.  An equation with one or more variables is an open sentence.

Copyright © Ed2Net Learning, Inc.33 Classifying Equations  State whether each equation is true, false, or an open sentence = 18 true, because 18 = 18 6 = false, because 6 ≠ 7 6y = y an open sentence, because there is a variable

Copyright © Ed2Net Learning, Inc.34 Try It!  State whether each equation is true, false, or an open sentence. 9 – 7 = 3 false; because 2 ≠ x = 2 an open sentence, because there is a variable

Copyright © Ed2Net Learning, Inc.35 Writing an equation  Write an equation for Nine times the opposite of five is forty-five. State whether the equation is true, false, or an open sentence. 9 times -5 is 45 Equation: 9 x (-5) = 45 The equation is false. 9 x (-5) = -45, and -45 ≠ 45

Copyright © Ed2Net Learning, Inc.36 Try It!  Write an equation for Twenty minus x is three. State whether the equation is true, false, or an open sentence.  20 – x = 3; open sentence, because it has a variable

Copyright © Ed2Net Learning, Inc.37 Checking Equations using Substitution  A solution of an equation is a value for a variable that makes an equation true. Substitute a number for a variable to determine whether the number is a solution of the equation. Is 30 a solution of the equation x = 200?  x = 200  =? 200  200 = 200 Yes, 30 is a solution of the equation.

Copyright © Ed2Net Learning, Inc.38 Try it!  Is the given number a solution of the equation? 8 + t = 2t; = 2 x 1 9 =? 2 9 ≠ 2; 1 is not a solution to the equation

Copyright © Ed2Net Learning, Inc.39 Assessment 1. Simplify (5 + 23) Simplify = Evaluate x(y.z), for x = 4, y = 27, and z = At the annual Pancake Breakfast, 397 people ate 4 pancakes each. How many pancakes were served? 1, Simplify (16)7 – (11)7 = 35

Copyright © Ed2Net Learning, Inc.40 Assessment 6. Multiply (6m + 1) (3) = 18m Name the property shown: m[t + (-t)] =mt + m(-t) Distributive property 8. Simplify 4x + 3 – 2(5 + x) = 2x A diver’s equipment weighs 35 lb. The diver plus the equipment weighs 165 lb. Can the diver’s weight be 200lb? No, the diver’s weight cannot be 200 lb 10. Is the given number a solution of the equation ? c/2 – 8 = 3(-3); -2 Yes

Copyright © Ed2Net Learning, Inc.41 Good Job!  Remember to do the practice worksheets!!!