7th grade math expressions & equations
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7th Grade Math
Expressions & Equations
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Table of Contents
Inverse OperationsOne Step EquationsTwo Step EquationsMulti-Step EquationsDistributing Fractions in Equations
Graphing & Writing Inequalities with One Variable
The Distributive Property and FactoringCombining Like Terms
Simple Inequalities involving Addition & SubtractionSimple Inequalities involving Multiplication & Division
Common Core Standards: 7.EE.1, 7.EE.3, 7.EE.4
Simplifying Algebraic Expressions
Translating Between Words and Equations
Commutative and Associative Properties
Using Numerical and Algebraic Expressions and Equations
Commutative and Associative Properties
Day 1
Commutative Property of Addition: The order in which the terms of a sum are added does not change the sum.a + b = b + a5 + 7 = 7 + 5 12= 12Commutative Property of Multiplication: The order in which the terms of a product are multiplied does not change the product.ab = ba4(5) = 5(4)
Associative Property of Addition: The order in which the terms of a sum are grouped does not change the sum.(a + b) + c = a + (b + c)(2 + 3) + 4 = 2 + (3 + 4) 5 + 4 = 2 + 7
9 = 9
The Associative Property is particularly useful when you are combining integers.
Example:-15 + 9 + (-4)=-15 + (-4) + 9= Changing it this way allows for the -19 + 9 = negatives to be added together first. -10
Associative Property of Multiplication: The order in which the terms of a product are grouped does not change the product.
1 Identify the property of -5 + 3 = 3 + (-5)A Commutative Property of Addition B Commutative Property of Multiplication C Associative Property of Addition D Associative Property of Multiplication
2 Identify the property of a + (b + c) = (a + c) + bA Commutative Property of Addition B Commutative Property of Multiplication C Associative Property of Addition D Associative Property of Multiplication
3 Identify the property of (3 x -4) x 8 = 3 x (-4 x 8)A Commutative Property of AdditionB Commutative Property of MultiplicationC Associative Property of AdditionD Asociative Property of Multiplication
Discuss why using the associative property would be useful with the following problems:
1. 4 + 3 + (-4)
2. -9 x 3 x 0
3. -5 x 7 x -2
4. -8 + 1 + (-6)
Combining Like Terms
Term – can be a number, a variable,or a product of numbers and variables
Coefficient – a number that isMultiplied by a variable in an algebriacexpression
2x2
2x2Coefficient
Exponent
Variable
An Expression - contains numbers, variables and at least one operation.
Like terms: terms in an expression that have the same variable raised to the same power
Examples:
LIKE TERMS NOT LIKE TERMS
6x and 2x 6x2 and 2x
5y and 8y 5x and 8y
4x2 and 7x2 4x2y and 7xy2
Group the Like Terms
2t 3y2 7t k
4z x2
5a 4.5y2
4 Identify all of the terms like 2x
A 5xB 3x2
C 5yD 12yE 2
5 Identify all of the terms like 8y
A 9yB 4y2
C 7yD 8E -18x
6 Identify all of the terms like 8xy
A 8xB 3x2yC 39xyD 4yE -8xy
7 Identify all of the terms like 2y
A 51wB 2xC 3yD 2wE -10y
8 Identify all of the terms like 14x2
A -5xB 8x2
C 13y2
D xE -x2
If two or more like terms are being added or subtracted, they can be combined.
To combine like terms add/subtract the coefficient but leave the variable alone.
7x +8x =15x9v-2v = 7v
Sometimes there are constant terms that can be combined.9 + 2f + 6 =9 + 2f + 6 =
2f + 15Sometimes there will be both coeffients and constants to
be combined.3g + 7 + 8g - 2
11g + 5Notice that the sign before a given term goes with the
number.
It helps if you circle each term firstincluding the operation sign beforethe numbers, variables, and constants.
-5x3 + 3y + 7x3 - 2y – 4x2
-5x3 +3y +7x3 -2y -4x2
2x3 + y – 4x2
Try These:
1.) 2b +6g(3) + 4f + 9f
2.) 9j + 3 + 24h + 6 + 7h + 3
3.) 7a + 4 + 2a -1 9 + 8c -12 + 5c
4.) 8x + 56xy + 5y
9 8x + 3x = 11xA TrueB False
10 7x + 7y = 14xy
A TrueB False
11 2x + 3x = 5xA TrueB False
12 9x + 5y = 14xyA TrueB False
13 6x + 2x = 8x2
A TrueB False
14 -15y + 7y = -8yA TrueB False
15 -6 + y + 8 = 2yA TrueB False
16 -7y + 9y = 2yA TrueB False
17 9x + 4 + 2x =A 15x B 11x + 4 C 13x + 2x D 9x + 6x
18 12x + 3x + 7 - 5 A 15x + 7 - 5 B 13x C 17x D 15x + 2
19 -4x - 6 + 2x - 14A -22x B -2x - 20 C -6x +20 D 22x
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