mcgraw-hill/irwin 2011 the mcgraw-hill companies, all rights reserved chapter 5 solving for the...
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List the steps for solving word problems 2. Complete blueprint aids to solve word problems; check the solutions Solving for the Unknown: A how-to Approach for Solving Equations #5 Learning Unit Objectives Solving Word Problems for the Unknown LU5.2TRANSCRIPT
McGraw-Hill/Irwin ©2011 The McGraw-Hill Companies, All Rights Reserved
Chapter 5
Solving for the Unknown: A Solving for the Unknown: A How-to Approach for How-to Approach for
Solving EquationsSolving Equations
5-2
1. Explain the basic procedures used to solve equations for the unknown
2. List the five rules and the mechanical steps used to solve for the unknown in seven situations; know how to check the answers
Solving for the Unknown: A how-to Approach for Solving Equations#5Learning Unit ObjectivesSolving Equations for the UnknownLU5.1
5-3
1. List the steps for solving word problems2. Complete blueprint aids to solve word
problems; check the solutions
Solving for the Unknown: A how-to Approach for Solving Equations#5Learning Unit ObjectivesSolving Word Problems for the UnknownLU5.2
5-4
Expression – A meaningful combination of numbers and letters called terms.
Equation – A mathematical statement with an equal sign showing that a mathematical expression on the left equals the mathematical expression on the right.
Formula – An equation that expresses in symbols a general fact, rule, or principle.
Variables and constants are terms of mathematical expressions.
Terminology
5-5
Solving Equations for the Unknown
Left side of equation Right side of equation
Equality in equations
A + 8 58
Dick’s age in 8 years will equal 58
5-6
Variables and Constants Rules
1. If no number is in front of a letter, it is a
1: B = 1B; C = 1C
2. If no sign is in front of a letter or
number, it is a +: C = +C; 4 = +4
5-7
Solving for the Unknown Rule
Whatever you do to one side of an
equation, you must do to the other side.
5-8
Opposite Process Rule
If an equation indicates a process such as addition,
subtraction, multiplication, or
division, solve for the unknown or variable by using the opposite
process.
5-9
Opposite Process Rule
A + 8 = 58
- 8 - 8
A = 50
Check
50 + 8 = 58
5-10
Equation Equality Rule
You can add the same quantity or number to both
sides of the equation and subtract the same quantity or number from both sides of the equation without affecting the equality of the equation. You
can also divide or multiply both sides of the equation by the same quantity or number (except 0) without affecting the equality of the equation.
5-11
Equation Equality Rule
7G = 35
7G = 357 7
G = 5
Check7(5) = 35
5-12
Multiple Processes Rule
When solving for an unknown that
involves more than one process, do the
addition and subtraction before the
multiplication and division.
5-13
Multiple Process Rule
H + 2 = 5 4
H + 2 = 5 4
-2 -2
H = 3 4
H = 4(3) 4
H = 12
( )(4)Check12 + 2 = 5 43 + 2= 5
5-14
Parentheses Rule
When equations contain parentheses (which indicates
grouping together, you solve for the unknown by first
multiplying each item inside the parentheses by the number or
letter just outside the parentheses. Then you continue
to solve for the unknown with the opposite process used in the equation. Do the addition and
subtractions first; then the multiplication and division.
5-15
Parentheses Rule
5(P - 4) = 20
5P – 20 = 20
+20 +20
5P = 40
5P = 405 5
P =8Check
5(8-4) = 20 5(4) = 20 20 = 20
5-16
Like Unknown Rule
To solve equations with like unknowns, you first combine the unknowns and then
solve with the opposite process used
in the equation.
5-17
Like Unknown Rule
4A + A = 20
5A = 20
5A = 205 5
A = 4Check4(4) +4 = 20 16 + 4 = 20
5-18
Solving Word Problems for Unknowns1) Read the entire Problem
2) Ask: “What is the problem looking for?”
3) Let a variable represent the unknown
4) Visualize the relationship between the unknowns and variables. Then set up an equation to solve for unknown(s)
5) Check your results to ensure accuracy
Y = Computers
4Y + Y = 600
Read again if necessary
5-19
Solving Word Problems for the Unknown
Unknown(s) Variable(s) Relationship
Blueprint aid
5-20
Solving Word Problems for the Unknown
Unknown(s) Variable(s) Relationship
ICM Company sold 4 times as many computers as Ring Company. The difference in their sales is 27. How many computers of each company were sold?
4C - C = 273C = 27
3 3C = 9
Ring = 9 computers
ICM = 4(9) = 36 Computers
Cars SoldICM 4C 4CRing C -C
27
Check 36 - 9 = 27