Transcript CH1-L1-3

Solving
Equations
by by
Solving
Equations
1-3
1-3 Multiplying
or Dividing
Multiplying
or Dividing
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal
Algebra 1 Algebra 1
Solving Equations by
1-3 Multiplying or Dividing
Warm Up 9/1 Turn these into
YOUR tray when finished!
Evaluate each expression.
1. (–7)(2.8)
2. 0.96 ÷ 6
3. (–9)(–9)
Holt McDougal Algebra 1
Solving Equations by
1-3 Multiplying or Dividing
Objective
Solve one-step equations in one variable by
using multiplication or division.
Holt McDougal Algebra 1
Solving Equations by
1-3 Multiplying or Dividing
Solving an equation that contains multiplication or
division is similar to solving an equation that
contains addition or subtraction. Use inverse
operations to undo the operations on the variable.
Inverse Operations
Operation
Multiplication
Division
Holt McDougal Algebra 1
Inverse Operation
Division
Multiplication
Solving Equations by
1-3 Multiplying or Dividing
Properties of Equality
WORDS
Subtraction Property of Equality
You can subtract the same number from
both sides of an equation, and the
statement will still be true.
NUMBERS
ALGEBRA
Holt McDougal Algebra 1
7=7
7–5=7–5
2=2
a=b
a–c=b–c
Solving Equations by
1-3 Multiplying or Dividing
Properties of Equality
WORDS
Addition Property of Equality
You can add the same number to both
sides of an equation, and the statement
will still be true.
NUMBERS
ALGEBRA
Holt McDougal Algebra 1
3=3
3+2=3+2
5=5
a=b
a+c=b+c
Solving Equations by
1-3 Multiplying or Dividing
Properties of Equality
WORDS
Multiplication Property of Equality
You can multiply both sides of an
equation by the same number, and the
statement will still be true.
NUMBERS
ALGEBRA
Holt McDougal Algebra 1
6=6
6(3) = 6(3)
18 = 18
a=b
ac = bc
Solving Equations by
1-3 Multiplying or Dividing
Properties of Equality
WORDS
Division Property of Equality
You can divide both sides of an equation
by the same nonzero number, and the
statement will still be true.
NUMBERS
8 = 8
8
8
=
4
4
2 =2
ALGEBRA
a=b
(c ≠ 0)
a = a
c
c
Holt McDougal Algebra 1
Solving Equations by
1-3 Multiplying or Dividing
Check It Out! Example 2a
Solve the equation. Check your answer.
16 = 4c
Since c is multiplied by 4,
divide both sides by 4 to
undo the multiplication.
4=c
Check
16 = 4c
16
16
Holt McDougal Algebra 1
4(4)
16 
To check your solution,
substitute 4 for c in the
original equation.
Solving Equations by
1-3 Multiplying or Dividing
Example 1A: Solving Equations by Using
Multiplication
Solve the equation.
j
–8 =
3
Since j is divided by 3,
multiply both sides by 3
to undo the division.
–24 = j
Check
j
–8 =
3
–24
–8
3
–8 –8 
Holt McDougal Algebra 1
To check your solution,
substitute –24 for j in the
original equation.
Solving Equations by
1-3 Multiplying or Dividing
Example 2A: Solving Equations by Using Division
Solve the equation. Check your answer.
9y = 108
y = 12
Check
Since y is multiplied by 9,
divide both sides by 9 to
undo the multiplication.
9y = 108
9(12)
108
Holt McDougal Algebra 1
108 To check your solution,
substitute 12 for y in the
108 
original equation.
Solving Equations by
1-3 Multiplying or Dividing
Example 1B: Solving Equations by Using
Multiplication
Solve the equation.
n
= 2.8
6
Since n is divided by 6,
multiply both sides by 6
to undo the division.
n = 16.8
n
= 2.8
Check
6
To check your solution,
16.8 2.8
substitute 16.8 for n in the
6
2.8 2.8  original equation.
Holt McDougal Algebra 1
Solving Equations by
1-3 Multiplying or Dividing
Scavenger Hunt!
Directions:
1.
Find someone with the same card as you (Jack, Queen, King,
Ace)
2.
When you have found a partner, both of you need to come up
and pick a piece of paper from my hand.
3.
Around the room, there are different equations with numbers
(solutions) in the top left corner. YOU WILL START AT THE
POSTER THAT HAS YOUR NUMBER FROM THE PIECE
OF PAPER IN THE TOP LEFT CORNER.
4.
Start at number 1 on your sheet wherever you start. Once you
solve an equation, find the next problem sheet that has that
solution in the top left corner and that will go in slot number
2, etc. Continue until finished. Winners get a prize!
Holt McDougal Algebra 1
Solving Equations by
1-3 Multiplying or Dividing
Warm-Up 9/6
MAKE A NEW WARM-UP SHEET
1. Solve the equation AND
CHECK YOUR ANSWER
–4.8 = –6v
2. Solve the equation AND
CHECK YOUR ANSWER
y
–13 =
3
Holt McDougal Algebra 1
Solving Equations by
1-3 Multiplying or Dividing
Warm-Up 9/7
1. What does the word
‘reciprocal’ mean?
2. Why do we check our work
on homework, tests, quizzes,
etc.?
Holt McDougal Algebra 1
Solving Equations by
1-3 Multiplying or Dividing
VOCABULARY
Reciprocal
Holt McDougal Algebra 1
Solving Equations by
1-3 Multiplying or Dividing
Check It Out! Example 1c
Solve the equation. Check your answer.
c
=7
8
Since c is divided by 8,
multiply both sides by 8
to undo the division.
c = 56
Check
c
=7
8
56 7
8
7 7
Holt McDougal Algebra 1
To check your solution,
substitute 56 for c in the
original equation.
Solving Equations by
1-3 Multiplying or Dividing
Check It Out! Example 1a
Solve the equation. Check your answer.
p
= 10
5
Since p is divided by 5,
multiply both sides by 5
to undo the division.
p = 50
Check
p
= 10
5
To check your solution,
50 10
substitute 50 for p in the
5
10 10  original equation.
Holt McDougal Algebra 1
Solving Equations by
1-3 Multiplying or Dividing
Check It Out! Example 2b
Solve the equation. Check your answer.
0.5y = –10
y = –20
Since y is multiplied by 0.5,
divide both sides by 0.5 to
undo the multiplication.
Check 0.5y = –10
To check your solution,
0.5(–20) –10
–10 –10  substitute –20 for y in the
original equation.
Holt McDougal Algebra 1
Solving Equations by
1-3 Multiplying or Dividing
Remember that dividing a fraction by a
fraction is the same as multiplying by
the reciprocal.
What is a reciprocal?
Holt McDougal Algebra 1
Solving Equations by
1-3 Multiplying or Dividing
Example 3A: Solving Equations That Contain
Fractions
Solve the equation.
5
w = 20
6
The reciprocal of 5 is 6 . Since w is
6
5
5
multiplied by , multiply both sides
6
6
by
.
5
w = 24
Check
5
w = 20
6
20
20 20 
Holt McDougal Algebra 1
To check your solution,
substitute 24 for w in the
original equation.
Solving Equations by
1-3 Multiplying or Dividing
Warm-Up 9/12
Use the same warm up sheet you were
using last week.
1) When our operation is multiplication
or division, what do we want our
coefficient (the number in front of
our variable), to be? (0, 3, 1,
620,000,021,023??)
2) Why in world do we even care about
solving one-step equations? How
does it apply to you?
Holt McDougal Algebra 1
Solving Equations by
1-3 Multiplying or Dividing
Example 3B: Solving Equations That Contain
Fractions
Solve the equation.
3
= 1 z
16
8
The reciprocal of 1 is 8. Since z is
8
1
multiplied by , multiply both sides
8
by 8.
3=z
2
3 =1z
Check
16
8
To check your solution,
substitute 3 for z in the
2
original equation.
3
3

16 16
Holt McDougal Algebra 1
Solving Equations by
1-3 Multiplying or Dividing
In groups of four…
In groups of four, you are going to work together to solve
the next few problems. Each of you will be assigned one
step of the problem. 1 whiteboard, 1 marker, 1 eraser PER
GROUP
Step 1: The oldest person will complete step one of the
problem.
Step 2: The next oldest person will complete step 2 of the
problem.
Step 3: The third oldest person will complete step 3 of the
problem.
Step 4: The youngest person will complete step 4 of the
problem.
ALL TOGETHER, COME UP WITH YOUR ANSWER ON ONE
WHITE BOARD!
Holt McDougal Algebra 1
Solving Equations by
1-3 Multiplying or Dividing
Check It Out! Example 3b
Solve the equation.
4j = 2
3
6
j=1
Holt McDougal Algebra 1
4j
is the same as 4 j.
6
6
The reciprocal of 4 is 6 . Since j is
6
4
4
multiplied by , multiply both sides
6
6
by .
4
Solving Equations by
1-3 Multiplying or Dividing
Check It Out! Example 3b Continued
Solve the equation.
4j = 2
3
6
Check
4j = 2
6
3
To check your solution,
substitute 1 for j in the
original equation.

Holt McDougal Algebra 1
Solving Equations by
1-3 Multiplying or Dividing
Check It Out! Example 3c
Solve the equation.
1
w = 102
6
The reciprocal of 1 is 6. Since w is
6
multiplied by 1 , multiply both sides
6
by 6 .
w = 712
Check
1
w = 102
6
102
102 102 
Holt McDougal Algebra 1
To check your solution,
substitute 712 for w in the
original equation.
Solving Equations by
1-3 Multiplying or Dividing
Check It Out! Example 3a
Solve the equation. Check your answer.
1
– 1 =
b
5
4
5=b
–4
Check
The reciprocal of 1 is 5. Since b is
5
1
multiplied by , multiply both sides
5
by 5.
1b
1
=
–
4
5

Holt McDougal Algebra 1
To check your solution,
substitute – 5 for b in the
4
original equation.
Solving Equations by
1-3 Multiplying or Dividing
Example 4: Application
Ciro puts 1
4 of the money he earns from mowing
lawns into a college education fund. This year
Ciro added $285 to his college education fund.
Write and solve an equation to find how much
money Ciro earned mowing lawns this year.
one-fourth
times
earnings
equals
college fund
Write an equation to represent the relationship.
Substitute 285 for c. Since m is divided
by 4, multiply both sides by 4 to undo
the division.
m = $1140
Holt McDougal Algebra 1
Ciro earned $1140 mowing lawns.
Solving Equations by
1-3 Multiplying or Dividing
Check it Out! Example 4
The distance in miles from the airport that a plane
should begin descending, divided by 3, equals the
plane's height above the ground in thousands of
feet. A plane began descending 45 miles from the
airport. Use the equation to find how high the
plane was flying when the descent began.
Distance
divided by 3
equals
height in thousands of feet
Write an equation to represent the
relationship.
Substitute 45 for d.
15 = h
The plane was flying at 15,000 ft when the descent began.
Holt McDougal Algebra 1
Solving Equations by
1-3 Multiplying or Dividing
Exit Ticket
Using a sticky note, write your
initials then put it in the area how
you are feeling right now
1)I have no idea what is going on
1)I kind of understand this but
need more help
2)I GOT THIS!
Holt McDougal Algebra 1