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Solving Multiplication and Division Equations

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Solving Multiplication and Division Equations 1-4 Warm Up Problem of the Day Lesson Presentation Pre-Algebra Warm Up Solve. x = 12 n = 7 k = 1 t = 66 x = 13 1-4 ... – PowerPoint PPT presentation

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Title: Solving Multiplication and Division Equations


1
Solving Multiplication and Division Equations
1-4
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
2
Warm Up Solve.
x 12
1. x ? 3 9
n 7
2. 16 n 9
k 1
3. 5 k 6
4. 47 t ? 19
t 66
x 13
5. 15 x 2
3
Problem of the Day Jackie went shopping for a
new wardrobe. She bought seven new shirts and
four new pairs of pants. She made sure that they
can all be worn together in combinations. How
many outfits can she put together?
28
4
Learn to solve equations using multiplication and
division.
5
Vocabulary
Division Property of Equality Multiplication
Property of Equality
6
You can solve a multiplication equation using the
Division Property of Equality.
You can divide both sides of an equation by the
same nonzero number, and the equation will still
be true.
4 3 12
x y
4 3 12
x y
2
2
z
z
7
Additional Example 1 Solving Equations Using
Division
Solve 8x 32.
8x 32
Divide both sides by 8.
8x 32
8
8
1x 4
1 x x
x 4
Check
8x 32
Substitute 4 for x.
?
8
Try This Example 1
Solve 9x 36.
9x 36
Divide both sides by 9.
9x 36
9
9
1x 4
1 x x
x 4
Check
9x 36
Substitute 4 for x.
?
9
You can solve a division equation using the
Multiplication Property of Equality.
You can multiply both sides of an equation by the
same number, and the statement will still be true.
2 3 6
x y
2 3 6
x y
8 3 24
10
Additional Example 2 Solving Equations Using
Multiplication
Solve 7.
7
7
Multiply both sides by 7.
n 49
Check
Substitute 49 for n.
?
11
Try This Example 2
Solve 16
4
4
Multiply both sides by 4.
n 64
Check
Substitute 64 for n.
?
12
Additional Example 3 Food Application
Joe has enough flour to bake one sheet cake but
would rather make cookies. How many dozen cookies
can he make?
13
Additional Example 3 Continued
cups of flour for 1 dozen cookies
cups of flour in 1 cake
?



2
c
8
Write the equation.
2c 8
2c 8
Divide both sides by 2.
2
2
c 4
Joe can make 4 dozen cookies with the same amount
of flour that he would need for 1 sheet cake.
14
Try This Example 3
cups of flour for bread pudding
cups of flour in 1 cake

?


4
b
8
Write the equation.
4b 8
4b 8
Divide both sides by 4.
4
4
c 2
Joe can make 2 bread pudding desserts with the
same amount of flour that he would need for 1
sheet cake.
15
Additional Example 4 Money Application
Meg has saved 50, which is one-fourth of the
amount she needs for a school trip. What is the
total amount she needs?
fraction of amount raised so far
amount raised so far
total amount needed
?



x
50
Write the equation.
Multiply both sides by 4.
4
4
x 200
Meg needs 200 total.
16
Try This Example 4
The school library needs money to complete a new
collection. So far, the library has raised 750,
which is only one-eighth of what they need. What
is the total amount needed?
amount raised so far
total amount needed

?


x
750
Write the equation.
8
Multiply both sides by 8.
8
x 6000
The library needs to raise a total of 6000.
17
Sometimes it is necessary to solve equations by
using two inverse operations. For instance, the
equation 6x ? 2 10 has multiplication and
subtraction.
Variable term
6x ? 2 10
Multiplication
Subtraction
To solve this equation, add to isolate the term
with the variable in it. Then divide to solve.
18
Additional Example 5 Solving a Simple Two-Step
Equation
Solve 3y 7 20.
Add 7 to both sides to isolate the term with y in
it.
3y 7 20
Step 1
7
7
3y 27
Step 2
3y 27
Divide both sides by 3.
3
3
y 9
19
Try This Example 5
Solve 4y 5 29.
Subtract 5 from both sides to isolate the term
with y in it.
4y 5 29
Step 1
5
5
4y 24
Step 2
4y 24
Divide both sides by 4.
4
4
y 6
20
Lesson Quiz
Solve. 1. 3 2. 16t 112 3. 14 4.
3n 17 29 5. Joan is making a scrapbook of
her pictures. She wants to put three pictures on
each page. She has 63 photos. Write and solve an
equation to find how many pages she will need for
all of the photos.
k 18
t 7
b 126
n 4
3x 63 21 pages
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