solving equations by multiplying or dividing
DESCRIPTION
Solving Equations by Multiplying or Dividing. Warm Up. Simplify:. 1) a = -2.8. 1) -5.2 + a = -8. 2) 90 = -22 + a. 2) a = 112. 3) -12 + f = 3. 3) f = -9. 4) -1200 + j = 345. 4) j = 1545. Introduction. - PowerPoint PPT PresentationTRANSCRIPT
CONFIDENTIAL 1
Solving Equations bySolving Equations byMultiplying or DividingMultiplying or Dividing
CONFIDENTIAL 2
Warm UpWarm Up
1) -5.2 + a = -8
Simplify:
2) 90 = -22 + a
3) -12 + f = 3
4) -1200 + j = 345
1) a = -2.8
2) a = 112
3) f = -9
4) j = 1545
CONFIDENTIAL 3
Introduction
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 OperationsOperation Inverse Operation
Multiplication Division
Subtraction Addition
An equation is like a balanced scale. To keep the balance, whatever you do on one side of the equation, you must also do on the other side.
CONFIDENTIAL 4
Solve each equation. Check your answer.
Solving Equations by Using Multiplication
-4 = k -5
A)
(-5) (-4) = (-5) ( k) -5
Since k is divided by -5, multiply both sides by -5 to undo the division.
20 = k
Check
-4 = k -5
-4
-4 -4
20-5
To check your solution, substitute 20 for k in the original equation.
CONFIDENTIAL 5
m = 1.5 3
B)
(3) × m = (3) × 1.5 3
m = 4.5
Check
m = 1.5 3
1.5
1.5 1.5
4.5 3
Since m is divided by 3, multiply both sides by 3 to undo the division.
To check your solution, substitute 1.5 for m in the original equation.
CONFIDENTIAL 6
Solve each equation. Check your answer.
Now you try!
1) p = 10 5
2) -13 = y 3
3) c = 7 8
1) p = 50
2) y = -39
3) c = 56
CONFIDENTIAL 7
Solving Equations by Using Division
Solve each equation. Check your answers.
A) 7x = 56
7x = 56
7x = 56 7 7
Since x is multiplied by 7, divide both sides by 7 to undo the multiplication.
Check
7x = 56
56
56 56
7(8)
x = 8
To check your solution, substitute 8 for x in the original equation.
CONFIDENTIAL 8
B) 13 = -2w
13 = -2w
13 = -2w-2 -2
Since w is multiplied by -2, divide both sides by -2 to undo the multiplication.
Check
13 = -2w
-2(6.5)
13 13
13
-6.5 = w
To check your solution, substitute 8 for x in the original equation.
CONFIDENTIAL 9
Now you try!
1) 16 = 4c
2) 0.5y = -10
Solve each equation. Check your answer.
3) 15k = 75
1) c = 4
2) y = -20
3) k = 5
CONFIDENTIAL 10
Remember that dividing is the same as multiplying by the reciprocal.
When solving equations, you will sometimes find it easier to multiply by a reciprocal
instead of dividing.
This is often true when an equation contains fractions.
CONFIDENTIAL 11
Solving Equations That Contain Fractions
Solve each equation.
A) 5v = 35 9
The reciprocal of 5/9 is 9/5 . Since v is multiplied by 5/9 , multiply both sides by 9/5.
9 × 5v = 9 ×355 9 5
v = 63
CONFIDENTIAL 12
B) 5 = 4y 2 3
The reciprocal of 4/3 is 3/4 . Since v is multiplied by 4/3 , multiply both sides by 3/4.
3 × 5 = 3 ×4y4 2 4 3
15 = y 8
5 = 4y2 3
CONFIDENTIAL 13
Now you try!
1) -1 = b 4 5
2) 4j = 2 6 3
Solve each equation. Check your answer.
3) w = 102 6
1) b = -1.25
2) j = 1
3) w = 612
CONFIDENTIAL 14
The distance in miles from the airport that a plane shouldbegin descending, divided by 3, equals the plane’s height above the ground in thousands of feet. If a plane is 10,000 feet above the ground, write and solve an equation to find the distance at which the pilot should begin descending.
Distance divided by 3 equals height in thousands of feet.
Solution:
d = h3
Write an equation to represent the relationship.
Substitute 10 for h. Since d is divided by 3, multiply both sides by 3 to undo the division.
d = 30
The pilot should begin descending 30 miles from the airport.
d = 103
(3)d = (3) × 103
CONFIDENTIAL 15
Properties of Equality
WORDS NUMBERS ALGEBRA
Multiplication Property of Equality
You can multiply both sides of an equation by the same
number, and the statement will still be true.
6 = 66 (3) = 6 (3)
18 = 18
a = bac = bc
Division Property of EqualityYou can divide both sides of anequation by the same nonzero number, and the statement will
still be true.
8 = 88 = 8
2 = 2
a = b(c ≠ 0)a = b 4 4c c
CONFIDENTIAL 16
An orange contains about 80 milligrams of vitamin C, which is 10 times as much as an apple contains. Write
and solve an equation to find the amount ofvitamin C in an apple.
Now you try!
10x = 80
x = 10 milligrams
CONFIDENTIAL 17
Assignments
1) K = 8 4
2) z = -9 3
3) -2 = w-7
4) 6 = t-5
Solve each equation. Check your answer:
1) k = 321) k = 32
2) z = -27
3) w = 14
4) t = - 30
CONFIDENTIAL 18
5) g = 10 1.9
6) 2.4 = b 5
7) 4x = 28
8) -64 = 8c
9) -9 j = -45
Factor the trinomial. Check your answer.
5) g = 19
6) b = 12
7) x = 7
8) c = - 8
9) j = 5
CONFIDENTIAL 19
10) The Baseball Birthday Batter Package at a minor league ballpark costs $192. The package includes tickets, drinks, and cake for a group of 16 children.
Write and solve an equation to find the cost per child.
10) 16 c =$192
c = $12
CONFIDENTIAL 20
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 OperationsOperation Inverse Operation
Multiplication Division
Subtraction Addition
An equation is like a balanced scale. To keep the balance, whatever you do on one side of the equation, you must also do on the other side.
Let’s review
CONFIDENTIAL 21
Solve each equation. Check your answer.
Solving Equations by Using Multiplication
-4 = k -5
A)
(-5) (-4) = (-5) ( k) -5
Since k is divided by -5, multiply both sides by -5 to undo the division.
20 = k
Check
-4 = k -5
-4
-4 -4
20-5
To check your solution, substitute 20 for k in the original equation.
review
CONFIDENTIAL 22
m = 1.5 3
B)
(3) × m = (3) × 1.5 3
m = 4.5
Check
m = 1.5 3
1.5
1.5 1.5
4.5 3
Since m is divided by 3, multiply both sides by 3 to undo the division.
To check your solution, substitute 1.5 for m in the original equation.
review
CONFIDENTIAL 23
Solving Equations by Using Division
Solve each equation. Check your answers.
A) 7x = 56
7x = 56
7x = 56 7 7
Since x is multiplied by 7, divide both sides by 7 to undo the multiplication.
Check
7x = 56
56
56 56
7(8)
x = 8
To check your solution, substitute 8 for x in the original equation.
review
CONFIDENTIAL 24
B) 13 = -2w
13 = -2w
13 = -2w-2 -2
Since w is multiplied by -2, divide both sides by -2 to undo the multiplication.
Check
13 = -2w
-2(6.5)
13 13
13
-6.5 = w
To check your solution, substitute 8 for x in the original equation.
review
CONFIDENTIAL 25
Remember that dividing is the same as multiplying by the reciprocal.
When solving equations, you will sometimes find it easier to multiply by a reciprocal
instead of dividing.
This is often true when an equation contains fractions.
review
CONFIDENTIAL 26
Solving Equations That Contain Fractions
Solve each equation.
A) 5v = 35 9
The reciprocal of 5/9 is 9/5 . Since v is multiplied by 5/9 , multiply both sides by 9/5.
9 × 5v = 9 ×355 9 5
v = 63
review
CONFIDENTIAL 27
B) 5 = 4y 2 3
The reciprocal of 4/3 is 3/4 . Since v is multiplied by 4/3 , multiply both sides by 3/4.
3 × 5 = 3 ×4y4 2 4 3
15 = y 8
5 = 4y2 3
review
CONFIDENTIAL 28
The distance in miles from the airport that a plane shouldbegin descending, divided by 3, equals the plane’s height above the ground in thousands of feet. If a plane is 10,000 feet above the ground, write and solve an equation to find the distance at which the pilot should begin descending.
Distance divided by 3 equals height in thousands of feet.
Solution:
d = h3
Write an equation to represent the relationship.
Substitute 10 for h. Since d is divided by 3, multiply both sides by 3 to undo the division.
d = 30
The pilot should begin descending 30 miles from the airport.
d = 103
(3)d = (3) × 103
CONFIDENTIAL 29
Properties of Equality
WORDS NUMBERS ALGEBRA
Multiplication Property of Equality
You can multiply both sides of an equation by the same
number, and the statement will still be true.
6 = 66 (3) = 6 (3)
18 = 18
a = bac = bc
Division Property of EqualityYou can divide both sides of anequation by the same nonzero number, and the statement will
still be true.
8 = 88 = 8
2 = 2
a = b(c ≠ 0)a = b 4 4c c
review
CONFIDENTIAL 30
You did a great job You did a great job today!today!