Download 1.5 Solving Equations with Rational Numbers

1-5 Solving Equations with Rational Numbers
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
1-5 Solving Equations with Rational Numbers
Warm Up
Add or subtract.
1.
5
7
+
10
10
11
5
3
5
2. 2
–1
8
16
11
16
3. 4.8 + 3.6
8.4
4. 2.4 – 0.05
2.35
1-5 Solving Equations with Rational Numbers
Learn to solve equations with rational
numbers.
1-5 Solving Equations with Rational Numbers
Examples 1: Solving Equations with Decimals
A. Solve.
m + 4.6 = 9
m + 4.6 = 9
– 4.6 = – 4.6
m = 4.4
Use the Subtraction
Property of Equality.
Subtract 4.6 from
both sides.
Remember!
Once you have solved an equation it is a good
idea to check your answer. To check your
answer, substitute your answer for the variable
in the original equation.
1-5 Solving Equations with Rational Numbers
Examples 1: Solving Equations with Decimals
B. Solve.
8.2p = –32.8
8.2p = –32.8
8.2
8.2
p = –4
Use the Division Property
of Equality. Divide both
sides by 8.2
1-5 Solving Equations with Rational Numbers
Examples 1: Solving Equations with Decimals
C. Solve.
x
= 15
1.2
x
= 1.2 • 15
1.2 •
1.2
x = 18
Use the Multiplication
Property of Equality. Multiply
both sides by 1.2
1-5 Solving Equations with Rational Numbers
Check It Out
Solve.
D. m + 9.1 = 3
m + 9.1 = 3
–9.1 = –9.1
m = –6.1
Use the Subtraction
Property of Equality.
Subtract 9.1 from
both sides.
E. 5.5b = 75.9
75.9
5.5 b
=
5.5
5.5
b = 13.8
Use the Division Property
of Equality. Divide both
sides by 5.5
1-5 Solving Equations with Rational Numbers
Check It Out
Solve.
y = 90
F. 4.5
y
= 4.5 • 90
4.5 •
4.5
y = 405
Use the Multiplication
Property of Equality. Multiply
both sides by 4.5
1-5 Solving Equations with Rational Numbers
Example 2: Solving Equations with Fractions
A. Solve.
3
2
n+ =–
7
7
2 2
3 2
n– + =– –
7 7
7 7
n=–
5
7
2
Subtract
from both sides.
7
1-5 Solving Equations with Rational Numbers
Example 2: Solving Equations with Fractions
B. Solve.
1 2
y– =
6 3
1 y 1
2 1
+ – = +
6
6
3 6
4 1
y= +
6 6
5
y=
6
1
Add to both sides.
6
Find a common denominator; 6.
Simplify.
1-5 Solving Equations with Rational Numbers
Example 2: Solving Equations with Fractions
C. Solve.
5
5x
=
8
6
5
6
5
63
•
x= 8 •
5
6
5
4
3
x =
4
6
Multiply both sides by .
5
Simplify.
1-5 Solving Equations with Rational Numbers
Check It Out: Example 2A
D. Solve.
5
1
=–
9
9
1 1
5 1
n– + =– –
9 9
9 9
2
n=–
3
n+
1
Subtract 9 from both sides.
6
Simplify – .
9
1-5 Solving Equations with Rational Numbers
Check It Out
E. Solve.
1 3
y– 2 =
4
1 y 1
3 1
+ – = +
2
2
4 2
3 2
+
4 4
1
y=1
4
y=
1
Add to both sides.
2
Find a common denominator; 4.
Simplify.
1-5 Solving Equations with Rational Numbers
Check It Out
F. Solve.
6
3x
=
19
8
2
6
8
3
8
x
=
•
•
19 3 1
8
3
x =
16
19
Multiply both sides by
Simplify.
8
.
3
1-5 Solving Equations with Rational Numbers
Example 3: Solving Word Problems Using Equations
Mr. Rios wants to prepare a dessert, but only
has 2 2 tablespoons of sugar. If each serving
3
of the dessert has 2 tablespoon of sugar, how
3
many servings can he make for the party?
Write an equation:
Total servings
s


Amount
needed
for each
dessert
2
3
=
=
Amount of
sugar
2
23
1-5 Solving Equations with Rational Numbers
Additional Example 3 Continued
Now solve the equation.
s  2 = 22
3
3
3
2
3
2
3
Multiply both sides by
.
s 

=
2

2
3
2
3 2
8
3
s= 3  2
24
s = 6 , or 4 Simplify.
Mr. Rios can make 4 servings.
1-5 Solving Equations with Rational Numbers
Check It Out: Example 3
2
Rick’s car holds 3 the amount of gasoline as his
31
wife’s van. If the car’s gas tank can hold
2
gallons of gasoline, how much gasoline can the
tank in the minivan hold?
Write an equation:
Van’s gas
tank
g
•
Ratio of car’s tank
to van’s tank
•
2
3
=
Capacity of
car’s tank
=
31
2
1-5 Solving Equations with Rational Numbers
Check It Out: Example 3 Continued
Now solve the equation.
31
2
g•
=
2
3
3
g • 3 • 2 = 31 •
2
2
3
2
g = 93
4
Multiply both sides by 3 .
2
Simplify.
1
g = 23 4
The van’s gas tank holds 23
1
gallons of gasoline.
4
1-5 Solving Equations with Rational Numbers
Lesson
Quiz
1-5 Solving Equations with Rational Numbers
Lesson Quiz: Part I
Solve.
1. x – 23.3 = 17.8
x = 41.1
3
2
2. j +
= –14
4
3
5
j = –15
12
3. 9y = 3
5
y= 1
15
d = 23
4.
4
8
1
d=9
2