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2-6 Solving Equations with Rational Numbers
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
2-6 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
2-6 Solving Equations with Rational Numbers
Problem of the Day
A computer word is made of strings of 0’s
and 1’s. How many different words can be
formed using 3 characters?
(An example is 010.)
8
2-6 Solving Equations with Rational Numbers
Sunshine State Standards
MA.8.A.6.4 Perform operations on real
numbers (including…rational
numbers…)…using real-world problems…
2-6 Solving Equations with Rational Numbers
Additional Examples 1A: Solving Equations with
Decimals
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.
2-6 Solving Equations with Rational Numbers
Additional Examples 1B: Solving Equations with
Decimals
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.
2-6 Solving Equations with Rational Numbers
Additional Examples 1C: Solving Equations with
Decimals
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.
2-6 Solving Equations with Rational Numbers
Check It Out: Example 1A and 1B
Solve each equation.
A. m + 9.1 = 3
m + 9.1 = 3
–9.1
–9.1
= –6.1
m
B. – 3.1p = 15.5
15.1
–3.1 p
=
–3.1
–3.1
p = –5
2-6 Solving Equations with Rational Numbers
Additional Example 2A: Solving Equations with
Fractions
Solve.
3
2
n+ =–
7
7
2 2
3 2
n– + =– –
7 7
7 7
n=–
5
7
2
Subtract
from both sides.
7
2-6 Solving Equations with Rational Numbers
Additional Example 2B: Solving Equations with
Fractions
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.
2-6 Solving Equations with Rational Numbers
Additional Example 2C: Solving Equations with
Fractions
Solve.
5
5x
=
8
6
5 5
5x÷5
÷
=
6
8 6
6
5
6
5
63
•
x= 8 •
5
6
5
4
3
x =
4
Divide both sides by 5 .
6
Multiply by the reciprocal.
Simplify.
2-6 Solving Equations with Rational Numbers
Check It Out: Example 2A
Solve each equation.
1 5
=
3 8
5
1
m– =
8
3
1
5
1
1
m– + = +
3
8
3
3
15
8
m=
+
24 24
23
m=
24
m–
2-6 Solving Equations with Rational Numbers
Check It Out: Example 2B
Solve each equation.
3
6
x=
8
19
3
6
x=
8
19
6
3 ÷3
÷3
=
x
8
8 19 8
62 8
3
8
x • =
• 1
8
3 19 3
x = 16
19
2-6 Solving Equations with Rational Numbers
Additional 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
2-6 Solving Equations with Rational Numbers
Additional Example 3 Continued
Now solve the equation.
s  2 = 22
3
3
s
2
2 2
2
÷
= 2 ÷
3
3 3
3
Divide both sides by 2 .
3
2
3
2
3
s 

3
2 = 2 3  2 Multiply both sides by the
8
3 reciprocal.
s= 3  2
24
s = 6 , or 4 Simplify.
Mr. Rios can make 4 servings.
2-6 Solving Equations with Rational Numbers
Check It Out: Example 3
3
Rick’s car holds 5 the amount of gasoline as his
1
wife’s van. If the car’s gas tank can hold 16
2
gallons of gasoline, how much gasoline can the
tank in the minivan hold?
Amount of
gas in van
•
Three-fifths
=
Amount of
gas in car
2-6 Solving Equations with Rational Numbers
Check It Out: Example 3 Continued
1
3
x •
= 16
2
5
x • 3 = 33
2
5
3
3
33 3
x
÷
=
÷
5
5
2 5
x •1 =
5
33
•
3
2
55, or 27 1
33 • 5
x=
1=
2
2
2 •3
So, the tank in the minivan can hold 27 1 gallons of
2
gas.
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2-6 Solving Equations with Rational Numbers
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
2-6 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
2-6 Solving Equations with Rational Numbers
Lesson Quiz: Part II
2
5. Tamara can mow 5 acre in one hour. If
her yard is 2 acres, how many hours will
it take her to mow the entire yard?
5 hours
2-6 Solving Equations with Rational Numbers
Lesson Quiz for Student Response Systems
1. Solve.
a – 36 = 44.9
A. a = 36.7
B. a = 49.2
C. a = 59.9
D. a = 80.9
2-6 Solving Equations with Rational Numbers
Lesson Quiz for Student Response Systems
2. Solve.
c + 3 = –11 4
4
5
A. c = 12 11
20
C. c = 11 4
5
B. c = –12 11
20
D. c = 113
4
2-6 Solving Equations with Rational Numbers
Lesson Quiz for Student Response Systems
3. Solve.
8e = 2
3
A. e = 8 2
3
C. e = 1
12
B. e = 5 1
3
D. e = 3
20
2-6 Solving Equations with Rational Numbers
Lesson Quiz for Student Response Systems
4. Solve.
h = 35
3
6
A. h = 9 1
2
C. h = 11 1
2
B. h = 10 1
2
D. h = 12 1
2