Download Document

Equations
with
Rational
Numbers
2-7
Solving
Equations
with
Rational
Numbers
2-7 Solving
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
33
2-7 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
Course 3
2-7 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
Course 3
2-7 Solving Equations with Rational Numbers
Learn to solve equations with rational
numbers.
Course 3
2-7 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
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.
Course 3
2-7 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
Course 3
Divide both sides by 8.2
2-7 Solving Equations with Rational Numbers
Additional Examples 1C: Solving Equations with
Decimals
Solve.
x
= 15
1.2
1.2 •
x
= 1.2 • 15
1.2
x = 18
Course 3
Multiply both sides by 1.2
2-7 Solving Equations with Rational Numbers
Check It Out: Example 1A & 1B
Solve.
A. m + 9.1 = 3
m + 9.1 = 3
–9.1 = –9.1
Subtract 9.1 from
both sides.
m = –6.1
B. 5.5b = 75.9
75.9
5.5 b
=
5.5
5.5
b = 13.8
Course 3
Divide both sides by 5.5
2-7 Solving Equations with Rational Numbers
Check It Out: Example 1C
Solve.
y = 90
C. 4.5
4.5 •
y
= 4.5 • 90
4.5
y = 405
Course 3
Multiply both sides by 4.5
2-7 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=–
Course 3
5
7
2
Subtract
from both sides.
7
2-7 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
Course 3
1
Add to both sides.
6
Find a common denominator; 6.
Simplify.
2-7 Solving Equations with Rational Numbers
Additional Example 2C: Solving Equations with
Fractions
Solve.
5
5x
=
8
6
5
6
5
63
•
x= 8 •
5
6
5
4
3
x =
4
Course 3
6
Multiply both sides by .
5
Simplify.
2-7 Solving Equations with Rational Numbers
Check It Out: Example 2A
Solve.
5
1
=–
9
9
1 1
5 1
n– + =– –
9 9
9 9
2
n=–
3
n+
Course 3
1
Subtract 9 from both sides.
6
Simplify – .
9
2-7 Solving Equations with Rational Numbers
Check It Out: Example 2B
Solve.
1 3
y– 2 =
4
1 y 1
3 1
+ – = +
2
2
4 2
3 2
+
4 4
1
y= 1
4
y=
Course 3
1
Add to both sides.
2
Find a common denominator; 4.
Simplify.
2-7 Solving Equations with Rational Numbers
Check It Out: Example 2C
Solve.
6
3x
=
19
8
6
3x
=
19
8
2
6
8
3
8
•
• x =
19
31
8
3
16
x =
19
Course 3
8
Multiply both sides by .
3
Simplify.
2-7 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
Course 3


Amount
needed
for each
dessert
2
3
=
=
Amount of
sugar
2
23
2-7 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.
Course 3
2-7 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
Course 3
•
Ratio of car’s tank
to van’s tank
•
2
3
=
Capacity of
car’s tank
=
31
2
2-7 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
Course 3
1
gallons of gasoline.
4
2-7 Solving Equations with Rational Numbers
Lesson Quiz: Part 1
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
Course 3
2-7 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
Course 3