Transcript 3CH2L7

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.)
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Course 3
2-7 Solving Equations with Rational Numbers
TB P. 92-95
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
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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
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Multiply both sides by 1.2
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=–
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5
7
2
Subtract
from both sides.
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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
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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
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6
Multiply both sides by .
5
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
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

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
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