Download A. Pre-Algebra 3-6

3-6 Solving Equations with Rational Numbers
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Pre-Algebra
3-6 Solving Equations with Rational Numbers
11/12/13
Objective: Students will understand that real
numbers are either rational or irrational
(Understand the real number system) and
recognize that numbers with decimal expansions
that eventually repeat can be written as a fraction
and then convert them.
CCES: 8.NS.1, MP. 1, MP. 2, MP. 6
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Can you define or describe the following:
•Rational Numbers
•Irrational Numbers
•Integers
•Whole Numbers
•Natural Numbers
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Pre-Algebra
3-6 Solving Equations with Rational Numbers
The decimal equivalent of a fraction
will either terminate or repeat.
Did you know that fractions that
terminate will have denominators
containing only prime factors
of 2 and/or 5?
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Solving Equations with Rational
Numbers
Exploration
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Additional Example 1A: Solving Equations with
Decimals.
Solve.
A. m + 4.6 = 9
m + 4.6 = 9
Subtract 4.6 from
– 4.6 = – 4.6 both sides.
m = 4.4
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.
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Additional Examples 1B: Solving Equations with
Decimals
Solve.
B. 8.2p = –32.8
8.2p = –32.8
8.2
8.2
p = –4
Pre-Algebra
Divide both sides by 8.2
3-6 Solving Equations with Rational Numbers
Additional Examples 1C: Solving Equations with
Decimals
Solve.
x
C. 1.2 = 15
x
= 1.2 • 15
1.2 •
1.2
x = 18
Pre-Algebra
Multiply both sides by 1.2
3-6 Solving Equations with Rational Numbers
Try This: 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
Pre-Algebra
Divide both sides by 5.5
3-6 Solving Equations with Rational Numbers
Try This: Examples 1C
Solve.
y = 90
C. 4.5
y
= 4.5 • 90
4.5 •
4.5
y = 405
Pre-Algebra
Multiply both sides by 4.5
3-6 Solving Equations with Rational Numbers
Additional Examples 2A: Solving Equations with
Fractions
Solve.
3
2
A. n + = –
7
7
2 2
3 2
n– + =– –
7 7
7 7
n=–
Pre-Algebra
5
7
2
Subtract from both sides.
7
3-6 Solving Equations with Rational Numbers
Additional Examples 2B: Solving Equations with
Fractions
Solve.
B. y – 1 = 2
6
3
1 y 1
2 1
+ – = +
6
6
3 6
4 1
y= +
6 6
5
y=
6
Pre-Algebra
1
Add to both sides.
6
Find a common denominator; 6.
Simplify.
3-6 Solving Equations with Rational Numbers
Additional Examples 2C: Solving Equations with
Fractions
Solve.
C. 5 x = 5
6
8
5
6
5
63
•
x= 8 •
5
6
5
4
3
x =
4
Pre-Algebra
6
Multiply both sides by .
5
Simplify.
3-6 Solving Equations with Rational Numbers
Try This: Example 2A
Solve.
A. n + 1 = – 5
9
9
1 1
5 1
n– + =– –
9 9
9 9
2
n=–
3
Pre-Algebra
1
Subtract 9 from both sides.
6
Simplify – .
9
3-6 Solving Equations with Rational Numbers
Try This: Example 2B
Solve.
1
3
B. y – 2 =
4
1 y 1
3 1
+ – = +
2
2
4 2
3 2
+
4 4
1
y= 1
4
y=
Pre-Algebra
1
Add to both sides.
2
Find a common denominator; 4.
Simplify.
3-6 Solving Equations with Rational Numbers
Try This: Examples 2C
Solve.
6
3x
=
C. 8
19
6
3x
=
19
8
2
6
8
3
8
•
• x =
19
31
8
3
16
x =
19
Pre-Algebra
8
Multiply both sides by .
3
Simplify.
3-6 Solving Equations with Rational Numbers
Homework: Holt Practice 3-6
Pre-Algebra