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Student Learning Goal Chart
Lesson Reflections
3-1, 3-2, 3-3, 3-4, 3-5, 3-6
Pre-Algebra Learning Goal
Students will
understand rational
and real numbers.
Students will understand rational and real numbers
by being able to do the following:
• Learn to write rational numbers in equivalent forms (3.1)
• Learn to add and subtract decimals and rational numbers with like
denominators (3.2)
• Learn to add and subtract fractions with unlike denominators (3.5)
• Learn to multiply fractions, decimals, and mixed numbers (3.3)
• Learn to divide fractions and decimals (3.4)
• Learn to solve equations with rational numbers
(3.6)
3-6 Solving Equations with Rational Numbers
Today’s Learning Goal Assignment
Learn to solve
equations with
rational numbers.
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Pre-Algebra HW
Page 138
#14-26 all
Pre-Algebra
Equations
with
Rational
Numbers
3-6
Solving
Equations
with
Rational
Numbers
3-6 Solving
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Warm Up
Multiply.
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
Pre-Algebra
3-6 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 8 characters?
(An example is 01010101.) 256
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Today’s Learning Goal Assignment
Learn to solve
equations with
rational numbers.
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 and 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
Additional Examples 3: Solving Word Problems Using
Equations
Mr. Rios wants to prepare a casserole that
requires 2 1 cups of milk. If he makes the
2
casserole, he will have only 3 cup of milk left
4
for his breakfast cereal. How much milk does
Mr. Rios have?
2(2)+1 5
1
Convert fractions: 2 =
=
2
2
2
Write an equation:
Original
amount of milk
c
Pre-Algebra
–
–
Milk for
casserole =
5
2
=
Milk for
cereal
3
4
3-6 Solving Equations with Rational Numbers
Additional Examples 3 Continued
Now solve the equation.
c – 5 = 3
2
4
5
5
3
5
c –
2 +2 = 4 +2
3
10
c = 4 + 4
1
13
c = 4 , or 3 4
Mr. Rios has 3
Pre-Algebra
1
cups of milk.
4
Add 5 to both sides.
2
Find a common
denominator, 4.
Simplify.
3-6 Solving Equations with Rational Numbers
Try This: Examples 3
2
Rick’s car holds 3 the amount of gasoline as his
wife’s van. If the car’s gas tank can hold 15.5
gallons of gasoline, how much gasoline can the
tank in the minivan hold?
Convert decimal
15(2)+1 31
1
to a fraction:
15.5 = 15 =
=
2
Write an equation:
Van’s gas
tank
g
Pre-Algebra
•
Ratio of car’s tank
to van’s tank
•
2
3
2
2
=
Capacity of
car’s tank
=
31
2
3-6 Solving Equations with Rational Numbers
Try This: Examples 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
Pre-Algebra
1
gallons of gasoline.
4
3-6 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.
5
8
1
d=9
2
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Lesson Quiz: Part 2
5. Tamara had 6 bags of mulch for her
1
garden. Each bag contained 8 lb of
3
mulch. What was the total weight of
the mulch?
50 lb
Pre-Algebra
3-6 Solving Equations with Rational Numbers
Pre-Algebra