Download CHAPTER 3:

LORD MAY THY WILL BE DONE IN ALL THINGS. 
CHAPTER 5:
Rational Numbers
and Equations
SECTION: 5.1 Rational Numbers
Objective: TLW write fractions as decimals and vice versa.
Standards: M7.A.1.1, M7.A.1.1.1, M7.A.1.2, M7.A.1.2.1,
M7.A.1.2.3
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Vocabulary:
Rational number:
Terminating decimal:
Repeating decimal:
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 1: Show that the number is rational by writing it as a quotient
of two integers.
a. 7
b. -10
c.
5
b. -15
c.
10
3
4
d.
3
d.
8
1
2
Example 1 You try:
a. 22
1
2
Example 2: Writing fractions as decimals
a. Write
3
8
as a decimal
b. Write
5
11
as a decimal
1
3
Example 2 You try: Write the following fractions or mixed numbers as
decimals.
a.
3
10
b.

c.
2
3
1
9
20
d.
29
80
Example 3: Writing terminating decimals as fractions.
a. 0.7
b. -3.05
c. -9.42
Example 3 You try:
a. 1.7
b. 0.52
c. -1.45
Example 4: Writing a repeating decimal as a fraction.
 To write 0.93 as a fraction, let x  0.93 .
 Because 0.93 has 2 repeating digits, multiply each side of x  0.93 by
100.
 Subtract x from 100x.
 Solve for x and simplify.
***************************************************************************************************
Practice:
a. Write 0.72 as a fraction.
b. Write 0.34 as a fraction.
Example 4 You try:
a. Write 0.14 as a fraction.
b. Write 0.77 as a fraction.
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 5:
5
5 13
a. Order the numbers  ,  0.2 , 4.31 ,  3 ,  , 
from least to greatest.
4
2
3
b. Order the numbers 2.7 , 0.55 ,  0.9 ,
HOMEWORK:
9
9 13

,
,
from least to greatest.
4
8 7
SECTION: 4.3 Equivalent Fractions
Objective: TLW write equivalent fractions.
Standards: M7.2.1.8.F, M7.2.1.5.E, M7.2.1.5.G
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Warm Up: The following is a ______________________
a
b
b CANNOT be 0! Why? Remember the “trust game” from gym:
You wouldn’t want to fall back into an
empty area
EQUIVALENT FRACTIONS
Words: To write equivalent fractions, multiply or divide the
numerator and the denominator by the same nonzero number.
Algebra: For all numbers a, b, and c, where b  0 and c  0 ,
a ac
a a c


and
b bc
b bc .
1 1 2 2


Numbers:
3 3 2 6
2 22 1


6 62 3
Example 1: Write two fractions that are equivalent to the following.
Multiply or divide the numerator and the denominator by the same
nonzero number.
a.
5
10
b.
6
9
b.
18
24
Example 1 You Try:
a.
12
20
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Simplest form: A number is in simplest form when its numerator and
denominator are relatively prime.
1.
2.
Determine GCF of numerator and denominator.
Divide both the numerator and denominator by the
GCF.
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 2: Write the following fractions in simplest form.
a.
4
14
b.
GCF:
27
42
GCF:
Example 2 You Try:
a.
8
36
GCF:
b.
28
49
GCF:
Example 3: Mrs. Panza gave a test to 35 students. There were 28 “A’s”
on the test. Write the fraction, in simplest form, of
students who earned an “A” on their test.
Example 4: Simplifying Variable Expressions
14ab 2
a.
21a 2 b
6a 3bc 2
b.
9a 3 b
33d 2 e 4 f 2
c.
15d 3 e 2 f
10de 3 f 2
d.
8d 2 ef 2
10 fun 2
e.
8 f 3u 2 n
HOMEWORK:
SECTION: 5.2 Adding and Subtracting Like Fractions
Objective: TLW add and subtract like fractions.
Standards: M7.A.3.2, M7.A.3.2.1
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
ADDING AND SUBTRACTING LIKE FRACTIONS
Words: To add or subtract fractions with the same denominator,
write the sum or difference of the numerators over the denominator.
English:
Numbers:
Algebra:
Example 1: One night,
77
100
of the moon’s visible surface is illuminated.
The next night, an additional
9
100
is illuminated. What fraction of the
moon’s visible surface is illuminated on the second night?
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 2: Subtracting Like Fractions.
a. 
4 2

7 7
1  3
  
b.
10  10 
Examples 1 and 2 You try:
3 2

8 8
a.
b.

1 5

6 6
c.
2 7 4
 
15 15 15
To add or subtract mixed numbers, you can first write the mixed numbers
as improper fractions.
Example 3: Adding and Subtracting Mixed Numbers
a. 5
5
7
2
9
9
b.  10
7
8
5
15
15
Example 3 You try:
a.
c.
2
3
3
1
4
4
1
3
4 2
5
5
b.
d.
1
2
6 3
3
3
2
3
3 6
7
7
Example 4: Simplifying Variable Expressions.
3a 5a

a.
20 20
8  2

  
b.
3b  3b 
Example 4 You try:
a.
3k 9k

28 28
PUZZLER:
b.
4
9

7y 7y
On Monday, Jessica bought a box of iris bulbs and planted half of them
in her garden. On Tuesday, she planted half of the remaining bulbs. On Wednesday,
she again plated half of the bulbs that remained from the day before. On Thursday,
she planted half of the remaining bulbs. What fraction of the original bulbs was left in
the box when she finished her planting on Thursday?
HOMEWORK:
SECTION: 5.3 Adding and Subtracting Unlike Fractions
Objective: TLW add and subtract unlike fractions.
Standards: M7.A.3.2, M7.A.3.2.1
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 1: Adding and Subtracting Fractions
a.
5 1

12 3
b. 
5 7

6 9
Example 2: Adding Mixed Numbers.
a.  4
2 
6
  2 
5  11 
4
7
b. 3  7
9
12
Examples 1 and 2 You Try:
a.

2 1

3 4
b.
3 4

10 5
c. 
4 9

14 10
5
1
d. 3  2
9
6
e. 6
7  1
 1 
10  5 
1
3
f.  2  6
3
5
Example 3: Simplifying an Expression
a a

a.
2 6
a.
3a a

2 6
PUZZLER: What is the value of
HOMEWORK:
m 2m

b.
5
3
b. 
5w 7 w

12
9
1 1 1 1
   ?
2 4 6 8
SECTION: 5.4 Multiplying Fractions
Objective: TLW multiply fractions and mixed numbers.
Standards: M7.A.3.2, M7.A.3.2.1
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Area models how you find the product of two fractions.
3 1

Example:
5 4
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
MULTIPLYING FRACTIONS
Words: The product of two or more fractions is equal to the product
of the numerators over the product of the denominators.
English:
Numbers:
Algebra:
Example 1: Multiplying Fractions
a.
7  4
 
10  21 
b.
3  11 
  
5  12 
Example 1 You try:
a.
2 7

3 8
 5  3 
b.    
 12  10 
3

10


2


c.
11


3
d.     12 
4
Example 2: Multiplying Mixed Numbers
7 2
4
5
a.
8 3
b.
2 1
 3 1
7 2
Example 2 You try:
3 1

2
3
a.
4 5
 3  5 
b.   3   1 
 5  9 
1  2
4
  1 
c.
8  3
Example 3: Simplify the expression.
m  12 
 
a.
3  5
n 2  5n 3 
b. 10   9 


Example 3 You try:
a.
3y y7

4 9
c.
3z 5
25
 2z 4 

 
 15 
 x 4  16 x 
b.  6   3 

 
4v 2
d.  21
 7v 3 

 
 16 
Example 4: Find the area of the triangle.
4
7
2
ft
9
4
ft
5
PUZZLER: When Ruben’s friend Jake called and asked him how much of
his reading assignment he had finished, Ruben told him that his book was
open to two pages whose page numbers have a product of 1056. To which
two pages does Ruben have his book open?
HOMEWORK:
Worksheet 5.4 #’s: 1-26 odd
SECTION: 5.5 Dividing Fractions
Objective: TLW divide fractions and mixed numbers.
Standards: M7.A.3.2, M7.A.3.2.1
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
NUMBER
RECIPROCAL
JUSTIFICATION
5
2
7
5

8
0.1
USING RECIPROCALS TO DIVIDE
Words: To divide by any nonzero number, multiply by its reciprocal.
Algebra:
Numbers:
Example 1: Dividing a Fraction by a Fraction
a. 
2 4

5 7
Example 1 You try:
1 
6 
2
3
b. 4    1 
7 2

a.
12 3
b.    
3
1

9
c.
8
6
1
2

5

2
d.
4
5
4  8

9  11 
Example 2:
a.
6 2 3
 
7 3 7
b.
5 4 3 
  
9  9 18 
c. 1
29 11 7
1 
35 21 15
Example 3: Carissa mixes 2 gallons (32 cups) of fruit punch for a
cookout. If each of the tumblers she plans to serve the
punch in holds 2
1
cubs, how many tumblers can she fill?
3
PUZZLER: Chad, Daryl, and Emily painted a house. Daryl painted twice as much as
Chad and Emily painted three times as much as Chad. What fraction of the house did
Chad paint?
HOMEWORK:
SECTION: 5.6 Using Multiplicative Inverses to Solve
Equations
Objective: TLW use multiplicative inverses to solve equations.
Standards: M7.D.2.1, M7.D.2.2, M7.D.2.2.1
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
MULTIPLICATIVE INVERSE PROPERTY
Words: The product of a number and its multiplicative inverse is 1.
Algebra:
Numbers:
Example 1: Solving a One-Step Equation
a.
4
x  12
7
b.

7
k  56
8
Example 1 You try:
a.
5
m  20
6
b.
2
x  12
9
c.
3
x  15
8
Example 2: Solving a Two-Step Equation
a.
 16 
3
n  20
4
HOMEWORK:
b. 
2
1 5
p 
3
2 6