1.3 , 1.4 and 1.5

1.3 Positive and Negative Fractions

a) Fractions

Fraction

Numerator
Nominator

Positive Fraction Negative Fraction

b) Mixed Number

o is a number that names a whole and a

fraction.

c) Improper fraction

Change A Mixed Number To Improper Fraction

(-3) x 6 + 5 = 23

The Denominator does not change

Change A Improper Fraction to Mixed number

(-23) ÷ (- 6) = 3 remains 5

1. The Denominator does not change

2. Change the sign (-)(-) = (+)

Compare the value of fractions

Compare numbers. Hint: Use < , >, or =

21 > 15 4 11 < 53
6 6 16 16

1.3(a) Represent negative and positive fraction on a
number line

1. Fractions are represented by the small tick
marks between the whole numbers.

• The denominator represents the total number of
equal parts.
• The numerator represents the selected number of
equal parts.

Positive fractions are fractions with the positive sign (+), and their

values are greater than 0.
Negative fractions are fractions with the negative sign (–), and their

values are less than 0.

Example 1: Represent the fraction on a number line

− 1 , 1 , 2 1 , −2 3
44 2 4

−2 3 −1 1 21
4 44 2

-4 -3 -2 -1 0 12 34
Less than zero
More than zero

To order numbers is to arrange them from least to
greatest or greatest to least.

1. 3 , 3 3 , 2 1 , 1 13 21 33
44 44
4 4 44
1 , 3 , 21 , 33 01 23 4

Order from least to greatest ___4__4____4____4___ 33, 2 1, 3, 1
2. 1 , 3 1 , 3 , 2 3
Order from greatest to least _____4___4__4___4___
4 44 4
1, 3, 23, 31 13 23 31
44 44
Order from least to greatest ___4__4____4____4___
01 2 34

31, 23, 3, 1

Order from greatest to least ____4___4___4__4____

Relevance

1. Ordering fractions and mixed numbers will help you compare

quantities.

John and Mary are in a pie-eating contest. John ate 25 pies
8
and Mary ate 2 3 pies.
4

Who won the contest?

<2 5 23
8 4

John Mary
Mary ate more pies than John.

Independent Practice (continued)

To order numbers is to arrange them from least to greatest or greatest to least.

Negative Numbers

Use the (−) sign.

Order fractions and mixed numbers on a number line. −2 3 −1
Step #1: Place each fraction or mixed number on the number line one at a time. (label) 4 4

a. Read each number aloud.
b. Determine the sign and the value of the whole number or fraction. Hint: Move to right or the left of zero.
c. Determine the denominator and numerator. Hint: Move the number of selected equal parts.

Step #2: Order the numbers using the number line.

3. 3 1, −11, 22, −2 1
2 33 6

-2 1 -1 1 22 31
63 3 2

-4 -3 -2 -1 01 2 34

-2 1 , -11 , 2 2 , 3 1 3 1 , 2 2 , -11 , -2 1

Order from least to greatest ___6____3____3___2__ Order from greatest to least ____2___3____3____6_

2 1, −11, −3 1, 2

4. 6 6 3 3

-3 1 -1 1 2 2 1
3 6 36

-4 -3 -2 -1 01 2 34

-3 1 , -11 , 2 , 2 1 2 1 , 2 , -11 , -3 1

Order from least to greatest ____3____6___3___6__ Order from greatest to least ____6___3___6_____3_

Periodic Review 1 Name __________________________

To order numbers is to arrange them from least to greatest or greatest to least.

Negative Numbers

Use the (−) sign.

Order fractions and mixed numbers on a number line. −2 3 −1
Step #1: Place each fraction or mixed number on the number line one at a time. (label) 4 4

a. Read each number aloud.
b. Determine the sign and the value of the whole number or fraction. Hint: Move to right or the left of zero.
c. Determine the denominator and numerator. Hint: Move the number of selected equal parts.

Step #2: Order the numbers using the number line.

1. 1 , − 1 1 , 3 3 , − 1

4 44 2

-1 1 - 1 1 33
42 4 4

-4 -3 -2 -1 0 1 2 34

-1 1 , - 1 , 1 , 3 3 3 3 , 1 , - 1 , -1 1

Order from least to greatest ___4____2__4____4___ Order from greatest to least ____4___4___2____4__

2. −2 1 , 3 3 , − 3 , 1
4 4 44

-2 1 -3 1 33
4 44 4

-4 -3 -2 -1 01 2 3 4

-2 1 , - 3 , 1 , 3 3 3 3 , 1 , - 3 , -2 1

Order from least to greatest ____4___4___4___4___ Order from greatest to least ______4__4____4____4

Periodic Review 1 (continued)

To order numbers is to arrange them from least to greatest or greatest to least.

Negative Numbers

Use the (−) sign.

Order fractions and mixed numbers on a number line. −2 3 −1
Step #1: Place each fraction or mixed number on the number line one at a time. (label) 4 4

a. Read each number aloud.
b. Determine the sign and the value of the whole number or fraction. Hint: Move to right or the left of zero.
c. Determine the denominator and numerator. Hint: Move the number of selected equal parts.

Step #2: Order the numbers using the number line.

3. − 1, 12 , 3 1, − 2 2
33 3 3
-2 2
3 -1 12 31
3 3 3

-4 -3 -2 -1 01 2 34

-2 2 , - 1 , 12 , 3 1 3 1 , 12 , - 1 , -2 2

Order from least to greatest _____3___3____3___3_ Order from greatest to least ____3____3___3____3_

4. -2 1 32, 2, −31, −21 32
3 33 3 3 3
-3 1 2
3 3

-4 -3 -2 -1 01 2 34

-3 1 , -2 1 , 2 , 3 2 3 2 , 2 , -2 1 , -3 1

Order from least to greatest ____3____3___3____3_ Order from greatest to least ___3___3____3____3__

Periodic Review 2 Name __________________________

To order numbers is to arrange them from least to greatest or greatest to least.

Negative Numbers

Use the (−) sign.

Order fractions and mixed numbers on a number line. −2 3 −1
Step #1: Place each fraction or mixed number on the number line one at a time. (label) 4 4

a. Read each number aloud.
b. Determine the sign and the value of the whole number or fraction. Hint: Move to right or the left of zero.
c. Determine the denominator and numerator. Hint: Move the number of selected equal parts.

Step #2: Order the numbers using the number line.

1. 2 1, −11, −3 1, 3 3 21
4 4 24 4 4
−3 1
2 −1 1
4

-4 -3 -2 -1 01 2 3 4

-3 1 , -1 1 , 3 , 2 1 2 1 , 3 , -1 1 , -3 1

Order from least to greatest ___2____4___4___4___ Order from greatest to least ___4___4____4____2__

2. 2 3 , − 1 1 , 2 1 , − 3 1
4 44 4
−3 1 −1 1 21 23
44 44

-4 -3 -2 -1 01 2 3 4

-3 1 , -1 1 , 2 1 , 2 3 2 3 , 2 1 , -1 1 , -3 1

Order from least to greatest ____4____4___4____4_ Order from greatest to least ___4____4____4____4_

1.3(c) Combined operation of positive
and negative fraction

(i) Addition and subtraction
Example 1:

x3 x4

x3 x4

Convert the fraction
to the same
denominator

Example 2

(ii)Multiplication and division
Example 1:

11

35 = 5
8 6 16

2

2

(iii) Mixed operation
Example 1

1.4 Decimals

• Positive decimals are greater than zero
• Negative decimals are less than zero.

1.5 Rational Numbers



There are some number cards below :

Determine whether the numbers
below are the rational numbers.