RATIONAL NUMBERS

RATIONAL NUMBERS

Fractions

INTEGERS• WHAT IS AN INTEGER?

• The integers consist of the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero.

RATIONAL NUMBERS• WHAT IS A RATIONAL NUMBER?

• In mathematics, a rational number (commonly called a fraction) is a ratio or quotient of two integers, usually written as a fraction a/b, where b is not zero.

RATIONAL NUMBERS• WHAT IS A RATIONAL NUMBER?

• In mathematics, a rational number (commonly called a fraction) is a ratio or quotient of two integers, usually written as a fraction a/b, where b is not zero.

• EXAMPLES:•

14

RATIONAL NUMBERS• WHAT IS A RATIONAL NUMBER?

• In mathematics, a rational number (commonly called a fraction) is a ratio or quotient of two integers, usually written as a fraction a/b, where b is not zero.

• EXAMPLES:• , 0.25

14

RATIONAL NUMBERS• WHAT IS A RATIONAL NUMBER?

• In mathematics, a rational number (commonly called a fraction) is a ratio or quotient of two integers, usually written as a fraction a/b, where b is not zero.

• EXAMPLES:• , 0.25,

14

-5 4

RATIONAL NUMBERS• WHAT IS A RATIONAL NUMBER?

• In mathematics, a rational number (commonly called a fraction) is a ratio or quotient of two integers, usually written as a fraction a/b, where b is not zero.

• EXAMPLES:• , 0.25, , -0.125

14

-5 4

ADDING FRACTIONS

To add two fractions with the same denominator, add the numerators and place that sum over the common denominator

EXAMPLE:

35

+ 15

= 45

ADDING FRACTIONS

To Add Fractions with different denominators:

Find the Least Common Denominator (LCD) of the fractions

Rename the fractions to have the LCD Add the numerators of the fractions Simplify the Fraction

EXAMPLE

14

+13

To make the denominator of the first fraction 12, multiply both the numerator and denominator by 3.

Adding Fractions

14 +

13 ?=

x3

x3

?12

+ =

To make the denominator of the second fraction 12, multiply both the numerator and denominator by 4.

Adding Fractions

14 +

13 ?=

x4

x4

312

+ ?12

=

To make the denominator of the second fraction 12, multiply both the numerator and denominator by 4.

Adding Fractions

14

+ 13 ?=

x4

x4

312

+4

12 =

We can now add the two fractions.

Adding Fractions

14 +

13

?=

312

+ 412

=7

12

TRY THIS

13

+ 25

?=

TRY THIS

13

+ 25

?=

515

+ 615

?=

x5

x5

x3

x3

TRY THIS

13

+ 25

?=

515

+ 615

=

x5

x5

x3

x3

1115

SUBTRACTING FRACTIONS

To Subtract Fractions with different denominators:

Find the Lowest Common Denominator (LCD) of the fractions

Rename the fractions to have the LCD Subtract the numerators of the fractions The difference will be the numerator and the

LCD will be the denominator of the answer. Simplify the Fraction

TRY THIS

25

- 13

?=

TRY THIS

25

- 13

?=

615

- 515

?=

x3

x3

x5

x5

TRY THIS

25

- 13

?=

615

- 515

=

x3

x3

x5

x5

115

MULTIPLYING FRACTIONSTo Multiply Fractions: Multiply the numerators of the fractions Multiply the denominators of the fractions Place the product of the numerators over the product of the denominators Simplify the Fraction

To multiply fractions, simply multiply the two numerators

Multiplying Fractions

35

x 13

=

x =

??

Then simply multiply the two denominators.

35

x 13

=

x =

3?

Multiplying Fractions

Place the numerator over the denominator.

35

x 13

=

x =

315

Multiplying Fractions

State in simplest form.

35

x 13

= 315

= 15

Multiplying Fractions

DIVIDING FRACTIONS

To Divide Fractions: Multiply the reciprocal of the second term

( fraction) Multiply the numerators of the fractions Multiply the denominators of the fractions Place the product of the numerators over

the product of the denominators Simplify the Fraction

Example:

35

÷ 13

Dividing Fractions

=

35

x 31

=

Multiply by the reciprocal…

95

TRY THESE

1)

2)

23

x14 =

25

13

=÷

TRY THESE

1)

2)

23

x 14

=

25

13

=÷

212

TRY THESE

1)

2)

23

x 14 =

25

13

=÷

16

= 212

TRY THESE

1)

2)

23

x 14 =

25

13

=÷

16

= 212

25

31

x =

TRY THESE

1)

2)

23

x 14 =

25

13

=÷

16

= 212

25

31

x = 65

TRY THESE

1)

2)

23

x 14 =

25

13

=÷

16

= 212

25

31

x = 65

=151