RATIONAL NUMBERS

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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?

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### 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 fractiona/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 fractiona/b, where b is not zero.
• EXAMPLES:
• , 0.25, , -0.125

1

4

-5

4

• To add two fractions with the samedenominator, add the numerators and place that sum over the common denominator
• EXAMPLE:

3

5

1

5

4

5

+

=

• 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

1

4

1

3

+

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

1

4

1

3

x3

?

+

=

x3

?

12

+

=

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

1

4

1

3

x4

?

+

=

x4

3

12

?

12

+

=

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

1

4

1

3

x4

?

+

=

x4

3

12

4

12

+

=

• We can now add the two fractions.

1

4

1

3

?

=

+

7

12

3

12

4

12

+

=

TRY THIS

1

3

2

5

?

+

=

TRY THIS

1

3

2

5

x5

x3

?

+

=

x5

x3

5

15

6

15

?

+

=

TRY THIS

1

3

2

5

x5

x3

?

+

=

x5

x3

11

15

5

15

6

15

+

=

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

2

5

1

3

?

-

=

TRY THIS

2

5

1

3

x3

x5

?

-

=

x3

x5

6

15

5

15

?

-

=

TRY THIS

2

5

1

3

x3

x5

?

-

=

x3

x5

1

15

6

15

5

15

-

=

MULTIPLYING FRACTIONS
• To 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
Multiplying Fractions
• To multiply fractions, simply multiply the two numerators

x

=

3

5

?

?

1

3

x

=

Multiplying Fractions
• Then simply multiply the two denominators.

3

5

3

?

1

3

x

=

x

=

Multiplying Fractions
• Place the numerator over the denominator.

3

5

3

15

1

3

x

=

x

=

Multiplying Fractions
• State in simplest form.

3

5

3

15

1

5

1

3

x

=

=

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
Dividing Fractions
• Example:

3

5

1

3

=

÷

Multiply by the reciprocal…

9

5

3

5

3

1

x

=

TRY THESE
• 1)
• 2)

1

4

2

3

x

=

2

5

1

3

÷

=

TRY THESE
• 1)
• 2)

2

3

1

4

2

12

x

=

2

5

1

3

÷

=

TRY THESE
• 1)
• 2)

2

3

1

4

1

6

2

12

x

=

=

2

5

1

3

÷

=

TRY THESE
• 1)
• 2)

2

3

1

4

1

6

2

12

x

=

=

2

5

1

3

÷

=

2

5

3

1

x

=

TRY THESE
• 1)
• 2)

2

3

1

4

1

6

2

12

x

=

=

2

5

1

3

÷

=

2

5

3

1

6

5

x

=

TRY THESE
• 1)
• 2)

2

3

1

4

1

6

2

12

x

=

=

2

5

1

3

÷

=

1

5

2

5

3

1

6

5

1

x

=

=