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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

RATIONAL NUMBERS

Fractions


Integers
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 numbers1
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 numbers2
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


Adding fractions
ADDING FRACTIONS

  • 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

+

=


Adding fractions1
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
EXAMPLE

1

4

1

3

+


Adding fractions2
Adding Fractions

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

1

4

1

3

x3

?

+

=

x3

?

12

+

=


Adding fractions3
Adding Fractions

  • 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

+

=


Adding fractions4
Adding Fractions

  • 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

+

=


Adding fractions5
Adding Fractions

  • We can now add the two fractions.

1

4

1

3

?

=

+

7

12

3

12

4

12

+

=


Try this
TRY THIS

1

3

2

5

?

+

=


Try this1
TRY THIS

1

3

2

5

x5

x3

?

+

=

x5

x3

5

15

6

15

?

+

=


Try this2
TRY THIS

1

3

2

5

x5

x3

?

+

=

x5

x3

11

15

5

15

6

15

+

=


Subtracting fractions
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 this3
TRY THIS

2

5

1

3

?

-

=


Try this4
TRY THIS

2

5

1

3

x3

x5

?

-

=

x3

x5

6

15

5

15

?

-

=


Try this5
TRY THIS

2

5

1

3

x3

x5

?

-

=

x3

x5

1

15

6

15

5

15

-

=


Multiplying fractions
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 fractions1
Multiplying Fractions

  • To multiply fractions, simply multiply the two numerators

x

=

3

5

?

?

1

3

x

=


Multiplying fractions2
Multiplying Fractions

  • Then simply multiply the two denominators.

3

5

3

?

1

3

x

=

x

=


Multiplying fractions3
Multiplying Fractions

  • Place the numerator over the denominator.

3

5

3

15

1

3

x

=

x

=


Multiplying fractions4
Multiplying Fractions

  • State in simplest form.

3

5

3

15

1

5

1

3

x

=

=


Dividing 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


Dividing fractions1
Dividing Fractions

  • Example:

3

5

1

3

=

÷

Multiply by the reciprocal…

9

5

3

5

3

1

x

=


Try these
TRY THESE

  • 1)

  • 2)

1

4

2

3

x

=

2

5

1

3

÷

=


Try these1
TRY THESE

  • 1)

  • 2)

2

3

1

4

2

12

x

=

2

5

1

3

÷

=


Try these2
TRY THESE

  • 1)

  • 2)

2

3

1

4

1

6

2

12

x

=

=

2

5

1

3

÷

=


Try these3
TRY THESE

  • 1)

  • 2)

2

3

1

4

1

6

2

12

x

=

=

2

5

1

3

÷

=

2

5

3

1

x

=


Try these4
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 these5
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

=

=


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