RATIONAL NUMBERSRATIONAL NUMBERS

Mental Math Warm Up

• Number from 1-6

• 48+ 21=

• 56+38=

• 15+18+17=

• 125+186=

• 530+280=

• 176+125=

INTEGERSINTEGERS

• WHAT IS AN INTEGER?WHAT IS AN INTEGER?

• The The integersintegers consist of the positive consist of the positive natural numbersnatural numbers ( (11, , 22, , 33, …), their , …), their negativesnegatives (−1, −2, −3, ...) and the (−1, −2, −3, ...) and the number number zerozero. .

RATIONAL NUMBERSRATIONAL NUMBERS

• WHAT IS A RATIONAL NUMBER?WHAT IS A RATIONAL NUMBER?

• In In mathematicsmathematics, a , a rational numberrational number (commonly called a (commonly called a fractionfraction) is a ) is a ratioratio or quotient of two or quotient of two integersintegers, usually , usually written as awritten as a fraction fraction aa//bb, where , where bb is not is not zerozero..

RATIONAL NUMBERSRATIONAL NUMBERS

• WHAT IS A RATIONAL NUMBER?WHAT IS A RATIONAL NUMBER?

• In In mathematicsmathematics, a , a rational numberrational number (commonly called a (commonly called a fractionfraction) is a ) is a ratioratio or quotient of two or quotient of two integersintegers, usually , usually written as awritten as a fraction fraction aa//bb, where , where bb is not is not zerozero..

• EXAMPLES:EXAMPLES:•

14

RATIONAL NUMBERSRATIONAL NUMBERS

• WHAT IS A RATIONAL NUMBER?WHAT IS A RATIONAL NUMBER?

• In In mathematicsmathematics, a , a rational numberrational number (commonly called a (commonly called a fractionfraction) is a ) is a ratioratio or quotient of two or quotient of two integersintegers, , usually written as ausually written as a fraction fraction aa//bb, , where where bb is not is not zerozero..

• EXAMPLES:EXAMPLES:

• , , 0.250.2514

RATIONAL NUMBERSRATIONAL NUMBERS

• WHAT IS A RATIONAL NUMBER?WHAT IS A RATIONAL NUMBER?

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

• EXAMPLES:EXAMPLES:

• , , 0.25, 0.25, 14

-5 4

RATIONAL NUMBERSRATIONAL NUMBERS

• WHAT IS A RATIONAL NUMBER?WHAT IS A RATIONAL NUMBER?

• In In mathematicsmathematics, a , a rational numberrational number (commonly called a (commonly called a fractionfraction) is a ) is a ratioratio or quotient of two integers, or quotient of two integers, usually written as a fraction usually written as a fraction aa//bb, , where where bb is not zero. is not zero.

• EXAMPLES:EXAMPLES:

• , , 0.25, , -0.1250.25, , -0.12514

-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

+6

15?=

x5

x5

x3

x3

TRY THIS

13

+25

?=

515

+6

15=

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

-5

15?=

x3

x3

x5

x5

TRY THIS

25

- 13

?=

615

-5

15=

x3

x3

x5

x5

115

MULTIPLYING FRACTIONSMULTIPLYING FRACTIONS

To Multiply Fractions: To Multiply Fractions:

Multiply the numerators of the Multiply the numerators of the fractions fractions

Multiply the denominators of the Multiply the denominators of the fractions fractions

Place the product of the numerators Place the product of the numerators over the product of the denominators over the product of the denominators

Simplify the Fraction Simplify the Fraction

To multiply fractions, simply To multiply fractions, simply multiply the two numeratorsmultiply the two numerators

Multiplying FractionsMultiplying Fractions

35

x13

=

x =

??

Then simply multiply the two Then simply multiply the two denominators. denominators.

35

x13

=

x =

3?

Multiplying FractionsMultiplying Fractions

Place the numerator over the Place the numerator over the denominator.denominator.

35

x13

=

x =

315

Multiplying FractionsMultiplying Fractions

If possible, state in simplest If possible, state in simplest form. form.

35

x13

=3

15=

15

Multiplying FractionsMultiplying Fractions

DIVIDING FRACTIONSDIVIDING FRACTIONS

To Divide Fractions: To Divide Fractions: Multiply the reciprocal of the second term Multiply the reciprocal of the second term

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

the product of the denominators the product of the denominators Simplify the Fraction Simplify the Fraction

Example:Example:

35

÷ 13

Dividing FractionsDividing Fractions

=

35

x 31

=

Multiply by the reciprocal…

95

TRY THESETRY THESE

1) 1)

2) 2)

23

x14

=

25

13

=÷

TRY THESETRY THESE

1) 1)

2) 2)

23

x14

=

25

13

=÷

212

TRY THESETRY THESE

1) 1)

2) 2)

23

x14

=

25

13

=÷

16

= 212

TRY THESETRY THESE

1) 1)

2) 2)

23

x14

=

25

13

=÷

16

= 212

25

31

x =

TRY THESETRY THESE

1) 1)

2) 2)

23

x14

=

25

13

=÷

16

= 212

25

31

x =65

TRY THESETRY THESE

1) 1)

2) 2)

23

x14

=

25

13

=÷

16

= 212

25

31

x =65

=15

1