Dividing Rational Numbers

Introduction to Dividing Rational Numbers

The conditions for dividing positive and negative integers also apply to division with rational numbers.

Keep in mind that to divide by nonzero number, multiply by the reciprocal of that number.

Dividing Rational Numbers – Examples:

Dividing Rational Numbers – Example 1:

`(-39b +65)/13`

Step 1:

The Factor bar Indicates division:

`(-39b +65)/13 ` = -39b + 65 `-: ` 13

Step 2:

Multiply by 1/13 the reciprocal of 13.

= -39b+65(`1/13` )

Step 3:

Distributive Property

`(-39b)(1/13)` + `65(1/13)`

Answer:

-3b +5

Dividing Rational Numbers – Example 2:

Simplify:

(-51 + 34c)/-17

Step 1:

The Factor bar Indicates division:

= (-51+34c) `-:` (-17)

Step 2:

Multiply by` 1/17` the reciprocal of 17.

= (-51 + 34C). (`- 1/17` )

Step 3:

Distributive Property

= -51`(-1/17)` + (34C)`(-1/17)`

Answer:

= 3 -2c

Dividing Rational Numbers – Example 3:

Cricket pitch perimeter of a square cricket pitch is 36 feet. Find the length of one side of the rectangle

To find the length of one side, divide the perimeter by the number of sides.

Same signs -> Positive quotient

36` -:` 4 =9

Answer: The length of one side is 9 feet.

Dividing Rational Numbers – Example 4:

Solve:

`-56/27` `-:` ` -14/9`

Step 1:

Reciprocal of` -14/9 ` is `-9/14`

= `(-56/27) xx(-9/14)`

Step 2:

Multiply with reciprocated number

= `(56 xx 9 )/ (27 xx 14)`

Step 3:

Simplify

=`(4xx1)/(3xx1)`

Answer:

=` 4/3`

Dividing Rational Numbers – Example 5:

Solve: 

`35/32` `-: ``-21/16`

Step 1:

Reciprocal of` -21/16` is` -16/21`

`-35/32 xx 16/21`

Step 2:

Multiply with reciprocated number

= `(35xx16)/(-32 xx 21)`

Step 3:

Simplify

=`(5xx1)/(-2xx3)`

Answer:

= `-5/6`

Dividing Rational Numbers – Example 6:

`(-39b +65)/12`

Step 1:

The Factor bar Indicates division:

`(-39b +65)/12` = -39b + 65 `-: ` 12

Step 2:

Multiply by `1/12` the reciprocal of 12.

= -39b+65`(1/12)`

Step 3:

Distributive Property

`(-39b)(1/12) + 65(1/12)`

Answer:

`(-39b)/12 + (65/12)`

Dividing Rational Numbers – Example 7:

Cricket the perimeter of a square baseball diamond is 400 feet. Find the length of one side of the circle

To find the length of one side, divide the perimeter by the number of sides.

Same signs -> Positive quotient

400` -:` 4 =100

Answer: The length of one side is 100 feet.

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Dividing Rational Numbers – Practice Problems:

Solve

`(-40b +66)/12`

Answer

`((-10b)/3) + (33/6)`