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.
I am planning to write more post on simplify complex rational expressions, reducing rational expressions to lowest terms. Keep checking my blog.
Dividing Rational Numbers – Practice Problems:
Solve
`(-40b +66)/12`
Answer
`((-10b)/3) + (33/6)`
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.
I am planning to write more post on simplify complex rational expressions, reducing rational expressions to lowest terms. Keep checking my blog.
Dividing Rational Numbers – Practice Problems:
Solve
`(-40b +66)/12`
Answer
`((-10b)/3) + (33/6)`
