Question

Reduce each of the following fractions to its simplest form. a. 12⁄18 b. 48⁄54 c. 27⁄90 d. 63⁄77 e. 24⁄32 f. 73⁄365

Answer 1

a. 2/3
b. 8/9
c. 3/10
d. 9/11
e. 3/4
f. 1/5

Answer 2

(a)

`(12)/(18)=(2)/(3)`

(b)

`(48)/(54)=(8)/(9)`

(c)

`(27)/(90)=(3)/(10)`

(d)

`(63)/(77)=(9)/(11)`

(e)

`(24)/(32)=(3)/(4)`

(f)

`(73)/(365)=(1)/(5)`

Explanation:

(a)

`(12)/(18)`

we can factor numerator and denominator

and then we can simplify it

Numerator:

`12=2* 2* 3`

Denominator:

`18=2* 3* 3`

now, we can replace by factors

`(12)/(18)=(2* 2* 3)/(2* 3* 3)`

now, we can cancel and simplify it

`(12)/(18)=(2)/(3)`

(b)

`(48)/(54)`

we can factor numerator and denominator

and then we can simplify it

Numerator:

`48=2* 2* 2* 2* 3`

Denominator:

`54=2* 3* 3* 3`

now, we can replace by factors

`(48)/(54)=(2* 2* 2* 2* 3)/(2* 3* 3* 3)`

now, we can cancel and simplify it

`(48)/(54)=(8)/(9)`

(c)

`(27)/(90)`

we can factor numerator and denominator

and then we can simplify it

Numerator:

`27=3* 3* 3`

Denominator:

`90=2* 3* 3* 5`

now, we can replace by factors

`(27)/(90)=(3* 3* 3)/(2* 3* 3* 5)`

now, we can cancel and simplify it

`(27)/(90)=(3)/(10)`

(d)

`(63)/(77)`

we can factor numerator and denominator

and then we can simplify it

Numerator:

`63=3* 3* 7`

Denominator:

`77=7* 11`

now, we can replace by factors

`(63)/(77)=(3* 3* 7)/(7* 11)`

now, we can cancel and simplify it

we get

`(63)/(77)=(9)/(11)`

(e)

`(24)/(32)`

we can factor numerator and denominator

and then we can simplify it

Numerator:

`24=2* 2* 2* 3`

Denominator:

`32=2* 2* 2* 2* 2`

now, we can replace by factors

`(24)/(32)=(2* 2* 2* 3)/(2* 2* 2* 2* 2)`

now, we can cancel and simplify it

`(24)/(32)=(3)/(4)`

(f)

`(73)/(365)`

we can factor numerator and denominator

and then we can simplify it

since, 73 can not be factored

`365=5* 73`

now, we can plug it

`(73)/(365)=(73)/(5* 73)`

now, we can cancel and simplify it

`(73)/(365)=(1)/(5)`