Question

Divide a 5 1/4 inch line into three parts whose ratios are 1:2:3.

Answer 1

1:2:3...total is 6

1/6 of 5 1/4 = 1/6 * 21/4 = 21/24 = 7/8
2/6 of 5 1/4 = 2/6 * 21/4 = 42/24 = 1 3/4
3/6 of 5 1/4 = 3/6 * 21/4 = 63/24 = 2 5/8

7/8, 1 3/4, 2 5/8...total = 5 1/4 inches

Answer 2

Divide a
`5(1)/(4)` inch line into three parts are
`(7)/(8),(7)/(3),(21)/(8)`

Explanation:

To find : Divide a
`5(1)/(4)` inch line into three parts whose ratios are 1:2:3 ?

Solution :

Let the number be p which is divided into three parts in the ratio a : b : c.

then the solution of three parts are
`x=(ap)/(a+b+c)` ,
`y=(bp)/(a+b+c)` and
`z=(cp)/(a+b+c)`

On comparing,
`p=5(1)/(4)=(21)/(4)`

a=1 , b=2 , c=3

Substituting all the values to determine the three parts,

`x=(ap)/(a+b+c)`

`x=(1((21)/(4)))/(1+2+3)`

`x=((21)/(4))/(6)`

`x=(21)/(4* 6)`

`x=(21)/(24)`

`x=(7)/(8)`

`y=(bp)/(a+b+c)`

`y=(2((21)/(4)))/(1+2+3)`

`y=((21)/(2))/(6)`

`y=(21)/(2* 6)`

`y=(21)/(12)`

`y=(7)/(3)`

`z=(cp)/(a+b+c)`

`z=(3((21)/(4)))/(1+2+3)`

`z=((63)/(4))/(6)`

`z=(63)/(4* 6)`

`z=(63)/(24)`

`z=(21)/(8)`

Therefore, Divide a
`5(1)/(4)` inch line into three parts are
`(7)/(8),(7)/(3),(21)/(8)`