Question

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

Answer 1

Answer:

Divide a $5\frac{1}{4}$ inch line into three parts are $\frac{7}{8},\frac{7}{3},\frac{21}{8}$

Step-by-step explanation:

To find : Divide a $5\frac{1}{4}$ 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 $x=\frac{ap}{a+b+c}$ , $y=\frac{bp}{a+b+c}$ and $z=\frac{cp}{a+b+c}$

On comparing,  $p=5\frac{1}{4}=\frac{21}{4}$

a=1 , b=2 , c=3

Substituting all the values to determine the three parts,

$x=\frac{ap}{a+b+c}$

$x=\frac{1(\frac{21}{4})}{1+2+3}$

$x=\frac{\frac{21}{4}}{6}$

$x=\frac{21}{4\times 6}$

$x=\frac{21}{24}$

$x=\frac{7}{8}$

$y=\frac{bp}{a+b+c}$

$y=\frac{2(\frac{21}{4})}{1+2+3}$

$y=\frac{\frac{21}{2}}{6}$

$y=\frac{21}{2\times 6}$

$y=\frac{21}{12}$

$y=\frac{7}{3}$

$z=\frac{cp}{a+b+c}$

$z=\frac{3(\frac{21}{4})}{1+2+3}$

$z=\frac{\frac{63}{4}}{6}$

$z=\frac{63}{4\times 6}$

$z=\frac{63}{24}$

$z=\frac{21}{8}$

Therefore, Divide a $5\frac{1}{4}$ inch line into three parts are $\frac{7}{8},\frac{7}{3},\frac{21}{8}$

Answer 2

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