## Proportional Division

### Directly Proportional Division

The directly proportional division consists of dividing a number, in a directly proportional parts. The higher of the proportion,
the greater is the part.

Example 01:

Division of household expenses of $ 1,800.00; in proportion to the incomes of participants, as follow: A = $ 5,000.00; B = $ 3,000.00; C = $ 1,000.00;

Proportions:

a = 5000;

b = 3000;

c = 1000;

Solution:

N = 1800;

X = a + b + c = 900;

p1, p2 and p3 are the participants;

Divide the value of N, for X to find constant K.

Multiply the proportion of each participant by the constant K.

K = N / X = 18000 / (5000 + 3000 + 1000) = 0.20;

So, we have;

Participants:

P1 = a * K = 5000 * 0.20 = $1,000.00;

P2 = b * K = 3000 * 0.20 = $ 600.00;

P3 = c * K = 1000 * 0.20 = $ 200.00.

p1 + p2 + p3 = 1800;

Example 02:

Division of 6000 directly proportional to 3, 5 and 8;

Solution:

N = 6000;

Proportions:

a = 3;

b = 5;

b = 8;

X = a + b + c = 16;

K = N / X = 6000/16 = 375;

p1 = 3 * 375 = 1125;

P2 = 5 * 375 = 1875;

P3 = 8 * 375 = 3000;

p1 + p2 + p3 = 6000;

How to calculate the **Directly Proportional Division.**

### Inversely Proportional Division

A inversely proportional division consists of dividing one number in parts, inversely proportional. The higher of the proportion, smaller is the part.

Example 1:

A father decided to give, to her three daughters in inverse proportion of their salaries, the monthly value of $ 3,000.00;

Salaries:

Emily = $4,000.00;

Diana = $3,000.00;

Gracie = $2,000.00;

N = 3000;

Proportions:

a = 4000;

b = 3,000;

c = 2000;

Solution:

Calculating the constant K;

K = N / ((1 / a) + (1 / b) + (1 / c));

K = 2769230, 77;

Result:

P1 = (1 / a) * K = 692;

P2 = (1 / b) * K = 923;

P3 = (1 / c) * K; = 1385;

p1 + p2 + p3 = 3000;

So, we have;

Emily = $ 692.00;

Diana = $ 923.00;

Gracie =$1,385.00;

Example 2:

Division of 500 in parts inversely proportional to 3, 5 and 7.

Solution:

N =500;

a, b, c - proportions;

a = 3; b = 5; c = 7;

p1, p2, p3 - Parts;

K - Constant;

K = N / ((1 / a) + (1 / b) + (1 / c));

K = 500 /((1/3) + (1/5) + (1/7)) = 739.44;

P1 = (1 / a) * k = (1/3) * 739.44 = 246;

P2 = (1 / b) * k = (1/5) * 739.44 = 148;

p3 = (1 / c ) * k = (1/7) * 739.44= 106;

p1 + p2 + p3 = 500;

How to calculate the **Inversely Proportional Division**

### Division, simultaneously, direct and inversely proportional

Example:

Division of 800 in parts directly proportional to 2; 4; 6 and inversely to 3; 5 7.;

Solution:

N = 800;

n1, n2, n3 - dirtect proportions;

n1 = 2; n2 = 4; n3 = 6;

d1, d2, d3, - inverse proportions;

d1 = 3; d2 = 5; d3 = 7;

K = Constant;

p1, p2 e p3 - Parts;

K = N / (n1 /d1) + (n2 / d2) + (n3 / d3);

K = 800 / ((2 /3) + (4 / 5) + (6 / 7)) = 344,26;

P1 = (n1 /d1) * k = (2/3) * 344,26 = 230;

P2 = (n2 /d2) * k = (4/5) * 344,26 = 275;

p3 = (n3 /d3) * k = (6/7) * 344,26 = 295;

p1 + p2 + p3 = 800;

### Related topics

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