Examples of partitive proportions

1. Divide 1035 in the ratio of 2:3:4.
2. A father wants to leave $4675 to his four children in the ratio of 1:3:3:4. How much will each of the four children receive?
3. John plans to donate his collection of 3042 books to three libraries in the ratio of 1:3:5. How many books will each library get?

To get the answer, divide the number representing the total, by the sum of the terms in the ratio then, multiply the quotient by each of the term in the ratio.

1. 1035 = number representing the total
2, 3 and 4 = terms in the ratio
9 = sum of the terms in the ratio

1035 / 9 = 115

then, multiply 115 by each of the term in the ratio

115 X 2 = 230
115 X 3 = 345
115 X 4 = 460

Final Answer = 230, 345 and 460

To check, add them all
230 + 345 + 460 = 1035

2. $4675 = total amount father wants to leave to the children
1, 3, 3 and 4 = terms in the ratio
11 = sum of the terms in the ratio

$4675 / 11 = $425

so, we need to multiply this by each of the term in the ratio

$425 x 1 = $425
$425 x 3 = $ 1275
$425 x 3 = $ 1275
$425 x 4 = $ 1700

Final Answer = $425, $1275, $1275 and $1700

To check,
$425 + $ 1275 + $ 1275 + $ 1700 = $ 4675

3. 3042 = total number of books
1, 3 and 5 = terms in the ratio
9 = sum of the terms in the ratio

3042 / 9 = 338

when multiplied by each term in the ratio, we get

338 x 1 = 338
338 x 3 = 1014
338 x 5 = 1690

Final Answer = 338, 1014 and 1690

to check
338 + 1014 + 1690 = 3042