# PROPERTIES OF PROPORTION WORKSHEET

Properties of proportion worksheet :

Worksheet given in this section will be much useful for the students who would like to practice solving problems using the properties of proportion.

Before look at the worksheet, if you would like to know the properties of proportion,

## Properties of Proportion Worksheet - Problems

Problem 1 :

Find the value of x, if 10/3 : x  =  5/2 : 5/4.

Problem 2 :

Find the fourth proportional to 2/3, 3/7, 4.

Problem 3 :

Find the third proportion to 2.4 and 9.6

Problem 4 :

If a : b = c : d = 2.5 : 1.5, what are the values of ad : bc and a + c  :  b + d ?

Problem 5 :

If a : 3  =  b : 4  =  c : 7, then, find the value of (a+b+c) : c.

## Properties of Proportion Worksheet - Solutions

Problem 1 :

Find the value of x, if 10/3 : x  =  5/2 : 5/4.

Solution :

Using cross product rule, we get,

(10/3) ⋅ (5/4)  =  x ⋅ (5/2)

25/6  =  5x/2

(25/6) ⋅ (2/5)  =  x

5/3  =  x

So, the value of x is 5/3.

Problem 2 :

Find the fourth proportional to 2/3, 3/7, 4.

Solution :

Let "a" be the fourth proportional.

Then, we have

2/3 : 3/7  =  4 : a

Using cross product rule, we have

(2/3) ⋅ a  =  4 ⋅ (3/7)

2a/3  =  12/7

a  =  (12/7) ⋅ (3/2)

a  =  18/7

So, the fourth proportional is 18/7.

Problem 3 :

Find the third proportion to 2.4 and 9.6

Solution :

Let "a" be the third proportional.

Then, we have

2.4 : 9.6  =  9.6 : a

Using cross product rule, we have

2.4a  =  9.6 ⋅ 9.6

a  =  92.16/2.4

a  =  38.4

So, third proportion is 3.8.4

Problem 4 :

If a : b = c : d = 2.5 : 1.5, what are the values of ad : bc and a + c  :  b + d ?

Solution :

In the given proportion a : b and c : d, applying cross product rule, we get

Dividing by bc on both sides, we get

ad : bc  =  1 : 1

Given : a : b  =  c : d  =  2.5 : 1.5 ------ (1)

In the given proportion a : b and c : d, applying the property addendo, we get

a : b  =  c : d  =  (a+b) : (c+d) ------ (2)

From (1) and (2), we get

(a+b) : (c+d)  =  2.5 : 1.5

(a+b) : (c+d)  =  (2.5x10) : (1.5x10)

(a+b) : (c+d)  =  25 : 15

(a+b) : (c+d)  =  (25/5) : (15/5)

(a+b) : (c+d)  =  5 : 3

Problem 5 :

If a : 3  =  b : 4  =  c : 7, then, find the value of (a+b+c) : c.

Solution :

In the given proportion a : 3  =  b : 4  =  c : 7applying the property addendo, we get

a : 3  =  b : 4  =  c : 7  =  (a+b+c) : (3+4+7)

a : 3  =  b : 4  =  c : 7  =  (a+b+c) : 14

Now, all the above four ratios are equal.

Taking the last two ratios, we get

c : 7  =  (a+b+c) : 14

c / 7  =   (a+b+c) / 14

14 / 7  =   (a+b+c) / c

2  =   (a+b+c) / c

or

(a+b+c) / c  =  2/1

(a+b+c) : c  =  2 : 1

After having gone through the stuff given above, we hope that the students would have understood, how to solve problems using the properties of proportion.

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