Proportion

We will discuss about the proportion of four quantities.

Four quantities w, x, y, and z are in proportion if w : x :: y : z or, $\frac{w}{x}$ = $\frac{y}{z}$.

Definition: If four quantities w, x, y and z are such that the ratio w : x is equal to the ratio y : z then we say w, x, y and z are in proportion or, w, x, y and z are proportional. We express it by writing w : x :: y : z.

w : x :: y : z if and only if $\frac{w}{x}$ = $\frac{y}{z}$ i.e., wz = xy.

In w : x : : y : z, w, x, y and z are the first, second, third and fourth terms respectively.

Also, w and z are called the extreme terms while x and y are called the middle terms or mean terms.

That is in a proportion the first and fourth terms are called extremes, while the second and third terms are called means.

Product of extremes = product of means

or, wz = xy.

If w, x, y and z are in proportion then the last term z is also called the fourth proportional.

For example, 2 : 7 :: 8 : 28 because $\frac{2}{7}$ = $\frac{8}{28}$.

Solved examples on Proportion:

Check whether the following numbers form a proportion or not.

(i) 2.5, 4.5, 5.5, 9.9

(ii) 1$\frac{1}{4}$, 1$\frac{3}{4}$, 1.5, 1.4

Solution:

(i) 2.5 : 4.5 = $\frac{2.5}{4.5}$ = $\frac{25}{45}$ = $\frac{5}{9}$

5.5 : 9.9 = $\frac{5.5}{9.9}$ = $\frac{55}{99}$ = $\frac{5}{9}$

Therefore, $\frac{2.5}{4.5}$ = $\frac{5.5}{9.9}$

Hence, 2.5, 4.5, 5.5 and 9.9 are in proportion.

(ii) 1$\frac{1}{4}$ : 1$\frac{3}{4}$ = $\frac{5}{4}$ : $\frac{7}{4}$ = $\frac{5}{4}$ × 4: $\frac{7}{4}$ × 4 = 5 : 7 = $\frac{5}{7}$

1.5 : 1.4 = $\frac{1.5}{1.4}$ = $\frac{15}{14}$

Since, $\frac{5}{7}$  ≠ $\frac{15}{14}$

Hence, 1$\frac{1}{4}$, 1$\frac{3}{4}$, 1.5 and 1.4 are not in proportion.

● Ratio and proportion

• Basic Concept of Ratios
• Important Properties of Ratios
• Ratio in Lowest Term
  
• Types of Ratios
• Comparing Ratios
• Arranging Ratios
  
• Dividing into a Given Ratio
  
• Divide a Number into Three Parts in a Given Ratio
• Dividing a Quantity into Three Parts in a Given Ratio
  
• Problems on Ratio
  
• Worksheet on Ratio in Lowest Term
  
• Worksheet on Types of Ratios
  
• Worksheet on Comparison on Ratios
• Worksheet on Ratio of Two or More Quantities
  
• Worksheet on Dividing a Quantity in a Given Ratio
• Word Problems on Ratio
  
• Proportion
  
• Definition of Continued Proportion
  
• Mean and Third Proportional
  
• Word Problems on Proportion
  
• Worksheet on Proportion and Continued Proportion
  
• Worksheet on Mean Proportional
  
• Properties of Ratio and Proportion

10th Grade Math

From Proportion to HOME PAGE