Proportion Problems

We will learn how to solve proportion problems. We know, the first term (1st) and the fourth term (4th) of a proportion are called extreme terms or extremes, and the second term (2nd) and the third term (3rd) are called middle terms or means.

Therefore, in a proportion, product of extremes  = product of middle terms.

Solved examples:

1. Check whether the two ratios form a proportion or not:

(i) 6 : 8 and 12 : 16;                           (ii) 24 : 28 and 36 : 48

Solution:

(i) 6 : 8 and 12 : 16

6 : 8 = 6/8 = 3/4

12 : 16 = 12/16 = 3/4

Thus, the ratios 6 : 8 and 12 : 16 are equal.

Therefore, they form a proportion.

(ii) 24 : 28 and 36 : 48

24 : 28 = 24/28 = 6/7

36 : 48 = 36/48 = 3/4

Thus, the ratios 24 : 28 and 36 : 48 are unequal.

Therefore, they do not form a proportion.


2. Fill in the box in the following so that the four numbers are in proportion.

5, 6, 20, ____

Solution:

5 : 6 = 5/6

20 : ____ = 20/____

Since the ratios form a proportion.

Therefore, 5/6 = 20/____

To get 20 in the numerator, we have to multiply 5 by 4. So, we also multiply the denominator of 5/6, i.e. 6 by 4

Thus, 5/6 = 20/6 × 4 = 20/24

Hence, the required numbers is 24


3. The first, third and fourth terms of a proportion are 12, 8 and 14 respectively.  Find the second term.

Solution:

Let the second term be x.

Therefore, 12, x, 8 and 14 are in proportion i.e., 12 : x = 8 : 14

⇒ x × 8 = 12 × 14, [Since, the product of the means = the product of the extremes]

⇒ x = (12 × 14)/8

⇒ x = 21

Therefore, the second term to the proportion is 21.

More worked-out proportion problems:

4. In a sports meet, groups of boys and girls are to be formed. Each group consists of 4 boys and 6 girls. How many boys are required, if 102 girls are available for such groupings?

Solution:

Ratio between boys and girls in a group = 4 : 6 = 4/6 = 2/3 = 2 : 3

Let the number of boys required = x

Ratio between boys and girls = x : 102

So, we have, 2 : 3 = x : 102

Now, product of extremes = 2 × 102 = 204

Product of means = 3 × x

We know that in a proportion product of extremes = product of means

i.e., 204 = 3 × x

If we multiply 3 by 68, we get 204 i.e., 3 × 68 = 204

Thus, x = 68

Hence, 68 boys are required.


5. If a : b = 4 : 5 and b : c = 6 : 7; find a : c.

Solution:

a : b = 4 : 5

⇒ a/b = 4/5

b : c = 6 : 7

⇒ b/c  = 6/7

Therefore, a/b × b/c = 4/5 × 6/7

⇒ a/c = 24/35

Therefore, a : c = 24 : 35


6. If a :  b = 4 : 5 and b : c = 6 : 7; find a : b : c.

Solution:

We know that of both the terms of a ratio are multiplied by the same number; the ratio remains the same.

So, multiply each ratio by such a number that the value of b (the common term in both the ratios) acquires the same value.

Therefore, a :  b = 4 : 5 = 24 : 30, [Multiplying both the terms by 6]

And, b : c = 6 : 7 = 30 : 35, [Multiplying both the terms by 5]

Clearly,; a : b : c = 24 : 30 : 35

Therefore, a : b : c = 24 : 30 : 35

From, the above solved proportion problems we get the clear concept how to find whether the two ratios form a proportion or not and word problems.









6th Grade Page

From Proportion Problems to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. What is a Triangle? | Types of Triangle | Scalene Triangle | Isosceles

    Jun 17, 24 11:22 PM

    What is a triangle
    A simple closed curve or a polygon formed by three line-segments (sides) is called a triangle. The above shown shapes are triangles. The symbol of a triangle is ∆. A triangle is a polygon with three s…

    Read More

  2. Interior and Exterior of an Angle | Interior Angle | Exterior Angle

    Jun 16, 24 05:20 PM

    Interior of an Angle
    Interior and exterior of an angle is explained here. The shaded portion between the arms BA and BC of the angle ABC can be extended indefinitely.

    Read More

  3. Angles | Magnitude of an Angle | Measure of an angle | Working Rules

    Jun 16, 24 04:12 PM

    Naming an Angle
    Angles are very important in our daily life so it’s very necessary to understand about angle. Two rays meeting at a common endpoint form an angle. In the adjoining figure, two rays AB and BC are calle

    Read More

  4. What is a Polygon? | Simple Closed Curve | Triangle | Quadrilateral

    Jun 16, 24 02:34 PM

    Square - Polygon
    What is a polygon? A simple closed curve made of three or more line-segments is called a polygon. A polygon has at least three line-segments.

    Read More

  5. Simple Closed Curves | Types of Closed Curves | Collection of Curves

    Jun 16, 24 12:31 PM

    Closed Curves Examples
    In simple closed curves the shapes are closed by line-segments or by a curved line. Triangle, quadrilateral, circle, etc., are examples of closed curves.

    Read More