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. Converting Fractions to Decimals | Solved Examples | Free Worksheet

    Apr 28, 25 01:43 AM

    Converting Fractions to Decimals
    In converting fractions to decimals, we know that decimals are fractions with denominators 10, 100, 1000 etc. In order to convert other fractions into decimals, we follow the following steps:

    Read More

  2. Expanded Form of a Number | Writing Numbers in Expanded Form | Values

    Apr 27, 25 10:13 AM

    Expanded Form of a Number
    We know that the number written as sum of the place-values of its digits is called the expanded form of a number. In expanded form of a number, the number is shown according to the place values of its…

    Read More

  3. Converting Decimals to Fractions | Solved Examples | Free Worksheet

    Apr 26, 25 04:56 PM

    Converting Decimals to Fractions
    In converting decimals to fractions, we know that a decimal can always be converted into a fraction by using the following steps: Step I: Obtain the decimal. Step II: Remove the decimal points from th…

    Read More

  4. Worksheet on Decimal Numbers | Decimals Number Concepts | Answers

    Apr 26, 25 03:48 PM

    Worksheet on Decimal Numbers
    Practice different types of math questions given in the worksheet on decimal numbers, these math problems will help the students to review decimals number concepts.

    Read More

  5. Multiplication Table of 4 |Read and Write the Table of 4|4 Times Table

    Apr 26, 25 01:00 PM

    Multiplication Table of Four
    Repeated addition by 4’s means the multiplication table of 4. (i) When 5 candle-stands having four candles each. By repeated addition we can show 4 + 4 + 4 + 4 + 4 = 20 Then, four 5 times

    Read More