Four Numbers in Proportion

We will learn four numbers in proportion.

In general, a, b, c, d are said to be in proportion if a : b = c : d which is written as a : b :: c : d and read as a is to b as c is to d.

Here, a, b, c, d are respectively called the first, second, third and fourth term.

The first term a and the fourth term d are called the extreme terms or extremes.

The second term b and the third term c are called the middle terms or means.

If a, b, c, d are in proportions, then product of extremes = product of means

⟹ a × d = b × c

For example, in proportion 2 : 3 :: 24 : 36

Product of extremes = 2 × 36 = 72

Product of means = 3 × 24 = 72

Hence, product of extremes = product of means.

If the two given ratios are not equal, then they are not in proportions and the product of their extremes is not equal to the product of their means.


Solved Examples on Four Numbers in Proportion:

1. Are 50, 75, 30, 45 in proportion?

Solution:

50 : 75 = \(\frac{50}{75}\) = \(\frac{50 ÷ 25}{75 ÷ 25}\) = \(\frac{2}{3}\) = 2 : 3

30 : 45 = \(\frac{30}{45}\) = \(\frac{30 ÷ 15}{45 ÷ 15}\) = \(\frac{2}{3}\) = 2 : 3

50 : 75 = 30 : 45

Hence, 50, 75, 30, 45 are in proportion.


Alternative Method:

Product of extremes = 50 × 45 = 2250

Product of means = 75 × 30 = 2250

Product of extremes = Product of means

Hence, 50, 75, 30, 45 are in proportion.


2. Are the ratios 10 minutes : 1 hour and 6 hours: 36 hours in proportion?

Solution:

10 minutes : 1 hour = 10 minutes : 60 minutes

                              = 10 : 60

                              = \(\frac{10}{60}\)

                              = \(\frac{10 ÷ 10}{60 ÷ 10}\)

                              = \(\frac{1}{6}\)

                              = 1 : 6

and 6 hours : 36 hours = 6 : 36

                                  = \(\frac{6}{36}\)

                                  = \(\frac{6 ÷ 6}{36 ÷ 6}\)

                                  = \(\frac{1}{6}\)

                                 = 1 : 6 

Therefore, 10 minutes : 1 hour = 6 hours : 36 hours

Hence, the ratios 10 minutes : 1 hour and 6 hours : 36 hours are in proportion.


2. Christopher drives his car at a constant speed of 12 km per 10 minutes. How long will he take to cover 48 km?

Solution:

Let Christopher take x minutes to cover 48 km.

Speed (in km)

Time (in minutes)

12

10

48

x

Now, 12 : 10 :: 48 : x

⟹ 12x = 10 × 48

⟹ x = \(\frac{10 × 48}{12}\)

⟹ x = \(\frac{480}{12}\)

⟹ x = 40

Therefore, x = 40 minutes.


3. Are the ratios 45 km: 60 km and 12 hours: 15 hours form a proportion?

Solution:

45 km : 60 km = \(\frac{\textrm{45 km}}{\textrm{60 km}}\) = \(\frac{45}{60}\) = \(\frac{45 ÷ 15}{60 ÷ 15}\) = 3 : 4

and 12 hours : 15 hours = \(\frac{\textrm{12 hours}}{\textrm{15 hours}}\) = \(\frac{12}{15}\) = \(\frac{12 ÷ 3}{15 ÷ 3}\) = 4 : 5

Since 3 : 4 ≠ 4 : 5, therefore the given ratios do not form a proportion.



10th Grade Math

From Four Numbers in Proportion 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. Multiplying 2-Digit Number by 1-Digit Number | Multiply Two-Digit Numb

    Oct 21, 24 03:38 PM

    Multiplying 2-Digit Number by 1-Digit Number
    Here we will learn multiplying 2-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. Examples of multiplying 2-digit number by

    Read More

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

    Oct 21, 24 02:26 AM

    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

  3. Multiplying 3-Digit Number by 1-Digit Number | Three-Digit Multiplicat

    Oct 21, 24 02:16 AM

    Multiplying 3-Digit Number by 1-Digit Number
    Here we will learn multiplying 3-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. 1. Multiply 201 by 3 Step I: Arrange the numb…

    Read More

  4. Concept of Multiplication | What is Multiplication? | Basics Math

    Oct 21, 24 01:05 AM

    Multiplication Fact 8 × 2
    Multiplication is repeated addition of a number to itself. Study the following example to understand it: Example: Take 3 groups of 2 pens each as shown below. How many pens are there in all?

    Read More

  5. Properties of Multiplication | Multiplicative Identity | Whole Numbers

    Oct 21, 24 12:50 AM

    Properties of Multiplication of Whole Numbers
    There are six properties of multiplication of whole numbers that will help to solve the problems easily. The six properties of multiplication are Closure Property, Commutative Property, Zero Property…

    Read More