**13.1 Introduction**: Two quantities having a same ratio are said to be in proportion. Proportion refers to the equality of two ratios. It can be written in two ways.

< a - c

< < b -d

for example if we write

1 pencil : 3 erasers

This means that for every pencil there are three erasers.

In simple words we can say “ a proportion is a comparison between two ratios”

Values in position of ‘b” and “c” are termed as means

**Extremes**: values in position of “a” and “d” are termed as Extremes.

**13.2 ****Direct proportions**: two quantities are said to be in direct proportion when the value of one of them increases or decreases with the other.

“α” is the sign used to represent direct proportion.

y α *x*

y=k*x*

k is the proportionality constant.

**Examples**

- The gravitational force acting on an object is directly proportional to its mass; the proportionality constant between mass and force is known as gravitational acceleration(g)

- Distance travelled by an object moving at a constant speed is proportional to the time spent in travelling, speed being the constant of proportionality.

- The circumference of a circle is proportional to its diameter, constant of proportionality is π.

**13.3 Inverse proportionality**: As stated above, two proportional variables are sometimes said to be directly proportional and two variables are said to be **inversely proportional** if one of the variables is directly proportional with the multiplicative inverse (reciprocal) of the other

y = k

- x

The constant can be found by multiplying *x* and y variable.

Inverse proportion means that as magnitude of one variable increases, the magnitude of another decreases, such that their product is always the same.

**Example**:

Time taken for a journey is inversely proportional to the speed of travel.

**13.4 Exponential and Logarithmic Proportionality**: A variable y is exponentially proportional to a variable x, if y is directly proportional to the exponential function of x.

y = k a^{x}

A variable y is logarithmically proportional to a variable x, if y is directly proportional to the logarithm of x.

y = k log_{a}(x)

**13.5.1 ****Solving proportion without variable: **By cross multiplying the numerator of the first ratio by the denominator of the second ratio and the denominator of the first ratio by the numerator of the second ratio.

If you encounter a proportion that has one of its means or extremes left blank, or uses another symbol such as a question mark you can treat it as if it was a variable. Or you can replace the question mark or blank space with a variable such as x. See the example below.

13.5.2 Solving a proportion with two variables:

A proportion with two of the same variable can be solved as shown below.

In these situations where a variable squared equals a number, you can do one of two things.

1. Find what number squared is equal to 25 using the perfect squares chart for reference.

(or)

2. Change the problem to *x *= square root of 25.

The resulting number from either method is equal to *x* and will be the answer.

**13.5.3 When a whole number is in place of a fraction:**

Take a look at the problem below, it doesn't have a fraction on one side.

And now it can be solved like any other proportion.

**To Schedule a Proportions tutoring session
To submit Proportions assignment click here.**

Assignment Writing Help

- Science Assignment Help
- Math Assignment Help
- Chemistry Assignment Help
- Physics Assignment Help
- Biology Assignment Help
- Psychology Assignment Help
- History Assignment Help
- Geography Assignment Help
- English Assignment Help
- Humanities Assignment Help
- Nursing Assignment Help
- Social Science Assignment Help
- Arts and Architecture Help
- Statistics Assignment Help
- Law Assignment Help
- Computational Mathematics Assignment Help

Engineering Assignment Services

- Programming Assignment Help
- Database Help
- Data Structure Assignment Help
- Operating Systems Assignment Help
- Computer Network Assignment Help
- UML Diagram Assignment Help
- IT Assignment Help
- Game Programming Help
- Computer Science Assignment Help
- Information Systems Assignment Help
- Chemical Engineering Assignment Help
- Civil Engineering Assignment Help
- Electrical, Electronics Help
- Mechanical Engineering Assignment Help
- Petroleum Engineering Assignment Help
- Biochemical and Biotechnology Help

Do My Assignment Help

- Accounting Assignment Help
- Finance Assignment Help
- Economics Assignment Help
- Marketing Assignment Help
- Human Resources Assignment Help
- Operations Management Assignment Help
- Strategy and Planning Help
- Project Management Help
- Case Studies Writing Help
- Political science
- Referencing Help
- Assignment Help Websites
- Online Assignment Help
- Do My Assignment
- Do My Homework

Write My Essay Services

- Essay Writing Help
- Business Essay Writing Help
- Assignment Writing Services
- Plagiarism Free Essay Writing
- Essay Editing Service
- Dissertation Writing Services
- Custom Writing Help
- Write My Essay
- Thesis Writing Help
- Write My Paper
- Paper Writing Service
- Academic help
- College Essay Writing
- Cheap Essay Writing