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What does increased mean in math?

In the English language, the word increase is nothing but becoming greater or larger in size, amount, number, or degree. It also means ‘to rise’. In mathematics also increase means getting rise in something.

For Example

Luna’s weight increased from 50.5 pounds to 64.9 pounds. How much weight did he gain?

We can solve the above example in the following steps.

Step1: The actual weight of Luna was 50.5 pounds.

Step2: The weight increased to 64.9 pounds.

Step3: The weight Luna gained = 64.9 – 50.5 = 14.4 pounds.

Step4: So, Increased weight for Luna or weight gained by Luna is 14.4 pounds.

In mathematics, there are four Main operations: add, subtract , multiply and  divide. Out of these four we can say add is the synonym for increase.

For Example:

Let us suppose we have a quantity x. An expression for 9 more than x is:

9 + x or x + 9.

This means the quantity has been increased by 9.

So, the word increase means a rise in the quantity of something. An upward arrow (↑ ) is used to depict the increase in something.

1. Something increases by over 100%.

Many people get confused by this .They assume that doubling something must be 200%. But this is not so.

Always remember:

If value is increased by 100%, it means the new value will be double the original value.

If it is increased by 200%, it means the new value will be triple the original value. We will be adding two times of the value to the original value.

If it is increased by 300%, it gets added three times of its own value to itself. This means that the new value is four times the original value.

And so on….

For example:

There are 500 pencils in a box. The number of pencils is increased by 200%. What is the new value of pencils?

Solution:

Number of pencils = 500

↑ in pencils = 200% = 200/100 * 500 = 1000

This means 1000 more pencils are added to the box, taking the total number of pencils

= 500 + 1000

= 1500 pencils.

2. Increased ‘to’ and increased ‘by’

There is always a confusion regarding the difference between a number increased by n times its value and number increased to n times its value. Where, n is a number.

When the number is increased by n times of its value, we multiply the number by ‘n’ and add this new value to the original number for the final result. While we just multiply the number by ‘n’ to get increased ‘to’ value.

For example:
Scenario: Increased by n times

Problem:  20 is increased by 10 times

# 20 x 10 = 200

# 200 + 20 = 200

When 20 is increased by 10 times of its value it becomes 220.

Scenario: Increased to n times

Problem:  20 is increased to 10 times

For Example:

# 20 x 10 = 200

So, When 20 is increased to 10 times of its value it becomes 200.

3. Increase in percentage

If number is increased from one value to another, let’s learn how to represent the increased value in percentage

For Example:

The number increased from 50 to 75. What is the increased %?

Sol: As we see the number is increased from 50 to 75.

To find the increase% we have to divide the increase in number by the base (original) number and then multiply it by 100.

Increase in number= increased number – original number = 75 – 50 = 25

Increase % = (25 / 50) * 100 = 50

So , the value has shown an increase of 50%.

 

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