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# Decrease|Definition & Meaning

## Definition

Literally, decrease means to reduce or make smaller, e.g., drinking water from a cup will decrease the amount of water left in that cup. Similarly, driving a car will decrease the fuel in its fuel tank. The term is closely related to decrement and one can think of it as a subtraction operation, though it is not strictly used in that context (e.g., sorting in decreasing order).

The process of making something smaller in** size or quantity is referred to as decreasing**. It is one of the most fundamental ideas in mathematics, and it is also extremely important in a wide variety of real-world applications, ranging from **business and economics to science and technology.**

## Decrease in Size

The term “**decreasing in size**” refers to the process of making an **object smaller in terms of its physical dimensions.** In mathematics, this may involve shortening the length of a **line segment, decreasing the area of a rectangle, or decreasing the volume of a three-dimensional object.**

The process of getting smaller can be expressed mathematically using **ratios, fractions, and decimals as the different parts of the expression.**

For instance, if we were to reduce the length of a **line segment by 50%, the new length of the line segment would be 5 units (10 times 0.5 equals 5)**. This would be the case if the line segment had **originally been 10 units long.**

In a similar fashion, if we start with a rectangle that is 10 units long and** 5 units wide,** cutting the length of the rectangle in half would give us a new rectangle that is** 5 units long and 2.5 units wide** (10 multiplied by 0.5 equals 5, 5 multiplied by 0.5 equals 2.5).

The reduction in size plays an essential part in the advancement of science and technology toward the creation of smaller and more** power-efficient devices, such as smartphones and laptops**. In day-to-day life, one can use decreasing in size as a tool to make more informed decisions, such as **selecting smaller portions of food in order to maintain a healthy weight**.

## Decrease in Quantity

**Bringing down the total number of items in a collection is what’s meant by the phrase “decreasing in quantity.**” For instance, if we begin with **10 balls and lose 2 of them,** we will now only have **8 balls**, which is a** reduction** in a **quantity equal to 20% of the original quantity**.

The idea of a quantity decreasing over time is** fundamental to the study of mathematics** and has important r**eal-world applications in a wide variety of fields, such as economics, inventory management, and environmental science.**

## Percentage Decrease

The term** “percent decrease”** refers to the proportional shift in the value that results from the **reduction of that value over a given amount of time**.

For instance, there has been a **decrease in the amount of rainfall,** as well as a decrease in the number of** patients suffering from Covid.** Utilizing the formula for percentage decrease, one is able to determine a **percentage decrease**.

### Percent Decrease Formula

**The percentage decrease formula calculates the amount by which the quantity has decreased in comparison to its starting value.** Before we can calculate the **percentage reduction,** we need to** first determine the difference between the two sets of values**. After that, multiply that** result by 100** after dividing the difference by the starting value.

The formula for calculating the percentage of a decrease can be written out as follows:

**Percent Decrease = [(Old Value – New Value) / Old Value] x 100**

The formula for calculating the percentage of a decrease can be broken down into two straightforward steps, and those steps are as follows:

**Step 1: **Calculate the difference between the two numbers, which is represented by the formula:

**Decrease = Old Value – New Value**

**Step 2: **Multiply the result of dividing the decrease by the old value and Multiply that by 100. This completes the formulation for the percentage drop:

**[ (Old Value – New Value) / Old Value ] x 100**

This gives you the percentage decrease.

## Types of Decrease

### Absolute Decrease

**The Absolute decrease is the difference between the original value and the new value**, **regardless of the size of the original value.** This difference is referred to as the **actual difference** between the two values. The fact that it is expressed in the** same units** as the** initial value** and provides a clear picture of the magnitude of the decrease are both characteristics of this expression.

The following is a representation of the formula for absolute decrease:

**Absolute Decrease = Original Value – New Value**

For instance, if a person begins with a total of** one hundred dollars** and spends **twenty dollars,** the **absolute decrease** in their wealth is** twenty dollars (100 – 80).**

The absolute decrease is a straightforward and easy-to-understand method of measuring **changes in size or quantity.** This method is utilised frequently in many facets of life, including the **business world, the scientific community, and everyday life.**

### Proportional Decrease

**A decrease that is proportional to the initial value is what is meant when we talk about a proportional decrease.** To put it another way, the **new value can be expressed as a constant fraction of the old value.** Instead of being expressed as a percentage of the total value, this kind of reduction is shown as a **ratio or a fraction of the starting point.**

One possible representation of the formula for proportional decrease is as follows:

**Proportional Decrease = New Value / Original Value**

For instance, if a person starts out with a** hundred dollars and wants to save twenty percent of what they earn each month,** the amount of money they have saved will **decrease proportionally by twenty percent, which is represented as a decimal.**

When the size of the decrease is

**directly proportional to the size of the original value, a useful mathematical technique known as proportional decrease can be used.**For instance, in the field of

**physics, the amount of force that an object experiences due to friction is directly proportional to its mass.**

A proportional decrease is a useful tool that is commonly used in many areas of science,

**including physics, engineering, and mathematics**. It is used for measuring changes in

**size or quantity**that are

**directly proportional to the initial value.**

### Incremental Decrease

**A decrease that takes place over the course of time in the form of small, incremental steps is referred to as an incremental decrease.** Instead of being expressed as a **single percentage or fraction of the initial value**, this kind of reduction is more commonly shown as a** series of changes over time.**

For instance, if a person starts with** a hundred dollars and saves ten dollars each month**, their **savings will gradually decrease by ten dollars each month** because they are **saving ten dollars less each month.**

The use of incremental decrease is beneficial in circumstances in which the** magnitude of the reduction takes place not all at once but rather gradually over the course of time.**

For instance, in the world of** finance, the amount of interest earned on a savings account may gradually decrease over the course of time due to fluctuations in interest rates.**

An incremental decrease is a useful tool for measuring** changes in size or quantity that occur gradually over time.** It is commonly used in many areas of life,** including finance, economics, and personal budgeting,** to name a few of these areas.

### Compound Decrease

**A decrease that is said to be compounded is one that is based on the combined effects of several different factors or processes over the course of time.** In other words, it is a decrease that happens as a **consequence of a series of smaller decreases that occur over the course of time,** each of which builds upon the previous one.

The following is a representation of the formula for compound decrease:

**Compound Decrease = (1 – factor 1) * (1 – factor 2) * … * (1 – factor n)**

For instance, if a person begins with **a hundred dollars and saves ten dollars each month and their savings also decrease by five percent each year due to inflation**, then that person’s savings **will decrease in a compound manner,** with both the **savings and the inflation affecting** the overall balance of their savings.

The compound decrease is useful in situations where the **size of the decrease is affected by multiple factors or processes over time.** One example of this is in **the field of finance**, where the balance of a savings account may be affected by both the a**mount saved and the interest earned,** as well as by **both inflation and taxes.**

A compound decrease is a useful tool for measuring** changes in size or quantity that are affected by multiple factors or processes over time.** It is commonly used in many areas of life, including **finance, economics, and personal budgeting.**

## Example of Decrease in Terms of Percentage

A student measures a length of 43 mm wrongly as 23 mm. Determine the percent decrease between the two by using the formula for the percent decrease. What is its significance?

### Solution

The new value is \$25, and the old value was \$43. If we plug these numbers into the formula for calculating the percentage decrease, we get:

Percent Decrease = [(Old Value – New Value) / Old Value] x 100

= $\mathsf{\dfrac{43-25}{43}}$ Ã— 100

= $\mathsf{\dfrac{18}{43}}$ Ã— 100

= 41.9%

As a result, the percentage decrease in the number is close to 42 percent. In this case, the percent decrease depicts the measurement error of the student.

*All images were created with GeoGebra.*