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# Minus|Definition & Meaning

## Definition

The termÂ **minus** can refer to **Â two meanings** that are closely related. It can either beÂ ** an operation or a symbol.** Minus operation is a fundamentalÂ **operation in mathematics** that is often employed to determine the numerical **difference**Â between twoÂ **numbers**Â orÂ **fractions**. The ASCII character ‘-,’ called the minus or minus sign, symbolizes this operation. The same operation is also termedÂ **subtraction.**

## Pictorial Intuition

The following figures and explanations describe the intuitive reasoning behind the minus or subtraction operator:

Figure 1 shows a pie chart that has been** divided into 10 equal sectors**. The total area of the pie represents the **number 10**. Now suppose that we wanted to perform the operation** ten minus three**. This mathematical operation is equivalent to **removing three parts** out of the total ten parts of the pie, as illustrated in the figure below:

The above figure shows that if we** remove three parts**, we are left with **seven parts** which is the result of the operation **ten minus three.** This proves graphically that **10 – 3 = 7**. Consider another case where we wanted to perform the operation **ten minus five**. This mathematical operation is equivalent to **removing five parts** out of the total ten parts of the pie, as illustrated in the figure below:

The above figure shows that if we **remove five parts,** we are left with **five parts** which is the result of the operation **ten minus five.** This proves graphically that **10 – 5 = 5**. We can understand the operation **10 – 7 = 3** in a similar manner utilizing **figure** **4** given below:

## Explanation of Minus Operation

A **minus** sign also refers to the **subtraction** of a part of a given value from itself. It is such a **mathematical process** where the subtraction method involves **pruning** or cutting out a portion of the **given numerical value** and subtracting it from itself. This process and the **background concepts** are further explained in detail in the following sections with the help of very easy-to-relate **numerical** and practical **examples.**

**Subtraction** is a very fundamental concept taught in elementary schools as a basis for the whole mathematics along with the other basic operations of addition, multiplication, and division. The key idea behind the subtraction process is very easy to learn.

Let us consider an example to understand its concept. Suppose you went out and bought twelve apples and must share two apples with your sibling. Now you intuitively know that if you give two apples to your sibling, you will only be left with ten apples. The operation that you performed in drawing this result is called minus or subtraction.

Carrying forward the above example, one can say that you performed the mathematical operation: twelve minus two equals ten. In symbolic terms, we would write this operation as **12 – 2 = 10.**

**Negative** or **additive** inverse is a very common sighting in almost all kinds of **numerical problems.** It is used to **cancel out** the effects of some physical quantity when we talk about the physical sense of things. This very same operation is used to represent the **negative integers.**

### Guidelines for Solving Minus Numerical Problems

Although the above figures perfectly develop the **graphical** or **intuitive understanding** of the subject, evaluating the minus operator in **numerical problems** is a different subject. Now we have to perform **certain numerical procedures** to calculate the final answer. The mathematical procedure for **evaluating** a **subtraction** can be reduced to a **simpler addition problem** by using the following step-by-step method:

**Step 1:** Write the problem in **mathematical form.** For example, 10 – 6.

**Step 2: Decompose** the first operand into parts such that one of them is the **additive inverse** of the second operand. For example, **10** can be divided into two parts, **+4** and **+6.** Here **+6** is the **additive inverse** of **-6,** which is the second operator. The expression reduces to **4 + 6 – 6**.

**Step 3:** Now that we have a number and its additive inverse added together, we can use the **additive inverse property** and sum both of these equal to zero. In above example, **+ 6 – 6 = 0**.

**Step 4:** Substituting the above solution results in the **final answer.** In above example, **4 + 6 – 6 = 4 + 0 = 4**.

## Example Numerical Problems

The **mathematical process** of evaluating minus or subtraction problems is explained with the help of **numerical examples** in this section. Here we suppose that we wanted to calculate the results of the **following minus operations:**

(a) 55 minus 38

(b) 100 minus 10

(c) 4 minus 5

(d) 1.55 – 0.55

### Solutions

**(a) 55 minus 38**

Here **55** can be **decomposed** into two parts, **17** and **38,** such that **17** plus **38** equals **55:**

**55 – 38 = ( 17 + 38 ) – 38 = 17 + 38 – 38**

Here + **38** and – **38** are the additive inverse or negative of one another, so their **sum** is **equal** to **zero:**

**55 – 38 = 17 + 0 = 17**

**(b) 100 minus 10**

Here **100** can be decomposed into two parts, **90** and **10,** such that **90** plus **10** equals **100:**

**100 – 10 = ( 90 + 10 ) – 10 = 90 + 10 – 10**

Here + **10** and – **10** are the additive inverse or negative of one another, so their **sum** is **equal** to **zero:**

**100 – 10 = 90 + 0 = 90**

**(c) 4 minus 5**

Here **4** can be decomposed into two parts, **-1** and **+5,** such that **-1** plus **5** equals **4**:

**4 – 5 = ( -1 + 5 ) – 5 = – 1 + 5 – 5 = – 1 + 0 = – 1**

Here **+5** and **-5** are the additive inverse or negative of one another, so their **sum** is **equal** to **zero:**

**4 – 5 = – 1 + 0 = – 1**

**(d) 1.55 minus 0.55**

Here **1.55** can be decomposed into two parts, **1** and **0.55,** such that **1** plus **0.55** equals **1.55:**

**1.55 – 0.55 = ( 1 + 0.55 ) – 0.55 = 1 + 0.55 – 0.55**

Here + **0.55** and – **0.55** are the additive inverse or negative of one another, so their **sum** is **equal** to **zero:**

**1.55 – 0.55 = 1 + 0 = 1**

*All mathematical drawings and images were created with GeoGebra.*