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# Difference|Definition & Meaning

## Definition

In mathematics, a **difference** is the consequence of one of the most significant **arithmetic computations**, which seems to be gained by **subtracting** two numbers. It indicates how much one number **differs** from another. In math, the goal of determining the **difference** is to determine how many numbers **lie** between two given figures. The difference has symbols **negative (-)**.

The first digit in the equation is the **minuend**. The next or second digit in the equation is **subtrahend**, and the result is the **difference **between two digits or two numbers.

Here in the above figure, as clearly mentioned, **9** is the **minuend,** **2** is the **subtrahend,** and **7** is the **difference**. So when we subtract **2** from **9, **the result will be **7**. Likewise, when we subtract **2** from** 8,** the result will be **2,** and when we find the difference between **7 **and **2,** the result will be** 5**.

## Various Procedures for Evaluating the Difference

### Difference Between the Numbers Using Number Line

The numbers are also **subtracted** by a **number line,** and it is extremely useful for quickly determining the difference between two smaller numbers. We move to the** left** side of a number line while calculating the difference between two numbers on a number line. We begin with minuend and work our way down to the number towards the subtrahend. As a result of this, we will find the **difference** between the two numbers.

One such problem is handled in **Example 1**.

### Difference Without Borrowing

To find the difference between the two numbers, the first and main step is to put the **bigger number** on the **top, **and the** smaller number** should be written **below**. We will start subtraction from the **right side**.

This sort of problem is dealt with in **Example 2**.

### Difference With Borrowing

The borrow concept is applicable where the digits in the **upper** number are **smaller** than the **lower** number. If the number is** less** in ones place then we need to borrow **one** from the next place value, which is **tens**. If the number is less in the** tens** place value, one will be borrowed from the next place value, which is **hundreds,** and so on.

The process is detailed in **Example 3**.

### Difference Between Decimals

The method of difference is the same as the usual whole numbers, but here we additionally have decimal points. The numbers before the decimal points are **whole numbers,** and the numbers which are after the **decimal point **are the **fractional part**.

We solve one such problem in **Example 4**.

### Difference Between Fractions

The difference between the fractions is different from the difference between whole numbers and decimals. In fractions, there is a numerator as well as a denominator, so the method of difference is also changed for it. There are different cases to find the difference between the fractions. For every case, there is a rule to solve the difference.

- Check whether the fraction is
**like**or**unlike.**If the fraction is like means the same denominator, we will simply subtract the numerator. - When the fractions are unlike, we will take the
**LCM**of the denominator or make the denominator the**same,**then simply subtract the numerator.

Example** 5** deals with the difference between two pairs of fractions (one like and one unlike pair).

## Solved Examples Corresponding to the Above Scenarios

### Example 1

Find the difference between **5** and **0** using a number line.

### Solution

The number line below shows the difference between **5** and **0**.

In the above figure, we have to find the difference between two numbers that is **5** and** 0** so we will move **backward** on the number line for subtraction, now here we will move four steps backward until we reach** 0,** so here:

**5 – 0 = 5**

The answer to the subtraction through the number line is **5**.

### Example 2

Find the difference between **7658** and **4237**.

### Solution

The figure here represents the difference between the two numbers, but the first number is **greater** than the other number. Like **7658** is greater than **4237,** so in this case, we do not have to borrow.

Here in the above figure, the **ones place value **is **8,** which is **bigger** than the **lower number’s** ones place value of **7,** so there is no need to borrow. This is the case for all digits here. Thus, when **4237** is subtracted from **7658,** the answer will be** 3421**.

If the ones place value of the upper number is **smaller** than the lower number then we have to borrow **1** from the tens place value of the upper number (next example).

### Example 3

**8556**and

**1227**.

### Solution

This is an example of the difference between borrow and carrying. The ones place value in the first number is 6, and the ones place value of the second number is **7** means here** 6** is smaller than** 7,** so we have to take carry or borrow one from the next place value.

Here in the figure above, the ones place value of the upper value is** less **than the ones place value of the lower number. We need to make the number in the upper number’s ones digit **bigger **than the lower number’s ones digit because a smaller digit can not be subtracted from a bigger one.

Here, **1** is borrowed from the tens place value, which makes the ones place become **16, **and the tens place is one less, which is **4.** Further, the subtraction now follows the casual rule.

### Example 4

**8556.50**and

**1227.30**.

### Solution

The difference between decimals is the same as whole numbers.

Here in the figure, the right-hand side numbers are whole numbers, whereas the left-hand side numbers of the decimal points are the fractional part. In the above figure,** 8556** is the whole number, whereas** 50** is the fractional part. In the other decimal number, **1227** is the whole number, and **30** is the fractional part. The subtraction of decimal numbers follows the same rule as simple whole numbers.

### Example 5

Find the difference between 9/5 and 3/5 and also the difference between **8/7** and** 3/5**?

### Solution

Here** 9/5** and** 3/5 **are two like fractions. So, we will take the difference of numerator.

The above figure shows the difference between the two like fractions because the denominator is the same. In this case, the numerator will be simply subtracted like **9/5 – 3/5 = 6/5**

In the next figure, the subtraction is between two unlike fractions; the numerators and denominators of both fractions are **different! **In this case, we have to convert **unlike** fractions to** like** fractions. To do that, we can take** LCM,** or another method is to make both the denominator **same** by multiplying and dividing one or both of the fractions with a **certain number**. After converting the fractions into like fractions, we can simply use the previous method (subtract numerators).

*All figures above are created on Geogebra. *