# What is Difference in Math? Definition, Symbol, Examples, Facts (2023)

Home»Difference in Math – Definition With Examples

• Introduction
• Without borrowing
• With borrowing
• Solved Examples
• Practice Problems

## Introduction

Let us look at two shapes:

Their color is also different. One is bigger, the other is smaller. That means their size is also different. Difference means a way in which two or more objects or persons are dissimilar.

But, difference in mathematics means something else. Let’s learn what difference means in math.

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## Definition for Difference in Math

Difference in math is the result of one of the important mathematical operations, which is obtained by subtracting two numbers. It tells us by how much a number differs from the other. The aim of finding the difference in math is to tell how many numbers lie between the two given numbers. The difference in math symbol is minus(-).

Minuend is the first number in the subtraction sentence. Subtrahend is the second number in the subtraction sentence and the result that we get is the difference between the two numbers.

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## Finding the Difference between Numbers Using a Number Line

The number line is useful in finding the difference of smaller numbers very easily. While finding the difference between the numbers on a number line, we move towards the left-hand side of a number line. We start with the minuend and move to the left to the number towards the subtrahend.

Example: Find the difference between 4 and -6 on the number line.

Difference =10

## Finding the Difference between Two Numbers

The following steps are involved to find the difference between natural numbers or whole numbers –

• The first step is to place the values vertically in the order of their place values. Also, make sure the greater number should be on the top and the smaller one should be on the bottom.
• Start subtracting the numbers, starting from the ones place.

## Without borrowing

For example, we have to find the difference between 2342 and 6758.

In this case, we saw that each digit of the subtrahend is less than the corresponding digit in the minuend. We get

## With borrowing

In this case, some digits in the subtrahend are greater at a certain place value than the corresponding value of the minuend.

Suppose we have to find the difference between 3456 and 1287.

1. Subtract 7 from 6. We cannot subtract the larger number from the smaller ones, so we borrow 1 from the digit that is at the ten’s place in the minuend. In this case, the number is 5. So we borrow 1 from 5, and the 5 at the tens place in the minuend becomes 4. But the number at the ones place of the minuend, after borrowing 1 becomes 16. Now we can subtract 7 from 16 and we get 9 at the ones place as the answer.
1. We move to subtract the tens place digit. Remember, the digit at the tens place is now 4, instead of the 5. So, we need to subtract 8 from 4, which again is not possible. Thus, we repeat the steps again that we did for subtracting the digits at the ones place. We will borrow 1 from the digit at the hundreds place, and give it to 4 at the tens place. So, 4 at the hundred place of the minuend becomes 3 and the 4 at the tens place of the minuend becomes 14. Now we can subtract 8 from 14 and we get 6 as the answer at the tens place.
1. Now, we look at the values at hundreds place. Here, we have 2 as the subtrahend and 3 as the minuend which can be easily subtracted. So, we get 1 as the answer at the hundreds place.
1. At last, we check the values at the thousands place. We have 1 as the subtrahend and 3 as the minuend. Hence, we get 2 as the answer at the thousands place.

Hence, 3456 – 1287 = 2169

## Finding the Difference between Two Decimal Numbers

The following steps are required to find the difference between two decimal numbers:

1. Convert unlike decimals into like decimals.
2. Place the decimal numbers such that the tens digit is below tens, ones is below ones, the decimal point is below the decimal point, the tenth digit is below the tenth digit, the hundredth digit is below the hundredth digit and so on.
3. Subtract in the same way as we do for the whole number. Borrow if necessary.
4. Place the decimal point in the difference exactly below the decimal point in the decimal numbers.

For example: We have to find the difference between 28.06 and 7.984.

We will first convert both the decimal numbers into like decimals by adding one zero in 28.06.

28.06 can be written as 28.060.

The next step is to subtract them like whole numbers and place a decimal point.

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## Finding the Difference between Two Fractions

In order to find the difference between two fractions, we have to use the following steps:

1. Checking whether the fractions are like fractions or not. If they are like fractions, we will go to Step 4, else we will go to Step 2.
2. When the fractions are unlike, we find the LCM of the denominators.
3. Converting each fraction into an equivalent fraction having the denominator equal to the LCM obtained in the previous step.
4. After the fractions become like fractions, subtracting them as we do for a like fraction, i.e., subtracting their numerators.
5. Reducing the fraction to its simplest form, if required.

For example: A recipe requires 2/7 teaspoon salt and 1/3 teaspoon paprika. How much more paprika is added compared to the salt?

Fraction of salt needed in the recipe = $\frac{2}{7}$

Fraction of red pepper salt needed in the recipe = $\frac{1}{3}$

LCM(7, 3) = 21

$\frac{2\times3}{7\times3}=\frac{6}{21}$ and $\frac{1\times7}{3\times7}=\frac{7}{21}$

Difference = $\frac{7}{21}-\frac{6}{21}=\frac{1}{21}$

## Solved Examples

1. Find the difference between -2 and 5 on the number line.

Solution:

Difference = 7

2. There are 2052 ants in the garden. 1156 ants flew away. How many ants are left now?

Solution: Number of ants in the garden = 2052

Number of ants that flew = 1156

Number of ants left now = 2052 – 1156

3. Peter purchased a syrup for $\$$40.00, a cookie box for \$$19.50 and a hair oil bottle for$\$$30. She gave \$$100 to the shopkeeper, how much money did the shopkeeper return as balance?

Solution: The amount Peter spent = $\$$40.00 + \$$19.50 +$\$$30 = \$$89.50

The amount Peter gave to the shopkeeper = $\$$100 The amount the shopkeeper will return in balance = \$$100 –$\$$89.50 The amount the shopkeeper will return in balance = \$$10.50

## Practice Problems

1

### How much is $\frac{1}{4}$ more than $\frac{1}{16}$?

$\frac{3}{16}$

$\frac{1}{4}$

$\frac{1}{2}$

$\frac{5}{16}$

CorrectIncorrect

Correct answer is: $\frac{3}{16}$
$\frac{1\times4}{4\times4}=\frac{4}{16}; \frac{4}{16}-\frac{1}{16}=\frac{3}{16}$

2

### What should be added to $-10$ to get $-198$?

188

$-208$

$-188$

208

CorrectIncorrect

Correct answer is: $-188$
$-198-(-10)=-198+10=-188$

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3

### If Sam gave $\frac{1}{3}$ part of his land to his sister and $\frac{1}{2}$ part of his land to his brother, how much part of land will he be left with?

$\frac{5}{6}$

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{1}{6}$

CorrectIncorrect

Correct answer is: $\frac{1}{6}$
Part of land he gave =$\frac{1}{3}+\frac{1}{2}=\frac{5}{6}$
Remaining land =$1-\frac{5}{6}=\frac{6}{6}-\frac{5}{6}=\frac{1}{6}$

Difference is used to figure out the distance, in understanding counting backwards, making change at the supermarket, and playing certain games, among others.

A difference is the result of subtraction whereas subtraction is an operation to find the difference of two numbers.

The absolute difference in math is the difference between two numbers irrespective of the sign. The absolute difference is always positive even if the numbers are negative. If A and B are two numbers, the absolute difference = A-B

On the other hand, the difference in math between two numbers is the result of subtraction. Here, signs matter. The difference can be negative as well as positive.

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## FAQs

### What is the symbol for difference in math? ›

The difference in math symbol is minus(-). Minuend is the first number in the subtraction sentence. Subtrahend is the second number in the subtraction sentence and the result that we get is the difference between the two numbers.

What does difference mean in math examples? ›

The result of subtracting one number from another. How much one number differs from another. Example: The difference between 8 and 3 is 5. Subtraction.

What is the symbol operations of difference? ›

b.

Subtraction gives us a difference. In 8 - 5 = 3, the difference is three.

What does difference mean in math word problems? ›

difference The difference between two numbers can be found by subtracting. find the difference To find the difference between 15 and 10, you can count the units from 10 up to 15 on the number line. benchmark numbers numbers that are easy to use, like 10, 50, 100, and 200, are benchmark numbers.

How do you express difference in math? ›

For example, find the difference between 10 and 4. To do this, subtract the smaller value from the larger value: 10 - 4 = 6. The difference between 10 and 4 is 6. In this example, 10 is the minuend, 4 is the subtrahend, and 6 is the difference.

What math equation is difference? ›

A difference equation is any equation that contains a difference of a variable. The classification within the difference equations depends on the following factors. Order of the equation. The order of the equation is the highest order of difference contained in the equation.

Whats the definition for difference? ›

ˈdi-fərn(t)s. : the quality or state of being dissimilar or different. the difference between right and wrong. : an instance of being unlike or distinct in nature, form, or quality.

What is the difference between two numbers called? ›

Answer: Formally, the number being subtracted is known as the subtrahend, while the number it is subtracted from is the minuend. The result is the difference.

What is the difference between two numbers? ›

To find the difference between two numbers, subtract the smaller number from the larger number. To find the difference between two numbers, subtract the smaller number from the larger number. 5 – 3 = 2 and so, the difference between 5 and 3 is 2.

What is the symbol for difference in statistics? ›

d = difference between paired data.

### What is sum and difference in math? ›

The outcome of adding two or more numbers gives the sum. Example: 2+8+3+4. Answer: 17. The outcome of subtracting the two numbers gives the difference. Example: 8-4.

Which of the following is the symbol for the difference of any two sets? ›

The difference of sets is denoted with a minus symbol. The set A − B will consist of elements that are present in A but not in B. For example, if A = {1,2,3} and B={3,5,7}, then A−B={1,2}.

What is a first difference in math examples? ›

You find the first differences in a table of values by finding the difference in consecutive values for the dependent variable when the values for the independent variable are increasing by the same amount. If the first differences are equal then the relationship is linear.

How do you show a difference? ›

Percentage difference equals the absolute value of the change in value, divided by the average of the 2 numbers, all multiplied by 100. We then append the percent sign, %, to designate the % difference. For example, how to calculate the percentage difference: What is the percentage difference between 5 and 7?

What function is difference? ›

The DIFFERENCE() function compares two SOUNDEX values, and returns an integer. The integer value indicates the match for the two SOUNDEX values, from 0 to 4.

What does difference mean for kids? ›

Difference is a word for things that are not the same.

Minuend – The number from which the subtrahend is subtracted is called minuend. Difference – The result of this subtraction is called the difference.

What is difference used in a sentence? ›

That is the fundamental difference between the two societies. There is no difference between the sexes. We do have problems here. The difference is that people try to help each other.

What is the difference between 3 and 5? ›

if we are told to find the difference between 3 and 5, then we usually subtract 3 from 5 ,5-3=2 and thus, we say that the difference is 2.

What is the difference between 2 and 7? ›

Answer. therefore, difference between 2 and 7 is 5.

### Does Delta mean difference in math? ›

Difference is the most common meaning of the uppercase delta. It is simply the difference, or change, in a certain quantity. When we say delta y, for example, we mean the change in y or how much y changes.

What does ∆ mean in sets? ›

The symbol of symmetric difference is “Δ” which is read as “delta” or “symmetric difference”. Therefore, “A Δ B” is read as “A delta B” or “set A symmetric difference set B”.

What does the D mean in math? ›

The d itself simply stands to indicate which is the independent variable of the derivative (x) and which is the function for which the derivative is taken (y).

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