- Quotient and Remainder (Word problems)
- Quotient and Remainder: Problem type 2
- Quotient and Remainder: Problem type 1
- Division With Trailing Zeros: Problem Type 2
- Division With Trailing Zeros: Problem Type 1
- Whole Number Division: 3-digit by 2-digit, No Remainder
- Whole Number Division: 2-digit by 2-digit, No Remainder
- Division Involving Zero
- Division With Carry
- Division Without Carry
- Unit Rates and Ratios of Whole Numbers (Word problems)
- Multiplication and Addition or Subtraction of Whole numbers (Word problems)
- Multiplication or Division of Whole Numbers (Word problems)
- Fact Families for Multiplication and Division
- Division Facts
- Multiples Problem Type 2
- Multiples Problem Type 1
- Multiplication of Large Numbers
- Multiplication of a Single Digit Number With Large Numbers
- Multiplication of 2-digit Numbers With 2-digit Numbers
- Multiplication With Trailing Zeros: Problem Type 2
- Multiplication With Trailing Zeros: Problem Type 1
- Multiplication With Carry
- Multiplication Without Carry
- Multiplication by 10, 100, and 1000
- Single Digit Multiplication
- Multiplication as Repeated Addition
- Home
Selected Reading
- Who is Who
- Computer Glossary
- HR Interview Questions
- Effective Resume Writing
- Questions and Answers
- UPSC IAS Exams Notes
Division Involving Zero
For any real number a, $frac{a}{0}$ is undefined
For any non-zero real number a, $frac{0}{a}$ = 0
$frac{0}{0}$ is indeterminate
For any real number a, $frac{a}{0}$ is undefined
Dividing any real number by zero is undefined and sometimes taken as infinity. Division is spptting into equal parts or groups.
Let us consider an example: Suppose there are 12 ice cream cups and 4 friends want to share them. How do they spanide the ice cream cups?
$frac{12}{4}$ = 3; So they get 3 each: Now, let us try spaniding the 12 ice cream cups among zero people. How much does each person get?
Does that question make sense? No, it doesn t.
We can t share among zero people, and we can t spanide by 0.
Suppose we could get some number k by spaniding any real number a by zero
Let us assume $frac{a}{0}$ = k. Then k × 0 = a. There is no such number k which when multipped by zero will give a. So k does not exist and therefore $frac{a}{0}$ is said to be undefined.
For any non-zero real number a, $frac{0}{a}$ = 0
If zero is spanided by any non-zero real number a, we get 0 as the result. If zero items are spanided among a number of people, share got by each person will be zero only
$frac{0}{0}$ is indeterminate
Division of zero by zero is a quantity that cannot be found and is called indeterminate.
Find the value of $frac{0}{5}$
Solution
Step 1:
For example, $frac{3}{4}$ = 3 × $frac{1}{4}$ .
Step 2:
Similarly, $frac{0}{5}$ = 0 × $frac{1}{5}$ = 0
as the product of zero and any number is zero.
Evaluate $frac{7}{0}$
Solution
Step 1:
By definition, spanision of any number by zero is not defined.
Step 2:
So, $frac{7}{0}$ is not defined.
Evaluate $frac{0}{13}$
Solution
Step 1:
Zero spanided by any number is zero.
Step 2:
So, $frac{0}{13}$ = 0