How do you divide decimals and fractions step by step?
The concept of How to Divide plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Division helps us split numbers or quantities into equal parts, and is used from calculating shares to solving word problems in school and competitive exams.
What Is How to Divide?
How to divide means finding out how many times one number (the divisor) fits into another number (the dividend). You’ll find this concept applied in areas such as splitting objects for kids, dividing decimals, and solving fraction problems. Division is a foundational operation, along with addition, subtraction, and multiplication.
Key Formula for How to Divide
Here’s the standard formula: \( \text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder} \)
Cross-Disciplinary Usage
How to divide is not only useful in Maths but also plays an important role in Physics, Computer Science, and daily logical reasoning. Students preparing for exams like JEE, NEET, or Olympiads will see its relevance in many questions involving ratios, data analysis, and real-life scenarios.
Division Terms Explained
| Term | Meaning | Example (10 ÷ 2 = 5) |
|---|---|---|
| Dividend | Number to be divided | 10 |
| Divisor | Number that divides the dividend | 2 |
| Quotient | Result of division | 5 |
| Remainder | Part left after division (if any) | 0 |
Step-by-Step Illustration
- Start with the Dividend and Divisor: For example, 52 ÷ 4
Dividend: 52, Divisor: 4 - Divide the first digit or first set of digits of the dividend by the divisor
4 goes into 5 one time. Write 1 as the first digit of the quotient. - Multiply and Subtract
1 × 4 = 4. Subtract 4 from 5 to get 1. - Bring down the next digit
Now bring down the 2. 12 is the new number. - Divide 12 by 4
4 goes into 12 three times. 3 × 4 = 12. Subtract to get 0. - Write the quotient
The answer is 13. So, 52 ÷ 4 = 13.
How to Divide Decimals
When dividing decimals, first remove the decimal place by multiplying both dividend and divisor by 10, 100 etc., as needed. Divide like whole numbers and place the decimal in the quotient at the correct spot.
How to Divide Fractions
To divide fractions, multiply the first fraction by the reciprocal of the second. For example, \( \frac{3}{5} \div \frac{2}{7} = \frac{3}{5} \times \frac{7}{2} = \frac{21}{10} \). See more fraction solutions at Division of Fractions and How to Solve Fractions.
Shortcuts and Tricks
Here’s a quick shortcut for dividing by 5: Multiply the number by 2, then move the decimal one place left. Example: 85 ÷ 5 → 85 × 2 = 170 → Move decimal left: 17.0. In timed exams, this saves precious seconds. Vedantu live sessions share more such Math tricks.
| Divisor Trick | How It Works |
|---|---|
| Dividing by 10, 100, 1000 | Move decimal point left by 1, 2, 3 places |
| Dividing by 9 | Sum of digits of dividend is the remainder |
Division Word Problems
Word problems connect division to real life, such as sharing money, distributing objects, or calculating time. Here’s an example:
Example: 20 candies are to be divided equally among 4 friends. Each gets 20 ÷ 4 = 5 candies. Find more practical worksheets at Division Word Problems and Division with Real Life Examples for Grade 2.
Frequent Errors and Misunderstandings
- Forgetting to align decimal points in decimal division
- Placing quotient digits in the wrong place in long division
- Confusing the remainder with the quotient
- Ignoring to multiply by the reciprocal in fraction division
Relation to Other Concepts
The idea of how to divide connects closely with Multiplication and Division, Long Division, and Division Algorithm Formula. Mastering this makes operations with numbers, fractions, and ratios much simpler in future chapters.
Classroom Tip
A quick way to remember division is: Dividend ÷ Divisor = Quotient, with leftover as the remainder. Drawing boxes for groups helps early learners. Vedantu teachers often use such visuals in their live sessions to make Maths simple.
Try These Yourself
- Solve: 84 ÷ 7
- Divide 3.27 by 3
- Find: \( \frac{5}{8} \div \frac{2}{3} \)
- Share 56 apples among 8 baskets
- What is the remainder when 45 is divided by 6?
We explored How to Divide—from definition, formula, step-by-step examples, fast tricks, and connections with other maths topics. Continue practicing with Vedantu to become confident in division and excel in your exams!
Quick links for more practice and deeper understanding:
FAQs on How to Divide Numbers in Maths: Simple Steps & Examples
1. What is division in Maths?
Division in mathematics is the process of splitting a whole number into equal parts. It's the inverse operation of multiplication. The key components are the dividend (the number being divided), the divisor (the number you're dividing by), the quotient (the result of the division), and the remainder (the amount left over if the division isn't exact).
2. How do you divide large numbers step by step?
Dividing large numbers involves the long division method. Here's a step-by-step guide:
- Set up the problem: Write the dividend and divisor in the long division format.
- Divide: Determine how many times the divisor goes into the first digit(s) of the dividend.
- Multiply: Multiply the quotient digit by the divisor.
- Subtract: Subtract the product from the part of the dividend you've used.
- Bring down: Bring down the next digit from the dividend.
- Repeat: Repeat steps 2-5 until all digits have been used.
- Remainder: The final number left is the remainder (if any).
3. How do you divide decimals by whole numbers?
Dividing decimals by whole numbers is similar to long division. The key difference is the placement of the decimal point. Place the decimal point in the quotient directly above the decimal point in the dividend. Then, perform long division as usual. For example, 12.6 ÷ 3 = 4.2.
4. What is the difference between dividend and divisor?
The dividend is the number being divided, while the divisor is the number you're dividing by. In the expression 12 ÷ 3, 12 is the dividend and 3 is the divisor.
5. What are some easy tricks to do division quickly?
Several tricks can speed up division:
- Dividing by 10, 100, 1000: Move the decimal point to the left by the number of zeros in the divisor.
- Dividing by 5: Double the dividend and then divide by 10.
- Dividing by 25: Multiply by 4, then divide by 100.
- Dividing by 9: Repeatedly subtract 9 until you reach 0 or a number less than 9.
6. Why does division sometimes have a remainder?
A remainder occurs when the dividend isn't perfectly divisible by the divisor. It represents the part of the dividend that's left over after the division is complete. For example, when you divide 17 by 5, the quotient is 3, and the remainder is 2 because 5 goes into 17 three times with 2 remaining.
7. How is division related to fractions or ratios?
Division is closely related to fractions and ratios. A fraction represents a division problem; the numerator is the dividend, and the denominator is the divisor. Similarly, a ratio can be expressed as a division problem, comparing the relative sizes of two or more quantities. For example, 3/4 is equivalent to 3 divided by 4.
8. What if the divisor is bigger than the dividend?
If the divisor is larger than the dividend, the quotient will be zero, and the remainder will be the dividend itself. For example, 5 ÷ 10 = 0 with a remainder of 5. This indicates that the dividend is a fraction or part of the divisor.
9. How do you estimate an answer before dividing?
Estimating helps check your answers. Use rounding to make the numbers easier to work with. For example, to estimate 789 ÷ 12, round 789 to 800 and 12 to 10. The estimate is 800 ÷ 10 = 80.
10. Why is division considered the inverse of multiplication?
Division is the inverse of multiplication because it undoes what multiplication does. If you multiply a number by another, you can divide the product by one of the original numbers to get back to the other original number. For example, if you multiply 3 x 4 = 12, you can then divide 12 by 3 to get back to 4 or divide 12 by 4 to get back to 3.
11. How to divide fractions?
To divide fractions, change the division to multiplication by flipping (finding the reciprocal of) the second fraction (divisor). Then, multiply the numerators and the denominators. Simplify the resulting fraction if necessary. For example: (2/3) ÷ (1/4) = (2/3) x (4/1) = 8/3 = 2 2/3
12. How to divide polynomials?
Polynomial division uses a method similar to long division for numbers. Divide the leading term of the dividend by the leading term of the divisor to find the first term of the quotient. Multiply the divisor by the first term of the quotient and subtract the result from the dividend. Bring down the next term and repeat the process until you have a remainder. This is often taught in higher grade levels.
