Decimal Division Worksheet With Answers

Mastering Decimal Division: A Comprehensive Worksheet Guide with Answers

Decimal division can seem daunting at first, but with the right approach and consistent practice, it becomes second nature. This comprehensive guide provides a detailed explanation of decimal division, complete with practice worksheets and answers. Whether you're a student struggling with the concept or a teacher looking for supplementary resources, this guide will equip you with the tools to conquer decimal division. We'll cover various techniques, from the fundamental steps to handling more complex problems involving multiple decimal places. By the end, you'll have a strong foundation and the confidence to tackle any decimal division problem you encounter.

Understanding Decimal Division: A Foundation for Success

Before diving into the worksheets, let's establish a solid understanding of the underlying principles. Decimal division involves dividing a number containing a decimal point by another number. The core concept remains the same as whole number division: we're figuring out how many times one number goes into another. The presence of decimals simply adds an extra layer of consideration for placement of the decimal point in the quotient (the answer).

Key Concepts:

• Divisor: The number you are dividing by (the number outside the division symbol).
• Dividend: The number being divided (the number inside the division symbol).
• Quotient: The result of the division (the answer).
• Decimal Point Placement: This is crucial in decimal division. Misplacing the decimal point will result in an incorrect answer.

Step-by-Step Guide to Decimal Division

Let's break down the process into manageable steps:

1. Set up the problem: Write the dividend inside the division symbol (long division bracket) and the divisor outside.

2. Handle the decimal point: If the divisor has a decimal point, move the decimal point to the right until it becomes a whole number. Then, move the decimal point in the dividend the same number of places to the right. Add zeros as needed. If the divisor is already a whole number, proceed to the next step.

3. Divide as you would with whole numbers: Begin the long division process, remembering to bring down digits and perform the necessary subtractions and multiplications.

4. Place the decimal point in the quotient: Place the decimal point in the quotient directly above the decimal point in the dividend (after you've moved it in step 2).

5. Continue dividing: Continue the long division process until you obtain a remainder of zero or reach a desired level of accuracy. You may need to add zeros to the dividend to continue the division process if necessary.

6. Check your answer: Multiply the quotient by the divisor. The result should be equal to the dividend (or very close, if you rounded).

Decimal Division Worksheet 1: Basic Problems

Let's start with some basic problems to build your confidence. Remember to follow the steps outlined above.

Instructions: Solve the following decimal division problems.

1. 12.6 ÷ 3 =
2. 25.5 ÷ 5 =
3. 48.8 ÷ 4 =
4. 63.9 ÷ 9 =
5. 72.5 ÷ 5 =
6. 9.6 ÷ 2 =
7. 15.2 ÷ 4 =
8. 125 ÷ 5 =
9. 36.9 ÷ 3 =
10. 50.5 ÷ 5 =

Answers to Worksheet 1:

1. 4.2
2. 5.1
3. 12.2
4. 7.1
5. 14.5
6. 4.8
7. 3.8
8. 25
9. 12.3
10. 10.1

Decimal Division Worksheet 2: Problems with Multiple Decimal Places

This worksheet introduces problems with more decimal places in both the dividend and the divisor.

Instructions: Solve the following decimal division problems.

1. 15.75 ÷ 2.5 =
2. 36.18 ÷ 9.3 =
3. 25.02 ÷ 3.1 =
4. 42.84 ÷ 6.2 =
5. 51.75 ÷ 7.5 =
6. 0.24 ÷ 0.8 =
7. 1.62 ÷ 0.9 =
8. 3.15 ÷ 0.05 =
9. 0.072 ÷ 0.08 =
10. 0.486 ÷ 0.09 =

Answers to Worksheet 2:

1. 6.3
2. 3.9
3. 8.0
4. 6.9
5. 6.9
6. 0.3
7. 1.8
8. 63
9. 0.9
10. 5.4

Decimal Division Worksheet 3: Challenging Problems

This worksheet includes more challenging problems, requiring careful attention to detail and potentially the addition of zeros to continue the division process.

Instructions: Solve the following decimal division problems.

1. 123.45 ÷ 0.05 =
2. 987.65 ÷ 2.5 =
3. 456.78 ÷ 1.2 =
4. 876.54 ÷ 0.3 =
5. 789.12 ÷ 0.04 =
6. 67.89 ÷ 0.01 =
7. 0.005 ÷ 0.001 =
8. 3.456 ÷ 0.008 =
9. 12.3456 ÷ 0.0012 =
10. 98.76543 ÷ 0.0003 =

Answers to Worksheet 3:

1. 2469
2. 395.06
3. 380.65
4. 2921.8
5. 19728
6. 6789
7. 5
8. 432
9. 10288
10. 329218.1

Dealing with Remainders and Rounding in Decimal Division

Sometimes, decimal division results in a remainder that doesn't equal zero. In such cases, you have several options:

• Express the remainder as a fraction: Write the remainder over the divisor to express the answer as a mixed number. For instance, if you have a remainder of 1 and a divisor of 5, you would write the answer as 10 + 1/5.

• Round to a specific decimal place: Round the quotient to the nearest tenth, hundredth, thousandth, or another place value as needed. Look at the digit in the place value after the place you are rounding to. If it is 5 or greater, round up; if it's less than 5, keep the digit the same.

• Continue dividing until you reach a repeating decimal: Some divisions result in repeating decimals, where a sequence of digits repeats infinitely. In this case, you can indicate the repeating part with a bar above it (e.g., 0.333... is written as 0.3̅).

Frequently Asked Questions (FAQ)

Q: What if I get a remainder?

A: As explained above, you can express the remainder as a fraction, round the answer to a specific decimal place, or continue dividing to find a repeating decimal. The best approach depends on the context of the problem.

Q: How can I check my work?

A: Multiply your quotient by the divisor. The result should equal the dividend (or be very close if you rounded).

Q: What if the divisor is a decimal?

A: Move the decimal point in both the divisor and the dividend to the right until the divisor becomes a whole number.

Q: Are there any online tools or calculators to help?

A: While practicing long division by hand is crucial for understanding the process, online calculators can be helpful for checking your work or solving very complex problems. However, reliance on these tools alone should be limited as the primary method of solving the problems.

Conclusion: Mastering Decimal Division for Future Success

Decimal division is a fundamental skill with broad applications in various fields, from everyday calculations to advanced mathematics and scientific computations. Consistent practice is key to mastering this skill. Through repeated use of the worksheets and understanding the steps explained, you will build proficiency and confidence. Remember to practice regularly, and don't hesitate to review the steps and concepts as needed. With dedication and practice, you can successfully conquer decimal division and improve your mathematical abilities. The effort you invest will pay dividends in future mathematical endeavors.