Decimals Divide By Decimals Worksheet

Mastering Decimal Division: A Comprehensive Guide with Worksheets

Dividing decimals can seem daunting, but with a structured approach and practice, it becomes manageable and even enjoyable! This comprehensive guide breaks down decimal division into digestible steps, providing clear explanations, examples, and worksheets to solidify your understanding. We'll cover various methods, tackling everything from simple divisions to more complex scenarios, equipping you with the skills to confidently solve any decimal division problem. Whether you're a student reinforcing your classroom learning or an adult learner brushing up on your math skills, this guide is your ultimate resource for mastering decimal division.

Understanding the Basics of Decimal Division

Before diving into complex problems, let's lay a solid foundation. Remember, decimals are simply fractions written in a different format. For instance, 0.5 is the same as ½. Understanding this equivalence is key to grasping decimal division. The core principle remains the same as with whole numbers: we're figuring out how many times one number (the divisor) goes into another (the dividend). The presence of decimals adds a slight twist, but the underlying logic remains consistent.

Key Terminology:

• Dividend: The number being divided (the larger number).
• Divisor: The number you are dividing by (the smaller number).
• Quotient: The result of the division.

Method 1: Converting Decimals to Fractions

One effective approach to decimal division involves converting decimals into fractions. This method simplifies the process, especially when dealing with complex decimal divisors.

Steps:

1. Convert decimals to fractions: Express both the dividend and the divisor as fractions. Remember, the decimal point represents the denominator as a power of 10 (e.g., 0.25 = 25/100, 0.5 = 5/10).

2. Simplify the fractions: Reduce the fractions to their simplest form by finding the greatest common divisor (GCD) of the numerator and denominator.

3. Invert and multiply: Rewrite the division as a multiplication problem by inverting (flipping) the divisor fraction and multiplying it with the dividend fraction.

4. Multiply numerators and denominators: Multiply the numerators together and the denominators together.

5. Simplify and convert back to decimal: Simplify the resulting fraction and convert it back to a decimal if required.

Example:

Divide 0.75 by 0.25.

1. Conversion: 0.75 = 75/100; 0.25 = 25/100

2. Simplification: 75/100 = 3/4; 25/100 = 1/4

3. Invert and multiply: (3/4) ÷ (1/4) = (3/4) x (4/1)

4. Multiplication: (3 x 4) / (4 x 1) = 12/4

5. Simplification and conversion: 12/4 = 3

Therefore, 0.75 divided by 0.25 equals 3.

Method 2: Using Long Division with Decimal Adjustment

This method directly addresses decimal division using long division, but with a crucial adjustment step. The key is to make the divisor a whole number.

Steps:

1. Adjust the divisor: Multiply both the dividend and the divisor by a power of 10 to make the divisor a whole number. The power of 10 depends on the number of decimal places in the divisor. For instance, if the divisor has two decimal places, multiply both by 100.

2. Perform long division: Carry out the long division process as you would with whole numbers.

3. Place the decimal point: Position the decimal point in the quotient directly above the decimal point in the dividend (after adjustment in step 1).

Example:

Divide 12.6 by 0.3.

1. Adjustment: Multiply both by 10: 126 ÷ 3

2. Long division:

   42
   ---
   3|126
    -12
     --
       6
       -6
       --
        0
   

3. Decimal placement: The quotient is 42.

Therefore, 12.6 divided by 0.3 equals 42.

Method 3: Using a Calculator

Calculators provide a quick and efficient way to perform decimal division. Simply input the dividend, the division operator (÷), and the divisor, and press the equals button. However, it's crucial to understand the underlying methods to accurately interpret the results and troubleshoot potential errors. Using a calculator should supplement, not replace, a thorough understanding of the underlying mathematical principles.

Decimal Division Worksheets: Practice Makes Perfect

Now let's put your newfound knowledge into practice! The following worksheets provide a range of exercises to solidify your understanding of decimal division. Remember to show your work, explaining each step, to ensure you understand the process thoroughly.

Worksheet 1: Basic Decimal Division

Instructions: Solve the following decimal division problems.

1. 1.5 ÷ 0.5 = ?
2. 2.4 ÷ 0.6 = ?
3. 3.6 ÷ 0.9 = ?
4. 0.8 ÷ 0.2 = ?
5. 4.5 ÷ 0.5 = ?
6. 6.3 ÷ 0.7 = ?
7. 10.8 ÷ 1.2 = ?
8. 25.5 ÷ 5.1 = ?
9. 0.72 ÷ 0.09 = ?
10. 1.44 ÷ 0.12 = ?

Worksheet 2: More Challenging Decimal Division Problems

Instructions: Solve the following problems using long division. Show all your working.

1. 15.75 ÷ 2.5 = ?
2. 27.36 ÷ 0.36 = ?
3. 128.7 ÷ 1.1 = ?
4. 3.456 ÷ 0.12 = ?
5. 87.5 ÷ 0.025 = ?
6. 0.0048 ÷ 0.0012 = ?
7. 21.87 ÷ 0.009 = ?
8. 100.005 ÷ 2.5 = ?
9. 0.000675 ÷ 0.000015 = ?
10. 3456.78 ÷ 10.12 = ?

Worksheet 3: Word Problems involving Decimal Division

Instructions: Translate the following word problems into mathematical equations and solve them.

1. A carpenter has a piece of wood measuring 12.5 meters long. If he wants to cut it into pieces that are 2.5 meters each, how many pieces will he have?

2. A marathon runner completes a 42.195 km race in 3.5 hours. What is the runner's average speed in km/hour?

3. A bag of flour weighs 2.25 kg. If you use 0.25 kg of flour for each batch of cookies, how many batches can you make?

4. You bought 7.5 kg of apples for $15. What is the cost per kilogram of apples?

5. A car travels 315.75 miles on 12.6 gallons of gas. What is the car's gas mileage in miles per gallon?

Frequently Asked Questions (FAQs)

Q: What happens if the divisor is larger than the dividend?

A: The result will be a decimal number less than 1. For example, 0.5 ÷ 2 = 0.25.

Q: How do I handle trailing zeros in the decimal?

A: Trailing zeros after the last non-zero digit do not change the value of the decimal. For instance, 1.200 is the same as 1.2.

Q: What if I get a repeating decimal in my answer?

A: Repeating decimals are perfectly valid results. You can express them using a bar notation (e.g., 0.333... = 0.3̅) or round them to a specific number of decimal places based on the context of the problem.

Q: Is there a way to check my answers?

A: Yes! You can check your answer by multiplying your quotient by the divisor. The result should equal the dividend. For example, if you found that 12.5 ÷ 2.5 = 5, check it by multiplying 5 x 2.5, which equals 12.5.

Conclusion: Mastering Decimal Division

Decimal division might seem challenging at first, but with consistent practice and a solid grasp of the underlying principles, it becomes a straightforward process. This guide has explored various methods—converting to fractions, long division, and calculator usage—offering flexibility in your approach. Remember, the key to success lies in consistent practice. Work through the provided worksheets, and don't hesitate to revisit the explanations and examples if you encounter difficulties. By mastering decimal division, you build a crucial foundation for more advanced mathematical concepts. Keep practicing, and you'll confidently tackle any decimal division problem that comes your way!