additional practice 6-5 divide by a decimal answer key

Lemon

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04-02-2025

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Dividing by decimals can seem tricky, but with a clear understanding of the process and some practice, it becomes much easier. This guide provides an answer key for Additional Practice 6-5 (assuming this refers to a specific worksheet or textbook exercise) and a comprehensive explanation to help you master this skill. Since I don't have access to the specific problems in your "Additional Practice 6-5" worksheet, I will provide a general approach and examples to cover various scenarios you might encounter.

Understanding Decimal Division

The key to dividing by a decimal is to eliminate the decimal point in the divisor (the number you're dividing by). We achieve this by multiplying both the divisor and the dividend (the number being divided) by a power of 10.

Steps:

1. Identify the divisor: Determine the decimal number you are dividing by.
2. Move the decimal point: Count how many places you need to move the decimal point in the divisor to make it a whole number.
3. Shift the decimal in the dividend: Move the decimal point in the dividend the same number of places to the right. Add zeros if necessary.
4. Perform long division: Now, perform the division as you would with whole numbers.
5. Place the decimal point: In the quotient (the answer), place the decimal point directly above where it now sits in the dividend.

Example Problems & Solutions

Let's work through a few examples to illustrate the process:

Example 1: 12.6 ÷ 0.3

1. Divisor: 0.3
2. Move the decimal: Move the decimal point one place to the right in 0.3 to make it 3.
3. Shift the dividend's decimal: Move the decimal point in 12.6 one place to the right, making it 126.
4. Long division: 126 ÷ 3 = 42
5. Place the decimal: The decimal point in the quotient is directly above where it now sits in the dividend (which is at the end of 126), so the answer is 42.

Example 2: 2.55 ÷ 0.05

1. Divisor: 0.05
2. Move the decimal: Move the decimal point two places to the right in 0.05 to make it 5.
3. Shift the dividend's decimal: Move the decimal point in 2.55 two places to the right, making it 255.
4. Long division: 255 ÷ 5 = 51
5. Place the decimal: The answer is 51.

Example 3: 0.072 ÷ 0.009

1. Divisor: 0.009
2. Move the decimal: Move the decimal point three places to the right in 0.009 to get 9.
3. Shift the dividend's decimal: Move the decimal point in 0.072 three places to the right to make it 72.
4. Long division: 72 ÷ 9 = 8
5. Place the decimal: The answer is 8.

Addressing Potential Challenges

• Remainders: If you have a remainder, you can add zeros to the dividend and continue dividing until you reach a desired level of accuracy or a repeating decimal pattern.
• Zeroes as placeholders: Remember to add zeros as placeholders when moving the decimal point in the dividend, ensuring that the number of decimal places is consistent.

Tips for Success

• Practice regularly: Consistent practice is key to mastering decimal division. Work through various problems, starting with simpler ones and gradually progressing to more complex ones.
• Check your work: Always double-check your calculations to ensure accuracy. You can verify your answer by multiplying the quotient by the original divisor to see if you get the original dividend.
• Seek help when needed: Don't hesitate to seek assistance from a teacher, tutor, or online resources if you encounter difficulties.

By following these steps and practicing regularly, you can confidently tackle decimal division problems in "Additional Practice 6-5" and beyond. Remember, the key is understanding the process of eliminating the decimal in the divisor and applying the rules of long division.