Find The Quotient And Enter Your Answer In The Space Provided.${ 85.8 \div 6 = ? }$Answer Here: __________

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Introduction

Division is a fundamental operation in mathematics that involves sharing a certain quantity into equal parts or groups. When dealing with decimal numbers, division can be a bit more complex, but with the right approach, it can be made easier. In this article, we will explore the concept of dividing decimal numbers and provide a step-by-step guide on how to find the quotient.

Understanding Decimal Numbers

Decimal numbers are numbers that have a decimal point, which separates the whole number part from the fractional part. For example, 85.8 is a decimal number, where 85 is the whole number part and 0.8 is the fractional part.

The Division Process

When dividing decimal numbers, we need to follow the same steps as when dividing whole numbers, but with an additional step to handle the decimal point. Here's a step-by-step guide on how to divide decimal numbers:

  1. Write the problem: Write the division problem, with the dividend (the number being divided) on top of the division bar and the divisor (the number by which we are dividing) below it.
  2. Check for zeros: Check if the divisor has any zeros after the decimal point. If it does, move the decimal point in the divisor to the right until there are no more zeros after the decimal point.
  3. Move the decimal point: Move the decimal point in the dividend the same number of places to the right as you moved the decimal point in the divisor.
  4. Divide the numbers: Divide the new dividend by the new divisor, just like you would with whole numbers.
  5. Check the remainder: Check if there is a remainder after dividing the numbers. If there is, you may need to adjust the decimal point in the quotient.
  6. Write the quotient: Write the quotient, which is the result of the division.

Example Problem

Let's use the example problem 85.8 ÷ 6 to illustrate the steps.

Step 1: Write the problem

85.8÷6=?{ 85.8 \div 6 = ? }

Step 2: Check for zeros

The divisor, 6, does not have any zeros after the decimal point.

Step 3: Move the decimal point

Since the divisor does not have any zeros after the decimal point, we do not need to move the decimal point in the dividend.

Step 4: Divide the numbers

Divide 85.8 by 6.

Step 5: Check the remainder

There is no remainder after dividing the numbers.

Step 6: Write the quotient

The quotient is 14.3.

Conclusion

Dividing decimal numbers can be a bit more complex than dividing whole numbers, but with the right approach, it can be made easier. By following the steps outlined in this article, you can find the quotient of any division problem involving decimal numbers.

Tips and Tricks

  • When dividing decimal numbers, make sure to move the decimal point in the dividend the same number of places to the right as you moved the decimal point in the divisor.
  • If the divisor has any zeros after the decimal point, move the decimal point in the divisor to the right until there are no more zeros after the decimal point.
  • Check the remainder after dividing the numbers to ensure that the quotient is accurate.

Practice Problems

Try the following practice problems to test your skills:

  • 23.4 ÷ 4 = ?
  • 56.2 ÷ 8 = ?
  • 17.8 ÷ 2 = ?

Answer Key

  • 23.4 ÷ 4 = 5.85
  • 56.2 ÷ 8 = 7.025
  • 17.8 ÷ 2 = 8.9

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Q: What is the difference between dividing decimal numbers and whole numbers?

A: The main difference between dividing decimal numbers and whole numbers is that decimal numbers have a decimal point, which separates the whole number part from the fractional part. When dividing decimal numbers, we need to move the decimal point in the dividend the same number of places to the right as we moved the decimal point in the divisor.

Q: How do I handle zeros after the decimal point in the divisor?

A: If the divisor has any zeros after the decimal point, move the decimal point in the divisor to the right until there are no more zeros after the decimal point. Then, move the decimal point in the dividend the same number of places to the right as you moved the decimal point in the divisor.

Q: What if I get a remainder after dividing the numbers?

A: If you get a remainder after dividing the numbers, you may need to adjust the decimal point in the quotient. To do this, move the decimal point in the quotient to the right by the number of places equal to the remainder.

Q: Can I use a calculator to divide decimal numbers?

A: Yes, you can use a calculator to divide decimal numbers. However, make sure to enter the numbers correctly and follow the order of operations (PEMDAS) to ensure that you get the correct result.

Q: How do I round the quotient to a specific number of decimal places?

A: To round the quotient to a specific number of decimal places, look at the digit to the right of the decimal place you want to round to. If it is 5 or greater, round up. If it is less than 5, round down.

Q: What if I'm dividing a decimal number by a decimal number?

A: If you're dividing a decimal number by a decimal number, you need to follow the same steps as when dividing a decimal number by a whole number. However, you may need to move the decimal point in both the dividend and the divisor to the right to eliminate the decimal points.

Q: Can I use a formula to divide decimal numbers?

A: Yes, you can use a formula to divide decimal numbers. The formula is:

Quotient = (Dividend x 10^n) ÷ (Divisor x 10^m)

where n and m are the number of places you moved the decimal point in the dividend and divisor, respectively.

Q: What if I'm dividing a decimal number by a negative number?

A: If you're dividing a decimal number by a negative number, the result will be a negative quotient. To divide a decimal number by a negative number, simply change the sign of the divisor and proceed with the division.

Q: Can I use a calculator to divide decimal numbers with negative numbers?

A: Yes, you can use a calculator to divide decimal numbers with negative numbers. However, make sure to enter the numbers correctly and follow the order of operations (PEMDAS) to ensure that you get the correct result.

Q: What if I'm dividing a decimal number by a decimal number with a negative sign?

A: If you're dividing a decimal number by a decimal number with a negative sign, the result will be a positive quotient. To divide a decimal number by a decimal number with a negative sign, simply change the sign of the divisor and proceed with the division.

Conclusion

Dividing decimal numbers can be a bit more complex than dividing whole numbers, but with the right approach, it can be made easier. By following the steps outlined in this article and answering the frequently asked questions, you can become more confident in your ability to divide decimal numbers.