How To Divide Decimals

What Is Decimal Division?

Decimal division is the process of dividing a number that contains a decimal point by another number. This process helps us split quantities into smaller, equal groups, even when those quantities are not whole numbers. For example, if you have $1.5$ liters of juice and want to share it equally among $3$ friends, you would use decimal division to find out that each friend gets $0.5$ liters. It's a fundamental skill used in many real-world situations, from calculating costs per item to measuring ingredients for a recipe.

Understanding how to divide decimals is built upon the foundation of long division. The key difference lies in how we handle the decimal point. Once you learn the simple rule for placing the decimal point in your answer, the rest of the process—dividing, multiplying, subtracting, and bringing down—is exactly the same as the long division you already know. The goal is to make the problem look familiar so you can solve it with confidence.

What Are the Key Parts of a Division Problem?

Before we dive into the steps, let's quickly review the vocabulary for any division problem. Knowing these terms will make the instructions much clearer. Every division equation has three main parts:

• Dividend: This is the number that is being divided. It's the total amount you are starting with.
• Divisor: This is the number you are dividing by. It's the number of equal groups you are making.
• Quotient: This is the answer to the division problem.

Think of it like this: Dividend $÷$ Divisor $=$ Quotient. Let's look at an example with the problem $18.6÷3=6.2$.

When you set up a long division problem, the dividend goes inside the division bracket (or "house"), the divisor goes outside to the left, and the quotient is written on top.

How Do You Divide a Decimal by a Whole Number?

This is the simplest type of decimal division because it requires the least amount of setup. When your divisor (the number you're dividing by) is a whole number, you can solve the problem in two easy steps.

1. Bring Up the Decimal Point: First, set up the long division problem. Locate the decimal point in the dividend (the number inside the bracket). Place a decimal point for your quotient directly above it on the answer line. This is the most important step!
2. Divide as Usual: Ignore the decimal point for the rest of the process and perform long division just as you would with whole numbers. Divide, multiply, subtract, and bring down the next digit until you have completed the problem.

How Do You Divide a Decimal by Another Decimal?

This is where the most important rule of decimal division comes into play. It's very difficult to divide by a number with a decimal point. To make it easy, we must first convert the divisor into a whole number.

Why does this work? When you move the decimal point one place to the right, you are really multiplying by $10$. As long as you multiply both the divisor and the dividend by the same number ($10$, $100$, etc.), the overall quotient remains the same. It's like simplifying a fraction!

Here are the steps:

1. Make the Divisor Whole: Count how many places you need to move the decimal point in the divisor to make it a whole number.
2. Move the Dividend's Decimal: Move the decimal point in the dividend the same number of places to the right. You might need to add zeros as placeholders.
3. Bring Up the New Decimal Point: Place the decimal point in your quotient directly above its new position in the dividend.
4. Divide: Perform long division as you normally would.

How Do You Divide a Whole Number by a Decimal?

This type of problem might look different, but it uses the exact same rule as dividing a decimal by a decimal. Your first goal is always to make the divisor a whole number. The only new trick is remembering that every whole number has an invisible decimal point at its end.

For example, the number $63$ is the same as $63.0$ or $63.00$. You can add a decimal point and as many zeros as you need after a whole number without changing its value. This is the key to solving these problems.

1. Make the Divisor Whole: Move the decimal in the divisor to the right to make it a whole number.
2. Add a Decimal and Zeros to the Dividend: Place a decimal point at the end of the whole number dividend. Move it to the right the same number of places as you did for the divisor, adding zeros as placeholders for each move.
3. Place the Decimal and Divide: Place the decimal in your quotient and divide as usual.

What If I Run Out of Numbers to Bring Down?

Sometimes, after you've brought down the last digit of the dividend, you still have a remainder that isn't zero. In whole number division, you might have written this as "R 8" for "remainder 8." With decimals, we can get a more precise answer by annexing zeros.

Annexing a zero means adding a zero to the end of the dividend after the decimal point. You can add as many zeros as you need without changing the dividend's value. For example, $12.5$ is the same as $12.50$, $12.500$, and so on.

Here's the process:

1. If you have a non-zero remainder after dividing, add a zero to the right of the last digit in the dividend.
2. Bring that zero down next to your remainder to create a new number.
3. Continue the division process.
4. Repeat by adding more zeros until your remainder is $0$ or you have reached the desired number of decimal places for your answer.

For instance, if we were solving $5÷4$, we would set it up as $5.00÷4$. After $4$ goes into $5$ once with a remainder of $1$, we would bring down the first zero to make $10$. Then $4$ goes into $10$ twice with a remainder of $2$. We bring down the next zero to make $20$, and $4$ goes into $20$ five times with no remainder. The final answer is $1.25$.

Sometimes, a decimal will repeat forever (like $1÷3=0.333...$). In these cases, your teacher will usually tell you which decimal place to round your answer to.

What Are Common Mistakes When Dividing Decimals?

Decimal division is straightforward once you get the hang of it, but a few common errors can trip students up. Being aware of these pitfalls is the best way to avoid them.

• Forgetting to Move the Dividend's Decimal: This is the most frequent mistake. Students remember to change the divisor to a whole number but forget to move the decimal in the dividend as well. Remember: Whatever you do to the divisor, you must do to the dividend.
• Misplacing the Decimal in the Quotient: The decimal point in your answer isn't just an afterthought. It must be placed correctly before you start dividing. After adjusting the dividend and divisor, bring the decimal point straight up into the quotient's position.
• Moving the Decimal the Wrong Way or Amount: Always move the decimal to the right to make the divisor a whole number. And be sure to count the number of places carefully. Moving it one place when you needed to move it two will give you a wrong answer.
• Simple Arithmetic Errors: Long division has many steps, and it's easy to make a small mistake in multiplication or subtraction. Always double-check your work, especially when you're multiplying the quotient digit by the divisor.
• Forgetting Placeholders: If you are dividing $5.15÷5$, the answer is $1.03$, not $1.3$. When you bring down the $1$ and $5$ can't go into it, you must put a $0$ in the quotient as a placeholder before bringing down the next digit.

Quick Summary: Your Decimal Division Checklist

Feeling confident? Here is a quick checklist to guide you through any decimal division problem. Follow these steps in order, and you'll always be on the right track.

1. Look at the Divisor: Is the number you are dividing by (the one outside the bracket) a whole number or a decimal?
2. If the Divisor is a Decimal: Move its decimal point all the way to the right to make it a whole number. Count how many places you moved it.
3. Adjust the Dividend: Move the decimal point in the dividend (the number inside the bracket) the exact same number of places to the right. Add zeros at the end if you need to.
4. Place the New Decimal Point: Immediately bring the decimal point straight up from its new position in the dividend to the answer line (the quotient).
5. Divide: Perform long division just like you would with whole numbers. Pay no more attention to the decimal points.
6. Annex Zeros if Necessary: If you have a remainder after using all the digits, add a zero to the end of the dividend, bring it down, and keep dividing.
7. Check Your Answer: Use multiplication (Quotient $\times$ Original Divisor $=$ Original Dividend) or a calculator to make sure your answer is correct.