Divide Decimals: Step-by-Step Solutions & Practice

Hey guys! Let's dive into the world of decimal division! We're going to break down some division problems step-by-step, using the traditional algorithm, and then double-check our answers with multiplication. Plus, we'll tackle a real-world problem to see how this stuff is actually used. So, grab your pencils, and let's get started!

1. Diving into Decimal Division

Understanding Decimal Division

Before we jump into the calculations, let's quickly recap what decimal division is all about. Decimal division is simply dividing a number that has a decimal point (a decimal) by another number. This could be dividing a decimal by a whole number, a whole number by a decimal, or even a decimal by another decimal. The basic principles of division remain the same, but we need to pay close attention to the placement of the decimal point in our final answer. Mastering decimal division is a crucial skill, not only in mathematics but also in everyday life scenarios like calculating costs, splitting bills, or measuring ingredients.

The traditional algorithm, which we'll be using, provides a structured approach to division, making it easier to manage the process, especially when dealing with decimals. This method involves setting up the division problem in a specific format and then following a series of steps, including dividing, multiplying, subtracting, and bringing down the next digit. By understanding the underlying principles of place value and how decimals work, we can confidently tackle any division problem that comes our way. So, let’s get our hands dirty with some examples and see how the traditional algorithm works in practice. Remember, practice makes perfect, and the more you work with decimal division, the more comfortable and proficient you'll become.

Problem 1: 48.6 ÷ 6

Okay, let's start with our first problem: 48.6 ÷ 6. We're going to use the traditional algorithm to solve this. Remember the traditional algorithm? It's that long division setup we all know and love (or maybe tolerate!).

Step 1: Set up the division.

Write the problem in the long division format. 6 goes on the outside (the divisor), and 48.6 goes on the inside (the dividend).

Step 2: Divide the whole number part.

How many times does 6 go into 48? It goes in 8 times (8 x 6 = 48). Write the 8 above the 8 in 48.

Step 3: Multiply and subtract.

Multiply 8 by 6, which is 48. Write 48 below the 48 in the dividend and subtract. 48 - 48 = 0.

Step 4: Bring down the decimal.

Bring down the 6 from 48.6. Now we have 6.

Step 5: Divide the decimal part.

How many times does 6 go into 6? It goes in 1 time (1 x 6 = 6). Write the 1 after the decimal point in the quotient (the answer). So, it will be 8.1

Step 6: Multiply and subtract again.

Multiply 1 by 6, which is 6. Write 6 below the 6 we brought down and subtract. 6 - 6 = 0.

Our answer is 8.1

Verification:

Now, let's verify our answer with multiplication. To do this, we'll multiply our quotient (8.1) by our divisor (6).

8. 1 x 6 = 48.6

Yep, it checks out! 8.1 x 6 = 48.6

Problem 2: 96.3 ÷ 3

Let's move on to our second problem: 96.3 ÷ 3. We'll follow the same steps using the traditional algorithm.

Step 1: Set up the division.

3 goes on the outside, and 96.3 goes on the inside.

Step 2: Divide the whole number part.

• How many times does 3 go into 9? It goes in 3 times (3 x 3 = 9). Write the 3 above the 9.
• How many times does 3 go into 6? It goes in 2 times (2 x 3 = 6). Write the 2 above the 6.

Step 3: Multiply and subtract.

• Multiply 3 by 3, which is 9. Write 9 below the 9 in the dividend and subtract. 9 - 9 = 0.
• Multiply 2 by 3, which is 6. Write 6 below the 6 in the dividend and subtract. 6 - 6 = 0.

Step 4: Bring down the decimal.

Bring down the 3 from 96.3. Now we have 3.

Step 5: Divide the decimal part.

How many times does 3 go into 3? It goes in 1 time (1 x 3 = 3). Write the 1 after the decimal point in the quotient. So, it will be 32.1.

Step 6: Multiply and subtract again.

Multiply 1 by 3, which is 3. Write 3 below the 3 we brought down and subtract. 3 - 3 = 0.

Our answer is 32.1

Verification:

Let's verify by multiplying 32.1 by 3.

32. 1 x 3 = 96.3

Perfect! 32.1 x 3 = 96.3

Problem 3: 84.4 ÷ 4

Alright, let's tackle the third problem: 84.4 ÷ 4. We're getting the hang of this!

Step 1: Set up the division.

4 goes on the outside, and 84.4 goes on the inside.

Step 2: Divide the whole number part.

• How many times does 4 go into 8? It goes in 2 times (2 x 4 = 8). Write the 2 above the 8.
• How many times does 4 go into 4? It goes in 1 time (1 x 4 = 4). Write the 1 above the 4.

Step 3: Multiply and subtract.

• Multiply 2 by 4, which is 8. Write 8 below the 8 in the dividend and subtract. 8 - 8 = 0.
• Multiply 1 by 4, which is 4. Write 4 below the 4 in the dividend and subtract. 4 - 4 = 0.

Step 4: Bring down the decimal.

Bring down the 4 from 84.4. Now we have 4.

Step 5: Divide the decimal part.

How many times does 4 go into 4? It goes in 1 time (1 x 4 = 4). Write the 1 after the decimal point in the quotient. So, it will be 21.1.

Step 6: Multiply and subtract again.

Multiply 1 by 4, which is 4. Write 4 below the 4 we brought down and subtract. 4 - 4 = 0.

Our answer is 21.1

Verification:

Let's verify by multiplying 21.1 by 4.

21. 1 x 4 = 84.4

Awesome! 21.1 x 4 = 84.4

Problem 4: 76.8 ÷ 16

Now let's try a slightly trickier one: 76.8 ÷ 16. Don't worry, we've got this!

Step 1: Set up the division.

16 goes on the outside, and 76.8 goes on the inside.

Step 2: Divide the whole number part.

How many times does 16 go into 76? It goes in 4 times (4 x 16 = 64). Write the 4 above the 6 in 76.

Step 3: Multiply and subtract.

Multiply 4 by 16, which is 64. Write 64 below the 76 in the dividend and subtract. 76 - 64 = 12.

Step 4: Bring down the decimal.

Bring down the 8 from 76.8. Now we have 128.

Step 5: Divide the decimal part.

How many times does 16 go into 128? It goes in 8 times (8 x 16 = 128). Write the 8 after the decimal point in the quotient. So, it will be 4.8.

Step 6: Multiply and subtract again.

Multiply 8 by 16, which is 128. Write 128 below the 128 we brought down and subtract. 128 - 128 = 0.

Our answer is 4.8

Verification:

Let's verify by multiplying 4.8 by 16.

4. 8 x 16 = 76.8

You got it! 4.8 x 16 = 76.8

Problem 5: 72.6 ÷ 11

Last one in this section! Let's solve 72.6 ÷ 11.

Step 1: Set up the division.

11 goes on the outside, and 72.6 goes on the inside.

Step 2: Divide the whole number part.

How many times does 11 go into 72? It goes in 6 times (6 x 11 = 66). Write the 6 above the 2 in 72.

Step 3: Multiply and subtract.

Multiply 6 by 11, which is 66. Write 66 below the 72 in the dividend and subtract. 72 - 66 = 6.

Step 4: Bring down the decimal.

Bring down the 6 from 72.6. Now we have 66.

Step 5: Divide the decimal part.

How many times does 11 go into 66? It goes in 6 times (6 x 11 = 66). Write the 6 after the decimal point in the quotient. So, it will be 6.6.

Step 6: Multiply and subtract again.

Multiply 6 by 11, which is 66. Write 66 below the 66 we brought down and subtract. 66 - 66 = 0.

Our answer is 6.6

Verification:

Let's verify by multiplying 6.6 by 11.

6. 6 x 11 = 72.6

Nailed it! 6.6 x 11 = 72.6

2. Real-World Decimal Division Problem

Now that we've mastered the calculations, let's see how decimal division helps us in real life. Here's a word problem:

Problem:

A factory produces 98.4 liters of juice. If it is packaged into 12 bottles, how many liters of juice are in each bottle?

Solving the Word Problem

Step 1: Identify the operation.

We need to divide the total amount of juice (98.4 liters) by the number of bottles (12) to find out how much juice goes into each bottle. So, this is a division problem: 98.4 ÷ 12.

Step 2: Set up the division.

Write the problem in the long division format: 12 goes on the outside, and 98.4 goes on the inside.

Step 3: Divide the whole number part.

• How many times does 12 go into 98? It goes in 8 times (8 x 12 = 96). Write the 8 above the 8 in 98.

Step 4: Multiply and subtract.

Multiply 8 by 12, which is 96. Write 96 below the 98 in the dividend and subtract. 98 - 96 = 2.

Step 5: Bring down the decimal.

Bring down the 4 from 98.4. Now we have 24.

Step 6: Divide the decimal part.

How many times does 12 go into 24? It goes in 2 times (2 x 12 = 24). Write the 2 after the decimal point in the quotient. So, it will be 8.2.

Step 7: Multiply and subtract again.

Multiply 2 by 12, which is 24. Write 24 below the 24 we brought down and subtract. 24 - 24 = 0.

Answer:

Each bottle contains 8.2 liters of juice.

Verification:

Let's verify by multiplying 8.2 by 12.

8. 2 x 12 = 98.4

It's correct! 8.2 liters per bottle is the right answer.

Conclusion: Decimal Division Mastered!

Awesome work, everyone! We've tackled decimal division using the traditional algorithm, verified our answers with multiplication, and even solved a real-world problem. You guys are now decimal division superstars!

Remember, the key to mastering any math skill is practice. So, keep practicing, and you'll become even more confident in your abilities. If you have any questions, feel free to ask. Happy dividing!