Multiplication and Division

Long Division

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#### Lesson 5: Long Division

### Long division

### Solving long-division problems

#### Try this!

### Problems with remainders

#### Try this!

### Decimal quotients

#### Try this!

### Checking your work

#### Long division with decimals

### Practice!

#### Set 1

#### Set 2: Type your answer using remainders.

#### Set 3: Type your answer using decimals.

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When you divide a number, you are splitting it **equally**. In Introduction to Division, you learned that division can be a way to understand real-life situations. For example, imagine a car dealership has **15** cars. The manager wants the cars parked in **three** equal rows.

You could write the situation like this and use a times table to solve it:

After the cars are divided, counting them shows that each row should have **five** cars. Now, let's say the car dealership has 42 cars and the manager wants to park them in three rows. The situation would look like this:

This problem is harder to solve. It would take a lot of time to divide that many cars into three groups. Plus, there's no 42 in the 3's column on the times table. Fortunately, there is a way to set up the problem that makes it easy to solve one step at a time. It's called **long division**.

Let's learn how to set up these problems. We'll look at the problem we discussed above: 42 / 3.

To solve long division problems, you'll use three math skills you've already learned: division, multiplication, and subtraction. It's a good idea to make sure you feel comfortable with all three skills. If you think you might need more practice, take some time to review those lessons first.

When solving a long division problem, the number under the division bracket is split into smaller numbers. This makes division easier. Plus, you can use a familiar tool, like a times table, to help.

Let's see how solving a long division problem works.

Solve these long division problems. Then, check your answer by typing it in the box.

63 ÷ 3 =

48 ÷ 4 =

214 ÷ 2 =

In Introduction to Division, you learned that some numbers can't be equally divided. When that happens, there will be an amount left over. This is called a **remainder**. For instance, let's say you want to share 8 treats equally among your 3 dogs. The answer is that each dog would get two treats with a remainder of two.

The remainder is written as part of the quotient: 8 / 3 = 2 r2.

Long division problems can have remainders too. Watch the slideshow to see how.

Solve these division problems with remainders. Then, check your answer by typing it into the boxes.

62 ÷ 5 =

r

27 ÷ 2 =

r

71 ÷ 6 =

r

On the last page, you learned how to find the **remainder** for a long division problem that can't be solved evenly. Remainders can be useful if you need to know how much is **left over** when you divide something, but they might not be very useful in every situation. For example, what if you wanted to divide a 9-**foot-long **board into 4 **equal pieces**? That problem could look like this:

9 / 4 = 2 r1

In other words, when you divide a board that's **nine feet long** into **four pieces**, each piece will be **two feet long**. There will be one **foot left** over.

What if you don't want to waste any wood? In that case, you can continue to divide until there is no longer a remainder. That way, you'd have four equal pieces of wood, with none left over. That problem would look like this:

9 / 4 = 2.25

The answer, 2.25, is a **decimal number. **You can tell, because it includes a symbol called a **decimal point (.)**. The number to the **left** of the decimal point, 2, is the whole number. The rest of the answer, .25, shows the **part** of the number that didn't divide evenly.

Click through the slideshow below to learn how to find the decimal answer to a division problem.

Sometimes, you may notice that a decimal can start to repeat as you continue to add zeros under the division bracket. This is known as a **repeating** decimal. When this happens, you can place a horizontal line over the digit that repeats.

Look at the image below. A horizontal line has been placed over the repeating digit.

Another way to handle a repeating decimal is to **round** it. **Rounding** creates a new number that has a value close to the original number.

When rounding a repeating decimal, you'll reduce the number of digits that come after the decimal point. First, decide which digit you are rounding to. Then look at the digit to the right of it. If the digit is 5 or more, increase the rounded digit by 1. If it is 4 or less, the rounded digit stays the same. The other digits after the rounded digit are not written.

Look at the image below. In this case, each of these repeating decimals has been rounded to the second digit after the decimal point.

Find the decimal quotient for each of the long division problems below.

49 ÷ 4 =

91 ÷ 8 =

533 ÷ 5 =

**Checking your work** after you divide is a good habit to develop. Checking helps you know that your answer is correct. To check the answer to a division problem, you'll need to use multiplication.

In the slideshow, we used multiplication to check our division. The answer to the multiplication problem should always be the same as the larger number in the division problem. If your two answers don't match, check to see if you added the remainder. If your answers are still different, you might have made a mistake the first time you were dividing. Try solving the problem again.

In this lesson, you also learned how to solve division problems that have a **decimal** in the answer. Checking your work for this type of problem is similar to checking other division problems. You'll follow the same steps.

We'll try checking this problem: 57 / 5 = 11.4.

Practice division by solving these problems. There are **3** sets of problems. Each set has **5 **problems.

104 ÷ 8 =

99 ÷ 3 =

205 ÷ 5 =

618 ÷ 6 =

143 ÷ 11 =

37 ÷ 3 =

r

71 ÷ 7 =

r

19 ÷ 8 =

r

29 ÷ 2 =

r

92 ÷ 6 =

r

525 ÷ 4 =

62 ÷ 5 =

137 ÷ 2 =

217 ÷ 4 =

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