### Key Concepts

■ Divide whole numbers by whole numbers

■Divide whole numbers by whole numbers with decimal quotients

■ Divide decimals

**Introduction**

**What is a division?**

Division** **is a repeated subtraction, denoted by the symbol ‘÷.’ It can be represented as

a ÷ b

**Example 1:** Divide 11 ÷ 2.

**Solution:** The below image shows the division process of 11 ÷ 2.

**Example 2:** Use a model diagram to divide 20 ÷ 4.

**Solution:**

Given question can be divided using a model diagram to find the quotient.

Now, we have to divide 20 ÷ 4 by arranging groups of 4 dots and then count the number of groups as shown below:

∴∴

There are 5 groups, then the quotient is 5. So, 20 ÷ 4 = 5.

**1.2.1 Divide whole numbers by whole numbers**

**How to divide a whole number by a whole number?**

The whole numbers division can be performed using standard division.

The following steps shows how to divide whole numbers using standard division:

**Step 1:** Divide the first digit of the dividend. Divide the first two digits, if the dividend is 3-digit

number.

**Step 2:** The quotient must be written above the dividend.

**Step 3:** Write the product below the dividend.

**Step 4:** Subtract the product from the dividend.

**Step 5:** Write the next digit of the dividend below the difference.

**Step 6:** Repeat the steps till the digits in the dividend got complete.

**Example 3:**

A courier company delivers 863 textile boxes to the textile shops every day. Each shop receives the same number of packages to complete the order and each box has 18 packages. How many shops will receive a complete order.

**Solution: **

Use a bar diagram to represent the problem

From the above image, n represents the number of shops that received the complete order.

Estimate the numbers to divide 863 ÷ 18.

863 rounds to 900

18 rounds to 20.

So, 900 ÷ 20 = 45

The quotient of 863 ÷ 18 is near to 45, the first digit of the quotient is in tens place.

Use the long division algorithm to divide 863 ÷ 18.

∴The quotient is 47 R17.

The courier company delivers complete orders to 47 shops.

**1.2.2 ****Divide whole numbers by whole numbers with decimal quotients**

**How can you write a decimal quotient when divided by whole numbers?**

The division of whole numbers with decimal quotient can be explained with the following steps:

**Step 1:** In the first step, divide the tens place.

**Step 2:** Divide the tens and once place in the next step.

**Step 3:** Write down the remainder as a decimal.

**Step 4:** Place the decimal point and add a zero in the tens place.

Let us consider the example, find the decimal quotient by dividing the whole numbers 180 ÷ 8.

**Solution:**

Estimate to divide 180 ÷ 8, 8 can be rounds to 10.

180 ÷ 10 = 18.

Use long division method to divide 180 ÷ 8.

The quotient is 22 R4.

Now, find the decimal quotient, place the decimal point and add a zero in the dividend after the tens place.

So, the decimal quotient is 22.5.

**Example 5:** Find the decimal quotient of 44 ÷ 10.

**Solution:**

Use long division method to find the decimal quotient of 44 ÷ 10.

The quotient is 4 R4

Now, find the decimal quotient, place the decimal point and add a zero in the dividend after the tens place.

So, the decimal quotient is 4.4.

**1.2.3. ****Divide decimals**

**How to divide decimal numbers?**

The number with a whole part and the fraction part, separated by a dot are called decimal numbers.

The number on the left side of the decimal point are a whole number,, whereas the number on the right side of the decimal point is a decimal number

The following steps explain the division of decimal numbers by a whole number:

**Step 1:** First, write the given numbers in the standard division form.

**Step 2:** The whole number part of the decimal number is divided by the divisor.

**Step 3:** Place the decimal point of the quotient above the dividend.

**Step 4:** Write the tenths digit from the dividend below the dividend obtained from the first dividend.

**Step 5:** Perform the division of the dividend by the divisor.

**Step 6:** Annex the zero in the dividend till the remainder becomes zero.

**Example 6:** Divide 230.5 ÷ 5.

So, the quotient is 46.1.

**Divide a decimal number by another decimal number:**

The division of two decimal numbers is possible when both the dividend and the divisor are multiplied by the multiples of 10. The divisor becomes a whole number.

**Example 6:** Divide 4.20 ÷ 1.40.

**Solution:**

Multiplying the dividend and the divisor by 100 to convert the given decimal numbers to whole numbers.

4.20 × 100 = 420

1.40 × 100 = 140

Now, divide the whole numbers.

So, the quotient is 3.

## Exercise:

1. Henrieta prepared 60 donuts for a party.The donuts are divided equally among 14 guests, how many donuts will each guest have? Also find the leftover donuts.

2. A container has 12 boxes of Oranges.Total boxes costs $184. How much each box cost?

3. A farmer is shipping 2,384 bananas. There are 70 crates in total, each crate has equal number of bananas. Find the number of bananas in each crate.

4. Divide 86 + 4.

5. Divide 232 + 40.

6. Use the division algorithm to divide 809.40 4. 8.

7. Divide 140 + S to find the decimal quotient

8. Divide 128.8 ÷ 1.4.

9. Divide 14.7 ÷ 2.1.

10. Divide 1.296 ÷ 0.108.

### What have we learned:

• Understand how to divide whole numbers.

• Division of a whole number by another whole number.

• Understand how to find the decimal quotient

• Division of whole numbers with decimal quotient

• Understand how to divide decimal numbers.

• Division of decimal numbers by a whole number.

• Understand how to divide a decimal number by another decimal number.

• Solve problems on decimal division.

**Concept Map**:

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