# Decimals – Addition, Subtraction, Division and Multiplication

## Decimals – Addition, Subtraction, Division and Multiplication Revision

**Decimals**

A **decimal** is any number with a decimal point. They are the numbers that fall between the integers.

Make sure you are happy with the following topics before continuing.

**Skill 1: Adding Decimals**

To add decimals, you should be familiar with the **column method** for addition. This method works exactly the same way for decimals, all you have to do is make sure you line up the decimal points when you write your numbers above one another.

**Example:** Evaluate 6.436 + 8.992.

So, 6.436 + 8.992 = 15.428

**Note:** Click here for Addition and Subtraction Worksheets and Revision.

**Skill 2: Subtracting Decimals**

Subtracting decimals is easy if you know how to add. Make sure you are confident with the **column method** for subtraction.

**Example:** Evaluate 567.63 - 92.478.

So, 567.63 - 92.478 = 475.152

**Skill 3: Multiplying Decimals**

The easiest way to multiply decimals is to use the following steps:

**Step 1:** Move the decimal place on each value to turn it into a whole number.

**Step 2:** Remember/write down how many decimal places you have moved in total.

**Step 3:** Complete the column or grid method for multiplication

**Step 4:** Move the decimal place back the same amount at the end to get your final answer.

**Example:** Evaluate 7.68 \times 2.5.

Use the column method as shown below (or the grid method). The decimal place is moved once on 2.5 to make it 25 and twice on 7.68 to make it 768. So in total the decimal place has moved 3 times.

We now need to move the decimal place back the same number of times, so we move it 3 times to the left to get

7.68 \times 2.5 = 19.200 = 19.2

**Skill 4: Dividing Decimals**

The easiest way to divide decimals is to use the following steps:

**Step 1: **Move the decimal place of the number you are dividing by to turn it into a whole number.

**Step 2:** Remember/write down how many decimal places you have moved in total.

**Step 3:** Complete the long division method.

**Step 4:** Move the decimal place back the same amount at the end to get your final answer.

**Example:** Evaluate 8.138 \div 1.3.

Using the long division method as shown, we move the decimal place of the number we are dividing by to make it a whole number. So we move the decimal place once on 1.3 to make it 13.

We now need to move the decimal place back the same number of times, so we move it 1 time to the left to get

8.138 \div 1.3 = \textcolor{purple}{6.26}

**Example 1: Adding Decimals**

Evaluate 985.4+81.767.

**[2 marks]**

Use the column method as shown below

So, 985.4+81.767 = 1067.167

**Example 2: Subtracting Decimals**

Evaluate 62.059 - 5.118.

**[2 marks]**

So, 62.059 - 5.118 = 56.941

**Example 3: Multiplying Decimals**

Evaluate 5.7\times 6.32.

**[3 marks]**

In this example we use the column method. The decimal place is moved once on 5.7 to make 57 and twice on 6.32 to make 632. Therefore in total the decimal place has moved 3 times to the right.

Now we need to move the decimal place back the same number of times, so we move it 3 times to the left to get

5.7 \times 6.32 = 36.024

**Example 4: Dividing Decimals**

Evaluate 7.488 \div 1.2.

**[3 marks]**

Similar to multiplying decimals, when dividing decimals we want to make it easy for us by moving the decimal place so that we can use long division. We do this by moving the decimal place of the number we are dividing by. So we move the decimal place once on 1.2 to make it 12.

Remember to move the decimal place back to get the final answer. In this example we only moved it one place, so we move it back once place to get

7.488 \div 1.2 = 6.24

## Decimals – Addition, Subtraction, Division and Multiplication Example Questions

**Question 1:** Evaluate 82.07 + 31.865

(Non-Calculator)

**[2 marks]**

By means of column addition or otherwise, we can add together the values that hold the same respective place. When the sum of two values is greater or equal to 10, we have to carry the tens unit value over to the next column,

\begin{array}{r}82{.{}^1\cancel0}70\\+31.865\\\hline 35\end{array}

Therefore we find,

\begin{array}{r}82.070\\+31.865\\\hline113.935\end{array}

**Question 2:** Evaluate 18.63 \div 2.3

(Non-calculator)

**[2 marks]**

We can make the calculation easier by converting the divisor to a whole number. We can do this and still have the same calculation by multiplying both 2.3 and 18.63 by 10, so now we have,

\begin{array}{c}\;\;\;\;\;\;\;\;\;\;\;\;\;8\;.\;1\\23\overline{\left)\cancel1^1\cancel8^{18}6\;.{}^23\right.}\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\end{array}

Hence the answer is,

18.63\div 2.3 = 8.1

**Question 3:** Evaluate 3.566\times 14

(Non-calculator)

**[3 marks]**

The latter number is already whole, so we just need to make the first number whole:

3.566\times 1,000 = 3,566

Thus the column multiplication is,

\begin{array}{r}3566\\\times14\\\hline14264\\35660\end{array}

Adding the two parts,

\begin{array}{r}\begin{array}{r}14264\\+35660\\\hline49924\end{array}\end{array}

We multiplied one of our numbers by 1000, which means our result is 1000 times too big. Therefore, the final answer is,

3.566 \times 14 = 49924\div 1000 = 49.924

**Question 4:** Evaluate 0.89+0.113

(Non-calculator)

**[3 marks]**

We can add together the values in each of the columns. When the sum of two values is greater or equal to 10, we have to carry the tens unit value over to the next column,

\begin{array}{r}\begin{array}{r}0.113\\+0.890\\\hline1.003\end{array}\end{array}

**Question 5:** Evaluate 0.002\times 0.043

(Non-calculator)

**[3 marks]**

**Question 5:** Evaluate 0.002\times 0.043

(Non-calculator)

**[3 marks]**

We can make the calculation easier by converting the decimals to a whole numbers.

If we multiply 0.002 and 0.043 by 1000, we have a simple integer multiplication,

\begin{array}{r}\begin{array}{r}2\\\times43\\\hline86\end{array}\end{array}

However this value is 1000\times1000=1000000 times too big, so we have to divide the result by this,

86\div1000000=0.000086