Addition and Subtraction of Decimals for Primary 4

Addition and Subtraction of Decimals

Performance Objectives

By the end of the lesson, students should be able to:

1. perform addition of decimal up to 3 places.
2. perform subtraction of decimals up to 3 places
3. solve quantitative aptitude problems involving addition and subtraction of decimals

Understanding Decimals

A decimal is a way to write numbers that are not whole numbers. It uses a decimal point to separate the whole number part from the fractional part. The digits after the decimal point represent parts of a whole.

Each digit after the decimal point has a special place value:

1. The first digit after the decimal point is the tenths place. It means one part out of ten equal parts.
2. The second digit after the decimal point is the hundredths place. It means one part out of one hundred equal parts.
3. The third digit after the decimal point is the thousandths place. It means one part out of one thousand equal parts.

For example, in the number 5.347:

1. 5 is the whole number part.
2. 3 is in the tenths place.
3. 4 is in the hundredths place.
4. 7 is in the thousandths place.

Adding Decimals

Adding decimals is similar to adding whole numbers, but there is one very important rule: you must always align the decimal points.

Follow these steps to add decimals:

1. Write the numbers vertically: Place the numbers one below the other so that their decimal points are directly in line.
2. Add zeros if needed: If the numbers have a different number of decimal places, add zeros to the end of the shorter decimal numbers so they all have the same number of decimal places. This helps to keep the place values aligned.
3. Add as usual: Start adding from the rightmost column, just like with whole numbers.
4. Place the decimal point: Bring the decimal point straight down into your answer.

Worked Examples of Decimal Addition

Example 1: Add $3.25$ and $1.43$.

Step 1: Write the numbers vertically, aligning the decimal points.

$$
\begin{array}{r}
3.25 \\
+1.43 \\
\hline
\end{array}
$$

Step 2: Add from right to left.

Add the hundredths: $5 + 3 = 8$

Add the tenths: $2 + 4 = 6$

Add the ones: $3 + 1 = 4$

Step 3: Place the decimal point in the answer.

$$
\begin{array}{r}
3.25 \\
+1.43 \\
\hline
4.68
\end{array}
$$

So, $3.25 + 1.43 = 4.68$.

Example 2: Add $7.8$ and $2.15$.

Step 1: Write the numbers vertically, aligning the decimal points. Add a zero to $7.8$ to make it $7.80$ so both numbers have two decimal places.

$$
\begin{array}{r}
7.80 \\
+2.15 \\
\hline
\end{array}
$$

Step 2: Add from right to left.

Add the hundredths: $0 + 5 = 5$

Add the tenths: $8 + 1 = 9$

Add the ones: $7 + 2 = 9$

Step 3: Place the decimal point in the answer.

$$
\begin{array}{r}
7.80 \\
+2.15 \\
\hline
9.95
\end{array}
$$

So, $7.8 + 2.15 = 9.95$.

Example 3: Add $12.345$ and $6.78$.

Step 1: Write the numbers vertically, aligning the decimal points. Add a zero to $6.78$ to make it $6.780$ so both numbers have three decimal places.

$$
\begin{array}{r}
12.345 \\
+\ 6.780 \\
\hline
\end{array}
$$

Step 2: Add from right to left, carrying over when necessary.

Add the thousandths: $5 + 0 = 5$

Add the hundredths: $4 + 8 = 12$. Write down $2$ and carry over $1$ to the tenths place.

Add the tenths: $3 + 7 + 1$ (carried over) $= 11$. Write down $1$ and carry over $1$ to the ones place.

Add the ones: $2 + 6 + 1$ (carried over) $= 9$

Add the tens: $1 + 0 = 1$

Step 3: Place the decimal point in the answer.

$$
\begin{array}{r}
12.345 \\
+\ 6.780 \\
\hline
19.125
\end{array}
$$

So, $12.345 + 6.78 = 19.125$.

Subtracting Decimals

Subtracting decimals also requires aligning the decimal points. It is similar to subtracting whole numbers.

Follow these steps to subtract decimals:

1. Write the numbers vertically: Place the numbers one below the other so that their decimal points are directly in line. The larger number usually goes on top.
2. Add zeros if needed: If the numbers have a different number of decimal places, add zeros to the end of the shorter decimal numbers so they all have the same number of decimal places. This is very important for subtraction.
3. Subtract as usual: Start subtracting from the rightmost column, just like with whole numbers. You may need to borrow from the left if a digit is too small.
4. Place the decimal point: Bring the decimal point straight down into your answer.

Worked Examples of Decimal Subtraction

Example 1: Subtract $2.14$ from $5.67$.

Step 1: Write the numbers vertically, aligning the decimal points.

$$
\begin{array}{r}
5.67 \\
-2.14 \\
\hline
\end{array}
$$

Step 2: Subtract from right to left.

Subtract the hundredths: $7 – 4 = 3$

Subtract the tenths: $6 – 1 = 5$

Subtract the ones: $5 – 2 = 3$

Step 3: Place the decimal point in the answer.

$$
\begin{array}{r}
5.67 \\
-2.14 \\
\hline
3.53
\end{array}
$$

So, $5.67 – 2.14 = 3.53$.

Example 2: Subtract $3.5$ from $8.72$.

Step 1: Write the numbers vertically, aligning the decimal points. Add a zero to $3.5$ to make it $3.50$ so both numbers have two decimal places.

$$
\begin{array}{r}
8.72 \\
-3.50 \\
\hline
\end{array}
$$

Step 2: Subtract from right to left.

Subtract the hundredths: $2 – 0 = 2$

Subtract the tenths: $7 – 5 = 2$

Subtract the ones: $8 – 3 = 5$

Step 3: Place the decimal point in the answer.

$$
\begin{array}{r}
8.72 \\
-3.50 \\
\hline
5.22
\end{array}
$$

So, $8.72 – 3.5 = 5.22$.

Example 3: Subtract $4.125$ from $9.000$.

Step 1: Write the numbers vertically, aligning the decimal points. In this case, $9$ can be written as $9.000$ to match the three decimal places of $4.125$.

$$
\begin{array}{r}
9.000 \\
-4.125 \\
\hline
\end{array}
$$

Step 2: Subtract from right to left, borrowing when necessary.

Subtract the thousandths: You cannot subtract $5$ from $0$. Borrow from the hundredths. The hundredths place is $0$, so borrow from the tenths. The tenths place is $0$, so borrow from the ones. Borrow $1$ from $9$ (ones), making it $8$. The tenths become $10$, then borrow $1$ from tenths, making it $9$. The hundredths become $10$, then borrow $1$ from hundredths, making it $9$. The thousandths become $10$.

$10 – 5 = 5$ (thousandths)

$9 – 2 = 7$ (hundredths)

$9 – 1 = 8$ (tenths)

$8 – 4 = 4$ (ones)

Step 3: Place the decimal point in the answer.

$$
\begin{array}{r}
\overset{8}{9}.\overset{9}{0}\overset{9}{0}\overset{10}{0} \\
-4.125 \\
\hline
4.875
\end{array}
$$

So, $9 – 4.125 = 4.875$.

Solving Quantitative Reasoning Problems with Decimals

Quantitative reasoning problems are word problems that require you to use addition or subtraction of decimals to find an answer. To solve these problems, read carefully to understand what is being asked and what operation (addition or subtraction) is needed.

Worked Examples of Quantitative Reasoning Problems

Example 1:

A tailor bought $3.5$ metres of blue fabric and $2.75$ metres of red fabric. How many metres of fabric did the tailor buy in total?

Understanding the problem: The word “total” tells us to add the lengths of the two fabrics.

Calculation:

Length of blue fabric = $3.5$ metres

Length of red fabric = $2.75$ metres

$$
\begin{array}{r}
3.50 \\
+2.75 \\
\hline
6.25
\end{array}
$$

Answer: The tailor bought $6.25$ metres of fabric in total.

Example 2:

A bucket contained $10.5$ litres of water. If $3.25$ litres of water were used to water plants, how much water is left in the bucket?

Understanding the problem: The phrase “how much water is left” tells us to subtract the amount of water used from the total amount.

Calculation:

Total water in bucket = $10.5$ litres

Water used = $3.25$ litres

$$
\begin{array}{r}
10.50 \\
-\ 3.25 \\
\hline
\ 7.25
\end{array}
$$

Answer: There are $7.25$ litres of water left in the bucket.

Example 3:

Chike bought a pencil for $N15.75$, an eraser for $N5.50$, and a ruler for $N20.25$. How much money did he spend altogether?

Understanding the problem: The word “altogether” tells us to add all the amounts Chike spent.

Calculation:

Cost of pencil = $N15.75$

Cost of eraser = $N5.50$

Cost of ruler = $N20.25$

$$
\begin{array}{r}
15.75 \\
\ 5.50 \\
+20.25 \\
\hline
41.50
\end{array}
$$

Answer: Chike spent $N41.50$ altogether.

Practising Decimal Operations

Practising regularly helps you become better at adding and subtracting decimals. You can use different tools and methods to make learning fun and effective.

Using Decimal Charts and Base 10 Blocks

Decimal charts and Base 10 blocks can help you visualise decimal numbers and understand addition and subtraction. For example, a large flat block can represent one whole, a long rod can represent one tenth, and a small cube can represent one hundredth.

To add $0.25 + 0.13$ using blocks:

1. Represent $0.25$ with $2$ tenths rods and $5$ hundredths cubes.
2. Represent $0.13$ with $1$ tenths rod and $3$ hundredths cubes.
3. Combine all the hundredths cubes ($5+3=8$ hundredths).
4. Combine all the tenths rods ($2+1=3$ tenths).
5. The total is $3$ tenths and $8$ hundredths, which is $0.38$.

Using Number Lines

A number line can be used to visualise addition and subtraction of decimals. Each mark on the number line can represent tenths, hundredths, or thousandths.

To add $0.5 + 0.3$ on a number line:

1. Start at $0.5$ on the number line.
2. Move $0.3$ units to the right (three tenths).
3. You will land on $0.8$. So, $0.5 + 0.3 = 0.8$.

To subtract $0.7 – 0.2$ on a number line:

1. Start at $0.7$ on the number line.
2. Move $0.2$ units to the left (two tenths).
3. You will land on $0.5$. So, $0.7 – 0.2 = 0.5$.

Decimal Challenges and Games

You can create simple challenges or games to practice. For example:

1. Flash Card Challenge: Write decimal addition or subtraction problems on flash cards. Solve them quickly and check your answers.
2. Decimal Target Game: Set a target decimal number. Use number cards with decimals and try to reach the target by adding or subtracting them.
3. Everyday Decimal Problems: Look for decimals in real life, like prices in a shop ($N120.50$), measurements ($2.3$ metres), or weights ($0.75$ kg). Create your own addition and subtraction problems using these numbers.