A decimal is a number that includes a decimal point to represent a whole number plus a fraction of a whole. For example, 4.75 has a whole number part (4) and a decimal part (.75). Decimals are a key part of our daily lives, especially when dealing with money, measurements, and data!
Adding Decimals
Adding decimals involves two main cases: when you’re adding a decimal to a whole number and when you’re adding two decimals.
Adding a Decimal to a Whole Number
When adding a whole number to a decimal, it’s important to line up the numbers correctly.
- Write the whole number and the decimal so that the decimal points line up. The whole number will not have any digits after the decimal point.
- If needed, add zeroes after the decimal point for the whole number to make the addition easier.
- Add the numbers starting from the right, just like with whole numbers.
Example: Add 6 and 3.45.
6.00 +
3.45
____
9.45
Adding Two Decimals
To add decimals, follow these steps:
- Line up the decimal points of the numbers you are adding.
- Add from right to left, just like you would with whole numbers.
- Place the decimal point directly below the other decimal points in your answer.
If the numbers have different decimal places, add zeroes to make the number of decimal places equal.
Example: Add 3.48 and 5.6
5.6 can be added as such to 3.48 or we can add a zero to make it 5.60.
3.48 + 3.48 +
5.6 5.60
____ ____
9.08 9.08
Subtracting Decimals
We can subtract a decimal from a whole number, a whole number from a decimal, and decimals from each other. Let’s explore each case with clear examples!
Subtracting a Decimal from a Whole Number
When subtracting a decimal from a whole number, you’ll need to rewrite the whole number with a decimal point.
- Rewrite the whole number by adding a decimal point and zeroes to match the number of decimal places in the decimal.
- Line up the decimal points.
- Subtract from right to left, borrowing if necessary.
Example: Subtract 6.31 from 9.
9.00 -
6.31
____
2.69
Subtracting a Whole Number from a Decimal
When subtracting a whole number from a decimal, the steps are similar. The whole number is subtracted from the whole number part of the decimal and the decimal places are written as such. We can add zeros to the whole number, if needed.
Example: 13.67 – 5
5 is subtracted from 13 to get 8 and the decimal is written to get the answer as 8.67
13.67 - 13.67 -
5 5.00
_____ _____
8.67 8.67
Subtracting Two Decimals
When subtracting two decimals, we need to make sure both numbers have the same number of decimal places.
Steps:
- Line up the decimal points of both numbers.
- If needed, add zeroes to match the number of decimal places.
- Subtract from right to left, borrowing if necessary.
Example:
7.50 - 17.05 -
5.28 9.40
_____ _____
2.22 7.55
Multiplying Decimals
When multiplying decimals:
- Ignore the decimal points and multiply the numbers as if they were whole numbers.
- Count the total number of decimal places in both numbers.
- Place the decimal point in the answer so it has the same number of decimal places as the total from step 2.
Example: 2.4 × 3.6
24 x 36 = 864
2.4 and 3.6 together have 2 decimal places.
So, the answer is 8.64.
Multiplying Decimals by Tens
Multiplying decimals by tens is simple and follows a pattern. When you multiply a decimal by 10, you move the decimal point one place to the right. This happens because multiplying by 10 makes the number 10 times larger, shifting the digits to higher place values.
Example: 4.5 x 10 = 45, 2.73 x 10 = 27.3
Dividing Decimals
Dividing decimals is easy when you know the steps. Let’s look at how to handle different situations where you divide whole numbers and decimals!
Dividing a Whole Number by a Decimal
When dividing a whole number by a decimal, the goal is to eliminate the decimal point from the divisor (the number you’re dividing by).
- Move the decimal point of the divisor (the number you’re dividing by) to the right until it becomes a whole number.
- Move the decimal point of the dividend (the number being divided) the same number of places to the right.
- Divide as you would with whole numbers.
- Place the decimal point in the answer directly above where it appears in the dividend.
Example: 12 ÷ 0.4
To make 0.4 a whole number, multiply it by 10 and shift the decimal point to the right. Multiply 12 also by 10. This turns the problem into 120 ÷ 4.
Now divide: 120 ÷ 4 = 30.
So, 12 ÷ 0.4 = 30.
Dividing a Decimal by a Whole Number
This is simpler. Just divide the decimal as you would a whole number, keeping the decimal point in the same position. Always make sure the decimal point in the answer is directly above the decimal in the number you’re dividing. It stays in the same place!
Example: 6.4 ÷ 2
- Start with 6. How many times does 2 go into 6? The answer is 3. So, write 3 above the 6.
- Once you reach the decimal in the number, place the decimal point directly above it in the answer.
- Now divide the remaining part (4). How many times does 2 go into 4? The answer is 2. Write 2 after the decimal point.
- The answer to 6.4 ÷ 2 is 3.2.
Dividing a Decimal by another Decimal
The first step is similar to dividing a whole number by a decimal. To divide a decimal by another decimal, first move the decimal point in the divisor to make it a whole number. Then move the decimal point in the dividend (the number being divided) by the same number of places.
Example: 0.63 ÷ 0.7
Multiply both 0.63 and 0.7 by 10 to eliminate the decimal point from 0.7. This turns the problem into 6.3 ÷ 7.
Now divide: 6.3 ÷ 7 = 0.9
So, 0.63 ÷ 0.7 = 0.9.
Practice Problems
7.3 + 4.56 = ?
9.12 – 6.07 = ?
5.2 × 1.3 = ?
12.5 ÷ 2.5 = ?
Practice Quiz On Operations on Decimals
FAQs on Operations on Decimals
- When multiplying a decimal by 10, 100, or 1000, simply move the decimal point to the right by the number of zeros in the factor. For example:
- 3.45×10=34.5
- 4.2×100=420
- When dividing a decimal by 10, 100, or 1000, move the decimal point to the left by the number of zeros in the divisor. For example:
- 45.6÷10=4.56
- 7.9÷100=0.079