Lesson 2: Decimal Operations

New Concept

Decimal operations build on your skills with whole numbers. You'll learn the rules for adding, subtracting, multiplying, and dividing decimals, focusing on how to correctly place the decimal point in your answers and apply these skills to money problems.

What’s next

Now, let's dive in! You will work through interactive examples and practice problems to master adding, subtracting, multiplying, and dividing decimals.

Property

How to add or subtract decimals:
Step 1. Write the numbers vertically so the decimal points line up.
Step 2. Use zeros as place holders, as needed.
Step 3. Add or subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers.

Examples

• To add $18.5 + 3.45$, we write the numbers vertically, aligning the decimal points and adding a placeholder zero: $18.50 + 3.45 = 21.95$.

• To subtract $50 - 22.18$, we treat $50$ as $50.00$ to align the decimal points and use placeholders: $50.00 - 22.18 = 27.82$.

Property

How to multiply decimal numbers:
Step 1. Determine the sign of the product.
Step 2. Write the numbers in vertical format, lining up the numbers on the right.
Step 3. Multiply the numbers as if they were whole numbers, temporarily ignoring the decimal points.
Step 4. Place the decimal point. The number of decimal places in the product is the sum of the number of decimal places in the factors. If needed, use zeros as placeholders.
Step 5. Write the product with the appropriate sign.

Examples

• To multiply $(6.2)(1.5)$, we calculate $62 \times 15 = 930$. Since there is one decimal place in each factor, the product has two decimal places: $9.30$.

• For $(-7.1)(0.25)$, the product is negative. We multiply $71 \times 25 = 1775$. With one plus two decimal places, the total is three. The answer is $-1.775$.

Property

How to multiply a decimal by a power of 10:
Step 1. Move the decimal point to the right the same number of places as the number of zeros in the power of $10$.
Step 2. Write zeros at the end of the number as placeholders if needed.

Examples

• To multiply $8.452 \times 10$, move the decimal point one place to the right because $10$ has one zero. The result is $84.52$.

• To multiply $0.73 \times 100$, move the decimal point two places to the right because $100$ has two zeros. The result is $73$.

Property

How to divide decimal numbers:
Step 1. Determine the sign of the quotient.
Step 2. Make the divisor a whole number by moving the decimal point all the way to the right. Move the decimal point in the dividend the same number of places to the right, writing zeros as needed.
Step 3. Divide. Place the decimal point in the quotient above the decimal point in the dividend.
Step 4. Write the quotient with the appropriate sign.

Examples

• To divide $35.5 \div 5$, the divisor is already a whole number. We place the decimal point in the quotient directly above the one in the dividend and divide as usual to get $7.1$.

• For $1.44 \div 1.2$, we move the decimal one place to the right in both numbers to get the equivalent problem $14.4 \div 12$, which gives the answer $1.2$.