Decimal Operations And The Order Of Operations

📝 Practice Worksheets

Order of Operations and Decimals - 1 Order of Operations and Decimals - 2 Order of Operations and Decimals - 3 Order of Operations Practice

🛠️ Related Tool

Order of Operations Practice Lab

🔑 Key Concepts

Order of operations still applies when working with decimal values.
Simplify exponents and parentheses before moving to multiplication and division.
Multiplication and division are done from left to right.
Addition and subtraction are done from left to right.
Underlining the part of the expression being simplified can help students stay organized and avoid mistakes.

✏️ Worked Examples — Order of Operations With Decimals

The red, underlined operation is the part completed next.

Example 1 — Exponents and Decimal Operations

Solve:

\(\displaystyle 2.5^2\div0.5\cdot2-3.4+1.4\)

Evaluate the exponent.

\(\displaystyle {\color{red}\underline{2.5^2}}\div0.5\cdot2-3.4+1.4\)

\(\displaystyle =6.25\div0.5\cdot2-3.4+1.4\)

Multiply and divide from left to right.

\(\displaystyle {\color{red}\underline{6.25\div0.5}}\cdot2-3.4+1.4\)

\(\displaystyle =12.5\cdot2-3.4+1.4\)

\(\displaystyle {\color{red}\underline{12.5\cdot2}}-3.4+1.4\)

\(\displaystyle =25-3.4+1.4\)

Add and subtract from left to right.

\(\displaystyle {\color{red}\underline{25-3.4}}+1.4\)

\(\displaystyle =21.6+1.4\)

\(\displaystyle {\color{red}\underline{21.6+1.4}}\)

Final Answer:

\(\boxed{23}\)

Example 2 — Parentheses First With Decimals

Solve:

\(\displaystyle 1.2(8-2.5+0.5)\div0.4+2\cdot3.5\)

Simplify inside the parentheses from left to right.

\(\displaystyle 1.2({\color{red}\underline{8-2.5}}+0.5)\div0.4+2\cdot3.5\)

\(\displaystyle =1.2(5.5+0.5)\div0.4+2\cdot3.5\)

\(\displaystyle 1.2({\color{red}\underline{5.5+0.5}})\div0.4+2\cdot3.5\)

\(\displaystyle =1.2(6)\div0.4+2\cdot3.5\)

Multiply and divide from left to right.

\(\displaystyle {\color{red}\underline{1.2(6)}}\div0.4+2\cdot3.5\)

\(\displaystyle =7.2\div0.4+2\cdot3.5\)

\(\displaystyle {\color{red}\underline{7.2\div0.4}}+2\cdot3.5\)

\(\displaystyle =18+2\cdot3.5\)

\(\displaystyle 18+{\color{red}\underline{2\cdot3.5}}\)

\(\displaystyle =18+7\)

Add the remaining values.

\(\displaystyle {\color{red}\underline{18+7}}\)

Final Answer:

\(\boxed{25}\)

Example 3 — Mixed Decimal Operations

Solve:

\(\displaystyle 4.8\div0.6\cdot1.5-2.7\cdot0.5+0.35\)

Multiply and divide from left to right.

\(\displaystyle {\color{red}\underline{4.8\div0.6}}\cdot1.5-2.7\cdot0.5+0.35\)

\(\displaystyle =8\cdot1.5-2.7\cdot0.5+0.35\)

\(\displaystyle {\color{red}\underline{8\cdot1.5}}-2.7\cdot0.5+0.35\)

\(\displaystyle =12-2.7\cdot0.5+0.35\)

\(\displaystyle 12-{\color{red}\underline{2.7\cdot0.5}}+0.35\)

\(\displaystyle =12-1.35+0.35\)

Add and subtract from left to right.

\(\displaystyle {\color{red}\underline{12-1.35}}+0.35\)

\(\displaystyle =10.65+0.35\)

\(\displaystyle {\color{red}\underline{10.65+0.35}}\)

Final Answer:

\(\boxed{11}\)

🧠 Math Vocabulary

Order of operations: The rules that tell the correct order for evaluating an expression.
Exponent: A number that tells how many times a base is multiplied by itself.
Grouping symbols: Symbols such as parentheses that tell which part to simplify first.
Evaluate: To find the value of an expression.
Decimal: A number written with a decimal point to represent part of a whole.

💡 Main Idea

This lesson shows that the same order of operations rules used with whole numbers also apply when expressions contain decimals. Students simplify exponents and parentheses first, then work through multiplication and division from left to right, and finally complete addition and subtraction from left to right. Underlining each part before simplifying it helps make the process clearer and more organized.

📚 What You Should Already Know

Before starting this lesson, students should know how to add, subtract, multiply, and divide decimal numbers. They should also be familiar with evaluating simple exponents and simplifying expressions with parentheses one step at a time.

🚀 What Comes Next

After this lesson, students can move on to more complex numerical expressions, writing algebraic expressions, and evaluating expressions with variables. This work also builds fluency for solving multi-step equations and applying operations accurately in real-world contexts.

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