Order of Operations (BEDMAS) with Integers, Fractions, and Decimals

If you can do basic calculations correctly but still loses marks on mixed expressions, the issue is often not the arithmetic itself. It is usually order of operations.

This is one of the most common foundational skills I review with students in Winnipeg. A student may know how to add fractions, multiply decimals, and solve equations, but if they do the steps in the wrong order, the final answer is still wrong.

In this post, we will go through BEDMAS carefully, including:

• integers (positive and negative numbers)

• fractions

• decimals

• common mistakes

• worked examples with full solutions

What is BEDMAS?

BEDMAS is a rule that tells us the correct order to evaluate expressions.

It stands for:

• B = Brackets

• E = Exponents

• D = Division

• M = Multiplication

• A = Addition

• S = Subtraction

Important note

Division and multiplication are the same level of priority. Addition and subtraction are also the same level of priority.

So when both appear, you work from left to right.

That means:

• Do D and M from left to right

• Do A and S from left to right

This is a major source of mistakes.

Why BEDMAS matters so much

BEDMAS shows up everywhere:

• arithmetic questions

• simplifying algebra expressions

• solving equations

• formulas in science and finance

• calculator use

A student who rushes BEDMAS often makes what looks like a "careless mistake," but it is actually a process mistake.

Before we start: key terms

1) Expression vs Equation

• An expression has numbers and operations, but no equals sign

  Example: 8 + 3 × 2

• An equation has an equals sign

  Example: 8 + 3 × 2 = 14

BEDMAS is used when evaluating expressions (and the expression parts inside equations).

2) Integer

An integer is a whole number (positive, negative, or zero), such as:

• −5, −1, 0, 3, 12

3) Fraction

A fraction represents part of a whole, such as:

• 1/2, 3/4, 7/10

4) Decimal

A decimal is another way of writing parts of a whole, such as:

• 0.5, 1.25, 3.08

The BEDMAS process (the safe way)

When solving a mixed expression, use this routine:

1. Look for brackets and simplify inside them first.

2. Look for exponents.

3. Do division and multiplication from left to right.

4. Do addition and subtraction from left to right.

5. Double-check signs (especially negatives).

This step-by-step habit prevents most errors.

Common BEDMAS mistakes (very important)

Mistake 1: Doing operations strictly in the order of the letters

Some students do multiplication before division just because M comes after D in BEDMAS. That is not correct.

Example: 24 ÷ 6 × 2

Correct method (left to right):

• 24 ÷ 6 = 4

• 4 × 2 = 8

So the answer is 8, not 2.

Mistake 2: Adding before multiplying

Example: 3 + 4 × 2

Wrong: (3 + 4) × 2 = 14 Correct:

• 4 × 2 = 8

• 3 + 8 = 11

Answer: 11

Mistake 3: Sign errors with negatives

Example: 5 − 8 + 2

You must go left to right:

• 5 − 8 = −3

• −3 + 2 = −1

Answer: −1

A common wrong answer is 5 − (8 + 2) = −5, but that changes the expression.

Mistake 4: Calculator input mistakes

Students often forget brackets when typing fractions or numerators/denominators with more than one term.

For example, if the expression is:

you should type:

(3+5)/2

If you type 3+5/2, the calculator reads it as:

which is different.

Worked Examples (with full solutions)

We will start simple and build up.

Example 1: Basic BEDMAS with integers

Question

Evaluate:

7 + 3 × 4

Solution

Use BEDMAS:

• No brackets

• No exponents

• Multiplication before addition

So do: 3 × 4 = 12

Now the expression becomes:

7 + 12

Then add:

7 + 12 = 19

Final answer

19

Example 2: Brackets first

Question

Evaluate:

(7 + 3) × 4

Solution

BEDMAS says brackets first:

7 + 3 = 10

Now the expression becomes:

10 × 4

Multiply:

10 × 4 = 40

Final answer

40

Why this matters

Compare Example 1 and Example 2:

• 7 + 3 × 4 = 19

• (7 + 3) × 4 = 40

Same numbers, different answer, because the brackets change the order.

Example 3: Division and multiplication (left to right)

Question

Evaluate:

30 ÷ 5 × 2

Solution

Division and multiplication are same priority, so go left to right.

First:

30 ÷ 5 = 6

Then: 6 × 2 = 12

Final answer

12

Example 4: Addition and subtraction with negatives

Question

Evaluate:

12 − 7 + 3 − 10

Solution

No brackets, exponents, multiplication, or division.

So do addition and subtraction from left to right.

Step 1:

12 − 7 = 5

Step 2:

5 + 3 = 8

Step 3:

8 − 10 = −2

Final answer

−2

Example 5: Integers with brackets and negatives

Question

Evaluate:

18 − (5 + 7)

Solution

Brackets first:

5 + 7 = 12

Now the expression becomes:

18 − 12

Subtract:

18 − 12 = 6

Final answer

6

Example 6: Decimals and multiplication

Question

Evaluate:

4.5 + 1.2 × 3

Solution

Multiplication before addition.

First:

1.2 × 3 = 3.6

Now:

4.5 + 3.6

Add:

4.5 + 3.6 = 8.1

Final answer

8.1

Example 7: Decimals with brackets

Question

Evaluate:

(6.8 − 2.3) ÷ 1.5

Solution

Brackets first:

6.8 − 2.3 = 4.5

Now:

4.5 ÷ 1.5

Divide:

4.5 ÷ 1.5 = 3

Final answer

3

Example 8: Fractions and multiplication before addition

Question

Evaluate:

Solution

Multiplication before addition.

First multiply:

Now the expression becomes:

Add fractions with the same denominator:

Final answer

2

Example 9: Fractions inside brackets

Question

Evaluate:

Solution

Brackets first.

To add 2/3 and 1/6, use a common denominator of 6.

Convert:

2/3 = 4/6

Now add:

So the expression becomes:

Write 3 as 3/1:

Simplify:

15/6 = 5/2 = 2.5

Final answer

5/2 or 2.5

Example 10: Mixed integers, decimals, and fractions

Question

Evaluate:

−3 + 2.5 × (4/5)

Solution

Brackets first (the fraction is already simplified), then multiplication.

Compute:

2.5 × (4/5)

Convert 2.5 to a fraction if helpful:

2.5 = 5/2

Then:

(5/2) × (4/5) = 20/10 = 2

Now the expression becomes:

−3 + 2

Add:

−3 + 2 = −1

Final answer

−1

Example 11: A common "trap" question

Question

Evaluate:

8 − 2(3 + 1)

Solution

Brackets first:

3 + 1 = 4

Now:

8 − 2(4)

The 2(4) means multiplication:

2 × 4 = 8

Now:

8 − 8 = 0

Final answer

0

Common mistake

Some students do 8 − 2 = 6 first, which is not allowed because the multiplication must happen before subtraction.

Example 12: A full mixed expression

Question

Evaluate:

(2.4 + 1.6) ÷ 2 + (3/4)

Solution

Step 1: Brackets first

2.4 + 1.6 = 4.0

Now the expression becomes:

4.0 ÷ 2 + (3/4)

Step 2: Division

4.0 ÷ 2 = 2

Now:

2 + (3/4)

Step 3: Add

If you want a decimal:

3/4 = 0.75

so

2 + 0.75 = 2.75

Final answer

Tips students can use right away

1) Rewrite one line at a time

Do not skip from the original expression to the final answer in your head.

Show each step.

This makes mistakes easier to catch.

2) Circle brackets first

If a student struggles with BEDMAS, have them physically mark:

• brackets

• exponents

• multiplication/division

• addition/subtraction

This slows them down in a good way.

3) Keep negatives attached to numbers

Treat negative numbers as one object when possible:

• −3

• −7

• −0.4

This helps avoid sign errors.

4) Use brackets when typing into a calculator

Examples:

• (3+5)/2

• (−4+7)*3

• (1/2)+(3/4)*2

If in doubt, add brackets.

Quick practice (with answers)

Try these on your own before checking.

1)

9 − 2 × 3

2)

(9 − 2) × 3

3)

6 ÷ 2 × 4

4)

1.5 + 0.5 × 6

5)

Answers

1. 3

2. 21

3. 12

4. 4.5

5. 6

Final thoughts

Order of operations is a foundational skill that supports almost every future math topic. Students often think they have a "hard math" problem when the real issue is a BEDMAS error earlier in the work.

If you are reviewing math fundamentals, this is one of the best topics to master early because it improves:

• accuracy

• confidence

• speed

• success in algebra and beyond

---

Need help with order of operations with integers, fractions, and decimals? If you’re in Winnipeg and looking for a tutor, Tutor Advance provides expert one-on-one support!

---