Mixed Operations (Grade 3)
Mixed operations means solving problems that use more than one operation — addition, subtraction, multiplication, and division — in the same question.
In Class 3, you begin solving problems that combine two or more operations. To get the correct answer, you must follow the right order of operations.
The basic rule is: First do multiplication and division (left to right), then do addition and subtraction (left to right). Brackets are always solved first.
What is Mixed Operations - Class 3 Maths (Addition and Subtraction (Grade 3))?
Mixed operations are maths problems where you need to use two or more of the four basic operations: addition (+), subtraction (−), multiplication (×), and division (÷).
Order: Brackets → Multiply / Divide → Add / Subtract
This order matters because doing operations in the wrong order gives the wrong answer.
Example: 3 + 4 × 2
- Wrong way: 3 + 4 = 7, then 7 × 2 = 14
- Right way: 4 × 2 = 8, then 3 + 8 = 11
Types and Properties
Types of Mixed Operation Problems
1. Addition and Subtraction Together
Work from left to right.
Example: 25 + 13 − 8 = 38 − 8 = 30
2. Multiplication and Addition/Subtraction
Do multiplication first, then add or subtract.
Example: 6 × 3 + 5 = 18 + 5 = 23
3. Division and Addition/Subtraction
Do division first, then add or subtract.
Example: 20 ÷ 4 + 7 = 5 + 7 = 12
4. Problems with Brackets
Solve what is inside the brackets first.
Example: (8 + 2) × 3 = 10 × 3 = 30
5. Multi-Step Word Problems
Real-life problems often need more than one step to solve.
Solved Examples
Example 1: Example 1: Addition and Subtraction
Question: Find 45 + 23 − 18.
Think:
- Work left to right
- 45 + 23 = 68
- 68 − 18 = 50
Answer: 50
Example 2: Example 2: Multiplication Then Addition
Question: Find 5 × 4 + 9.
Think:
- Multiply first: 5 × 4 = 20
- Then add: 20 + 9 = 29
Answer: 29
Example 3: Example 3: Division Then Subtraction
Question: Find 36 ÷ 6 − 2.
Think:
- Divide first: 36 ÷ 6 = 6
- Then subtract: 6 − 2 = 4
Answer: 4
Example 4: Example 4: Using Brackets
Question: Find (7 + 3) × 5.
Think:
- Brackets first: 7 + 3 = 10
- Then multiply: 10 × 5 = 50
Answer: 50
Example 5: Example 5: Two Operations Without Brackets
Question: Find 12 + 3 × 6.
Think:
- Multiply first: 3 × 6 = 18
- Then add: 12 + 18 = 30
Answer: 30
Example 6: Example 6: Word Problem – Shopping
Question: Ria buys 3 notebooks at ₹12 each and a pen for ₹8. How much does she spend in total?
Think:
- Cost of notebooks: 3 × 12 = ₹36
- Cost of pen: ₹8
- Total: 36 + 8 = ₹44
Answer: Ria spends ₹44.
Example 7: Example 7: Word Problem – Spending and Change
Question: Dev has ₹50. He buys 4 erasers at ₹5 each. How much money is left?
Think:
- Cost of erasers: 4 × 5 = ₹20
- Money left: 50 − 20 = ₹30
Answer: Dev has ₹30 left.
Example 8: Example 8: Brackets Change the Answer
Question: Compare: 2 + 3 × 4 and (2 + 3) × 4.
Think:
- 2 + 3 × 4 → Multiply first: 3 × 4 = 12, then 2 + 12 = 14
- (2 + 3) × 4 → Brackets first: 2 + 3 = 5, then 5 × 4 = 20
Answer: The answers are different — 14 and 20. Brackets change the order and the result.
Example 9: Example 9: Three Operations
Question: Find 40 ÷ 8 + 3 × 2.
Think:
- Divide: 40 ÷ 8 = 5
- Multiply: 3 × 2 = 6
- Add: 5 + 6 = 11
Answer: 11
Example 10: Example 10: Multi-Step Word Problem
Question: Neha picks 24 flowers. She gives 6 flowers to each of 3 friends. She keeps the rest. How many does she keep?
Think:
- Flowers given away: 6 × 3 = 18
- Flowers kept: 24 − 18 = 6
Answer: Neha keeps 6 flowers.
Real-World Applications
Where Do We Use Mixed Operations?
- Shopping: Calculating total cost when buying different items at different prices.
- Cooking: Doubling a recipe (multiply) and adding extra ingredients (add).
- Sports: Finding total runs scored across different overs in cricket.
- Sharing: Dividing items equally and then adding more.
- Saving money: Earning ₹10 per day for 5 days (multiply) and spending ₹15 (subtract).
Key Points to Remember
- Mixed operations use two or more of +, −, ×, ÷ in the same problem.
- Always do multiplication and division first, then addition and subtraction.
- Brackets are solved before everything else.
- When only + and − appear, work left to right.
- When only × and ÷ appear, work left to right.
- Brackets can change the answer — always look for them first.
- Word problems often need mixed operations to find the final answer.
Practice Problems
- Find 8 + 6 × 3.
- Find (15 − 5) × 2.
- Find 30 ÷ 5 + 12.
- Find 100 − 4 × 20.
- Arjun buys 5 bananas at ₹4 each and 2 oranges at ₹10 each. What is the total cost?
- Find 48 ÷ 6 − 3 + 10.
- Aditi has 35 stickers. She gives 5 stickers to each of 4 friends. How many stickers does she have left?
- Find (6 + 4) × (9 − 6).
Frequently Asked Questions
Q1. What are mixed operations in maths?
Mixed operations are problems that use more than one arithmetic operation (addition, subtraction, multiplication, or division) in the same expression or word problem.
Q2. Which operation do we solve first in a mixed problem?
Solve brackets first, then multiplication and division (left to right), and finally addition and subtraction (left to right).
Q3. Why do brackets matter in mixed operations?
Brackets tell you which part to solve first. They can change the answer completely. For example, 2 + 3 × 4 = 14, but (2 + 3) × 4 = 20.
Q4. What if there are only addition and subtraction?
When only addition and subtraction appear, work from left to right. For example, 20 − 5 + 3 = 15 + 3 = 18.
Q5. Is BODMAS taught in Class 3?
Class 3 introduces the basic idea of order: brackets first, then multiply/divide, then add/subtract. The full BODMAS rule is taught formally in higher classes.
Q6. How do I solve word problems with mixed operations?
Read the problem carefully. Identify which operations are needed. Perform multiplication and division before addition and subtraction to get the correct answer.
Q7. Can multiplication and division appear together?
Yes. When both appear without brackets, solve them left to right. For example, 12 ÷ 3 × 2 = 4 × 2 = 8.
Q8. What is the most common mistake in mixed operations?
The most common mistake is adding or subtracting before multiplying or dividing. Always do × and ÷ before + and −.
Q9. How can I practise mixed operations at home?
Create shopping problems with 2–3 items at different prices. Calculate totals and change. This naturally uses multiplication, addition, and subtraction together.
Related Topics
- Multiplication Word Problems (Grade 3)
- Division Word Problems (Grade 3)
- Addition of 3-Digit Numbers
- Addition Without Regrouping (3-Digit)
- Addition With Regrouping (3-Digit)
- Addition Word Problems (Grade 3)
- Subtraction of 3-Digit Numbers
- Subtraction With Regrouping (3-Digit)
- Subtraction Without Regrouping (3-Digit)
- Subtraction Word Problems (Grade 3)
- Mental Math (Grade 3)
- Adding 4 or More Numbers
