🔢 Mixed Operations - Grade 3
Understanding Mixed Operations!
Mixed operations means using addition, subtraction, multiplication, and division together to solve problems!
The Four Operations:
➕ Addition - Combining numbers
➖ Subtraction - Taking away
✖️ Multiplication - Repeated addition
➗ Division - Sharing equally
📚 Addition, Subtraction, Multiplication and Division Facts
What are Math Facts?
Math facts are basic calculations you should know quickly without having to count or use your fingers!
Addition Facts (up to 20):
\(7 + 8 = 15\)
\(9 + 6 = 15\)
\(8 + 9 = 17\)
\(5 + 5 = 10\)
Subtraction Facts (up to 20):
\(15 - 7 = 8\)
\(18 - 9 = 9\)
\(14 - 6 = 8\)
\(12 - 5 = 7\)
Multiplication Facts (up to 12):
\(3 \times 4 = 12\)
\(6 \times 7 = 42\)
\(8 \times 9 = 72\)
\(12 \times 5 = 60\)
Division Facts (up to 12):
\(24 \div 6 = 4\)
\(35 \div 7 = 5\)
\(56 \div 8 = 7\)
\(72 \div 9 = 8\)
💡 Tip: Practice these facts every day to get faster!
✏️ Complete the Sentence
What Does This Mean?
Find the missing number to make the math sentence true!
Examples:
Addition:
\(15 + ? = 23\)
Think: What number added to 15 gives 23?
\(23 - 15 = 8\)
Answer: \(15 + 8 = 23\) ✓
Multiplication:
\(7 \times ? = 42\)
Think: What number times 7 gives 42?
\(42 \div 7 = 6\)
Answer: \(7 \times 6 = 42\) ✓
Division:
\(? \div 4 = 8\)
Think: What number divided by 4 gives 8?
\(8 \times 4 = 32\)
Answer: \(32 \div 4 = 8\) ✓
✅❌ True or False?
How to Check if a Statement is True or False:
- Solve the left side - Do the calculation
- Compare with the right side - Are they equal?
- Decide: If equal → TRUE ✓ | If not equal → FALSE ✗
Multiplication Facts up to 5:
Example 1: \(3 \times 5 = 15\) → TRUE ✓
Example 2: \(4 \times 5 = 25\) → FALSE ✗ (Correct: \(4 \times 5 = 20\))
Multiplication Facts up to 10:
Example 1: \(7 \times 8 = 56\) → TRUE ✓
Example 2: \(9 \times 6 = 56\) → FALSE ✗ (Correct: \(9 \times 6 = 54\))
Division Facts up to 12:
Example 1: \(72 \div 9 = 8\) → TRUE ✓
Example 2: \(84 \div 12 = 6\) → FALSE ✗ (Correct: \(84 \div 12 = 7\))
🔢 Add, Subtract, Multiply and Divide
Order of Operations (PEMDAS):
When there are multiple operations, follow this order:
P - Parentheses (brackets) first
E - Exponents (powers)
M - Multiplication
D - Division
A - Addition
S - Subtraction
For Grade 3: Do parentheses first, then multiplication/division (left to right), then addition/subtraction (left to right)!
Examples:
Example 1: With Parentheses
\((8 - 3) \times 4\)
Step 1: Parentheses first: \(8 - 3 = 5\)
Step 2: Multiply: \(5 \times 4 = 20\)
Answer: 20 ✓
Example 2: Multiple Operations
\(20 - 6 \div 2 + 5\)
Step 1: Division first: \(6 \div 2 = 3\)
Step 2: Left to right: \(20 - 3 + 5\)
Step 3: Subtract: \(20 - 3 = 17\)
Step 4: Add: \(17 + 5 = 22\)
Answer: 22 ✓
📖 Word Problems
Steps to Solve Word Problems:
- Read carefully - What is the problem asking?
- Find the important information - Underline numbers and key words
- Decide which operation to use - Add, subtract, multiply, or divide?
- Solve the problem - Do the math
- Check your answer - Does it make sense?
Key Words Guide:
| Operation | Key Words |
|---|---|
| Addition | total, sum, altogether, in all, combined |
| Subtraction | difference, left, remaining, how many more |
| Multiplication | times, each, per, groups of, product |
| Division | share, equally, per, each, quotient |
Examples:
Addition Word Problem:
Sarah has 45 stickers. Her friend gives her 28 more stickers. How many stickers does Sarah have in all?
Key word: "in all" → Addition
Calculation: \(45 + 28 = 73\)
Answer: Sarah has 73 stickers. ✓
Multiplication Word Problem:
There are 6 boxes. Each box has 8 pencils. How many pencils are there in total?
Key word: "each" → Multiplication
Calculation: \(6 \times 8 = 48\)
Answer: There are 48 pencils in total. ✓
Division Word Problem:
A teacher has 36 crayons to share equally among 9 students. How many crayons does each student get?
Key word: "share equally" → Division
Calculation: \(36 \div 9 = 4\)
Answer: Each student gets 4 crayons. ✓
📊 Add and Subtract Data from Tables
How to Read Tables:
- Read the title - What is the table about?
- Check the column headers - What information is shown?
- Find the row you need - Look for the category
- Read the number - Where row and column meet
- Perform the operation - Add or subtract as needed
Example Table: Books Read by Students
| Student Name | Books Read |
|---|---|
| Ravi | 15 |
| Priya | 23 |
| Amit | 18 |
Questions:
Q1: How many books did Ravi and Priya read together?
A: \(15 + 23 = 38\) books ✓
Q2: How many more books did Priya read than Amit?
A: \(23 - 18 = 5\) books ✓
Q3: How many books did all three students read in total?
A: \(15 + 23 + 18 = 56\) books ✓
🎯 Multi-Step Word Problems
What are Multi-Step Problems?
Multi-step problems require you to do two or more operations to find the answer!
Steps to Solve Multi-Step Problems:
- Read the entire problem - Understand the whole story
- Identify what you need to find - What is the question asking?
- Break it into steps - What do you need to find first? Second?
- Solve step by step - Do one calculation at a time
- Use the first answer in the next step - Connect your steps
- Write your final answer - Answer the original question
Examples:
Example 1: Addition and Subtraction
Maya had 50 marbles. She bought 25 more marbles. Then she gave 18 marbles to her brother. How many marbles does Maya have now?
Step 1: Add marbles bought
\(50 + 25 = 75\) marbles
Step 2: Subtract marbles given away
\(75 - 18 = 57\) marbles
Answer: Maya has 57 marbles now. ✓
Example 2: Multiplication and Addition
A bakery made 8 trays of cookies. Each tray has 12 cookies. They made 15 more cookies separately. How many cookies did they make in total?
Step 1: Multiply trays by cookies per tray
\(8 \times 12 = 96\) cookies
Step 2: Add extra cookies
\(96 + 15 = 111\) cookies
Answer: They made 111 cookies in total. ✓
Example 3: All Four Operations
A farmer has 60 apples. He puts them equally into 5 baskets. He then picks 8 more apples and adds 4 to each basket. How many apples are in each basket now?
Step 1: Divide apples into baskets
\(60 \div 5 = 12\) apples per basket
Step 2: Add more apples to each basket
\(12 + 4 = 16\) apples per basket
Answer: Each basket now has 16 apples. ✓
❓ Missing Operators
What are Missing Operators?
Find the missing operation sign (+, −, ×, ÷) that makes the equation true!
How to Find Missing Operators:
- Look at the numbers - What are the given numbers?
- Look at the answer - What should the result be?
- Try each operation - Test +, −, ×, ÷
- Check which one works - Which makes the equation true?
Examples:
Example 1:
\(12 \, ? \, 8 = 20\)
Try addition: \(12 + 8 = 20\) ✓
Try subtraction: \(12 - 8 = 4\) ✗
Try multiplication: \(12 \times 8 = 96\) ✗
Try division: \(12 \div 8 = 1.5\) ✗
Answer: \(12 + 8 = 20\) ✓
Example 2:
\(56 \, ? \, 7 = 8\)
Try addition: \(56 + 7 = 63\) ✗
Try subtraction: \(56 - 7 = 49\) ✗
Try multiplication: \(56 \times 7 = 392\) ✗
Try division: \(56 \div 7 = 8\) ✓
Answer: \(56 \div 7 = 8\) ✓
Example 3: Multiple Operators
\(15 \, ? \, 5 \, ? \, 3 = 9\)
Try: \(15 - 5 + 3 = 10 + 3 = 13\) ✗
Try: \(15 \div 5 + 3 = 3 + 3 = 6\) ✗
Try: \(15 - 5 - 3 = 10 - 3 = 7\) ✗
Try: \(15 \div 5 \times 3 = 3 \times 3 = 9\) ✓
Answer: \(15 \div 5 \times 3 = 9\) ✓
📝 Important Formulas Summary
The Four Operations:
Addition: \(\text{Addend} + \text{Addend} = \text{Sum}\)
Subtraction: \(\text{Minuend} - \text{Subtrahend} = \text{Difference}\)
Multiplication: \(\text{Factor} \times \text{Factor} = \text{Product}\)
Division: \(\text{Dividend} \div \text{Divisor} = \text{Quotient}\)
Order of Operations (Simplified for Grade 3):
1. Parentheses ( ) first
2. Multiplication and Division (left to right)
3. Addition and Subtraction (left to right)
Inverse Operations:
Addition ↔ Subtraction
\(a + b = c\) means \(c - b = a\)
Multiplication ↔ Division
\(a \times b = c\) means \(c \div b = a\)
💡 Quick Learning Tips
- ✓ Practice math facts daily to get faster!
- ✓ Look for key words in word problems (total, each, left, etc.)
- ✓ Solve parentheses first, then × and ÷, then + and −
- ✓ Check your answer: Does it make sense?
- ✓ For multi-step problems: Break into smaller steps
- ✓ Use inverse operations to check your work
- ✓ When completing sentences, work backwards from the answer
- ✓ For true/false: Calculate the left side and compare
- ✓ Tables: Read carefully - find the right row and column
- ✓ Missing operators: Try all four operations to find the right one
- ✓ Draw pictures or diagrams for word problems
- ✓ Write down each step - don't try to do it all in your head
- ✓ Multiplication facts up to 12 × 12 = 144
- ✓ Division is the opposite of multiplication - use it to check!
- ✓ Practice makes perfect - do a little every day!