Real-world examples of inverse operations in Grade 5 math

📚 Quick Study Guide

• ➕ Addition & Subtraction: ➕ Addition and subtraction are inverse operations. One 'undoes' the other. For example, if you add 5 to a number, you can subtract 5 to get back to the original number.
• ➖ Multiplication & Division: ➗ Multiplication and division are also inverse operations. If you multiply a number by 3, you can divide by 3 to reverse the operation.
• 🔢 Real-World Examples: 🌎 We use inverse operations every day! Think about sharing cookies (division) and then putting them back together (multiplication), or adding money to your piggy bank and then spending some (subtraction).
• 💡 Key Idea: The goal of an inverse operation is to isolate the variable, or get it by itself, on one side of the equation.
• 📝 Formulas:
  • Addition: $a + b = c$ Inverse: $c - b = a$
  • Subtraction: $a - b = c$ Inverse: $c + b = a$
  • Multiplication: $a \times b = c$ Inverse: $c \div b = a$
  • Division: $a \div b = c$ Inverse: $c \times b = a$

Practice Quiz

1. Which operation is the inverse of adding 12?
1. Adding 12
2. Subtracting 12
3. Multiplying by 12
4. Dividing by 12
2. What is the inverse operation of dividing a number by 4?
1. Adding 4
2. Subtracting 4
3. Multiplying by 4
4. Dividing by 4
3. If you multiply a number by 6 and get 30, what inverse operation do you use to find the original number?
1. Adding 6
2. Subtracting 6
3. Multiplying by 6
4. Dividing by 6
4. Sarah added 8 stickers to her collection and now has 20. Which operation will help you find out how many she started with?
1. Adding 8
2. Subtracting 8
3. Multiplying by 8
4. Dividing by 8
5. Tom baked 24 cookies and wants to share them equally among 3 friends. What inverse operation would he use to figure out how many cookies each friend gets back if they combined their shares?
1. Adding 3
2. Subtracting 3
3. Multiplying by 3
4. Dividing by 3
6. What is the inverse operation used to solve: $x - 7 = 10$?
1. Adding 7 to both sides
2. Subtracting 7 from both sides
3. Multiplying both sides by 7
4. Dividing both sides by 7
7. What is the inverse operation used to solve: $3 \times x = 15$?
1. Adding 3 to both sides
2. Subtracting 3 from both sides
3. Multiplying both sides by 3
4. Dividing both sides by 3