Printable one-step equation word problems grade 6 with answers

📚 Understanding One-Step Equation Word Problems

One-step equation word problems are mathematical problems presented in the form of a sentence or short paragraph. They require you to identify an unknown quantity, represent it with a variable, and set up a one-step algebraic equation to solve for that unknown. These problems help bridge the gap between abstract equations and real-world applications.

📜 History and Background

The concept of algebra and solving for unknowns dates back to ancient civilizations, including the Babylonians and Egyptians. However, the formalization of algebraic notation and methods, as we know them today, developed gradually over centuries, with significant contributions from mathematicians in the Islamic world and Europe.

🔑 Key Principles

• 🔍 Identifying the Unknown: Read the word problem carefully to determine what quantity you are trying to find. This will be your variable (e.g., $x$, $y$, $n$).
• ✍️ Translating Words into an Equation: Look for keywords that indicate mathematical operations. For example, 'sum' means addition, 'difference' means subtraction, 'product' means multiplication, and 'quotient' means division.
• ⚖️ Setting up the Equation: Write the equation using the variable and the given information. Ensure the equation represents the relationship described in the word problem.
• ➗ Solving the Equation: Use inverse operations to isolate the variable and find its value. Remember, whatever you do to one side of the equation, you must do to the other side to maintain balance.
• ✔️ Checking Your Answer: Substitute the value you found for the variable back into the original equation to make sure it satisfies the equation. Also, check if the answer makes sense in the context of the word problem.

📝 Real-World Examples

Here are some examples of one-step equation word problems and their solutions:

1. 🍎Problem: Sarah has $x$ apples. After giving 5 apples to her friend, she has 7 apples left. How many apples did Sarah have initially?
   Equation: $x - 5 = 7$
   Solution: $x = 7 + 5 = 12$
   Sarah had 12 apples initially.
2. 📚Problem: John reads $y$ pages each day. After 3 days, he has read 36 pages. How many pages does John read each day?
   Equation: $3y = 36$
   Solution: $y = \frac{36}{3} = 12$
   John reads 12 pages each day.
3. 🍕Problem: Emily divides a pizza into $z$ slices. If each slice is 4 ounces and the pizza weighs 32 ounces, how many slices are there?
   Equation: $4z = 32$
   Solution: $z = \frac{32}{4} = 8$
   There are 8 slices.

💡 Practice Quiz

Solve the following one-step equation word problems:

1. A number $x$ plus 9 is 15. What is the number?
2. A number $y$ minus 6 is 4. What is the number?
3. 3 times a number $z$ is 21. What is the number?
4. A number $a$ divided by 5 is 3. What is the number?
5. After Ben spent $8, he had $11 left. How much money $b$ did Ben have to start with?
6. Lisa baked some cookies. She gave half to her friend and has 9 cookies left. How many cookies $c$ did Lisa bake originally?
7. If you add 12 to a number $d$ the result is 25. What is the number?

Answer Key:

1. 6
2. 10
3. 7
4. 15
5. $19
6. 18
7. 13

✅ Conclusion

Mastering one-step equation word problems is crucial for building a solid foundation in algebra. By understanding the key principles and practicing with various examples, you can confidently solve these types of problems. Remember to read carefully, identify the unknown, translate words into equations, and always check your answer!