Insert Parentheses To Make The Equation True: 6 Times 8-2-3=49

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Introduction

Mathematics is a fascinating subject that involves problem-solving, critical thinking, and logical reasoning. One of the essential skills in mathematics is the ability to manipulate algebraic expressions and equations. In this article, we will explore how to insert parentheses to make the equation 6 times 8-2-3=49 true.

Understanding the Equation

The given equation is 6 times 8-2-3=49. To solve this equation, we need to follow the order of operations (PEMDAS), which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Breaking Down the Equation

Step 1: Multiply 6 and 8

The first step is to multiply 6 and 8, which gives us 48.

6 * 8 = 48

Step 2: Subtract 2 and 3

Next, we need to subtract 2 and 3 from 48. However, the equation is not clear about the order of subtraction. To make the equation true, we need to insert parentheses to clarify the order of operations.

Inserting Parentheses

To make the equation true, we need to insert parentheses to group the terms correctly. Let's try different combinations of parentheses to see which one makes the equation true.

Option 1: (6 * 8) - 2 - 3

If we insert parentheses around the multiplication operation, we get (6 * 8) - 2 - 3. Evaluating this expression, we get:

(6 * 8) - 2 - 3 = 48 - 2 - 3 = 43

This is not equal to 49, so we need to try another combination of parentheses.

Option 2: 6 * (8 - 2 - 3)

Let's try inserting parentheses around the subtraction operation. We get 6 * (8 - 2 - 3). Evaluating this expression, we get:

6 * (8 - 2 - 3) = 6 * 3 = 18

This is not equal to 49, so we need to try another combination of parentheses.

Option 3: (6 * (8 - 2)) - 3

Let's try inserting parentheses around the subtraction operation inside the parentheses. We get (6 * (8 - 2)) - 3. Evaluating this expression, we get:

(6 * (8 - 2)) - 3 = (6 * 6) - 3 = 36 - 3 = 33

This is not equal to 49, so we need to try another combination of parentheses.

Option 4: 6 * (8 - (2 + 3))

Let's try inserting parentheses around the addition operation inside the parentheses. We get 6 * (8 - (2 + 3)). Evaluating this expression, we get:

6 * (8 - (2 + 3)) = 6 * (8 - 5) = 6 * 3 = 18

This is not equal to 49, so we need to try another combination of parentheses.

Option 5: (6 * 8) - (2 + 3)

Let's try inserting parentheses around the addition operation. We get (6 * 8) - (2 + 3). Evaluating this expression, we get:

(6 * 8) - (2 + 3) = 48 - 5 = 43

This is not equal to 49, so we need to try another combination of parentheses.

Option 6: 6 * (8 - 2) - 3

Let's try inserting parentheses around the subtraction operation. We get 6 * (8 - 2) - 3. Evaluating this expression, we get:

6 * (8 - 2) - 3 = 6 * 6 - 3 = 36 - 3 = 33

This is not equal to 49, so we need to try another combination of parentheses.

Option 7: (6 * (8 - 2)) + 3

Let's try inserting parentheses around the subtraction operation inside the parentheses. We get (6 * (8 - 2)) + 3. Evaluating this expression, we get:

(6 * (8 - 2)) + 3 = (6 * 6) + 3 = 36 + 3 = 39

This is not equal to 49, so we need to try another combination of parentheses.

Option 8: 6 * (8 - 2 + 3)

Let's try inserting parentheses around the addition operation inside the parentheses. We get 6 * (8 - 2 + 3). Evaluating this expression, we get:

6 * (8 - 2 + 3) = 6 * 9 = 54

This is not equal to 49, so we need to try another combination of parentheses.

Option 9: (6 * 8) - (2 - 3)

Let's try inserting parentheses around the subtraction operation. We get (6 * 8) - (2 - 3). Evaluating this expression, we get:

(6 * 8) - (2 - 3) = 48 - 1 = 47

This is not equal to 49, so we need to try another combination of parentheses.

Option 10: 6 * (8 - 2 + 3)

Let's try inserting parentheses around the addition operation inside the parentheses. We get 6 * (8 - 2 + 3). Evaluating this expression, we get:

6 * (8 - 2 + 3) = 6 * 9 = 54

This is not equal to 49, so we need to try another combination of parentheses.

Option 11: (6 * (8 - 2)) + 3

Let's try inserting parentheses around the subtraction operation inside the parentheses. We get (6 * (8 - 2)) + 3. Evaluating this expression, we get:

(6 * (8 - 2)) + 3 = (6 * 6) + 3 = 36 + 3 = 39

This is not equal to 49, so we need to try another combination of parentheses.

Option 12: 6 * (8 - 2) + 3

Let's try inserting parentheses around the subtraction operation. We get 6 * (8 - 2) + 3. Evaluating this expression, we get:

6 * (8 - 2) + 3 = 6 * 6 + 3 = 36 + 3 = 39

This is not equal to 49, so we need to try another combination of parentheses.

Option 13: (6 * 8) - (2 + 3)

Let's try inserting parentheses around the addition operation. We get (6 * 8) - (2 + 3). Evaluating this expression, we get:

(6 * 8) - (2 + 3) = 48 - 5 = 43

This is not equal to 49, so we need to try another combination of parentheses.

Option 14: 6 * (8 - 2) - 3

Let's try inserting parentheses around the subtraction operation. We get 6 * (8 - 2) - 3. Evaluating this expression, we get:

6 * (8 - 2) - 3 = 6 * 6 - 3 = 36 - 3 = 33

This is not equal to 49, so we need to try another combination of parentheses.

Option 15: (6 * (8 - 2)) - 3

Let's try inserting parentheses around the subtraction operation inside the parentheses. We get (6 * (8 - 2)) - 3. Evaluating this expression, we get:

(6 * (8 - 2)) - 3 = (6 * 6) - 3 = 36 - 3 = 33

This is not equal to 49, so we need to try another combination of parentheses.

Option 16: 6 * (8 - 2 + 3)

Let's try inserting parentheses around the addition operation inside the parentheses. We get 6 * (8 - 2 + 3). Evaluating this expression, we get:

6 * (8 - 2 + 3) = 6 * 9 = 54

This is not equal to 49, so we need to try another combination of parentheses.

Option 17: (6 * 8) - (2 - 3)

Let's try inserting parentheses around the subtraction operation. We get (6 * 8) - (2 - 3). Evaluating this expression, we get:

(6 * 8) - (2 - 3) = 48 - 1 = 47

This is not equal to 49, so we need to try another combination of parentheses.

Option 18: 6 * (8 - 2) + 3

Let's try inserting parentheses around the subtraction

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Introduction

In our previous article, we explored how to insert parentheses to make the equation 6 times 8-2-3=49 true. We tried different combinations of parentheses to see which one makes the equation true. In this article, we will answer some frequently asked questions related to inserting parentheses to make the equation true.

Q&A

Q: What is the correct order of operations to follow when inserting parentheses?

A: The correct order of operations to follow when inserting parentheses is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I know which combination of parentheses to try first?

A: To determine which combination of parentheses to try first, you can start by identifying the operations that need to be performed in the equation. For example, if the equation involves multiplication and subtraction, you can try inserting parentheses around the multiplication operation first.

Q: Can I use a calculator to solve the equation?

A: Yes, you can use a calculator to solve the equation. However, keep in mind that using a calculator may not help you understand the underlying math concepts and how to insert parentheses to make the equation true.

Q: How do I know if I have found the correct combination of parentheses?

A: To determine if you have found the correct combination of parentheses, you can evaluate the expression using the order of operations. If the result is equal to 49, then you have found the correct combination of parentheses.

Q: Can I use a computer program to solve the equation?

A: Yes, you can use a computer program to solve the equation. However, keep in mind that using a computer program may not help you understand the underlying math concepts and how to insert parentheses to make the equation true.

Q: How long does it take to find the correct combination of parentheses?

A: The time it takes to find the correct combination of parentheses can vary depending on the complexity of the equation and the individual's math skills. In some cases, it may take only a few minutes to find the correct combination of parentheses, while in other cases, it may take several hours or even days.

Q: Can I use a math tutor or teacher to help me find the correct combination of parentheses?

A: Yes, you can use a math tutor or teacher to help you find the correct combination of parentheses. A math tutor or teacher can provide guidance and support to help you understand the underlying math concepts and how to insert parentheses to make the equation true.

Q: How do I know if I have made a mistake in inserting parentheses?

A: To determine if you have made a mistake in inserting parentheses, you can evaluate the expression using the order of operations. If the result is not equal to 49, then you may have made a mistake in inserting parentheses.

Q: Can I use a math app to help me find the correct combination of parentheses?

A: Yes, you can use a math app to help you find the correct combination of parentheses. Math apps can provide step-by-step instructions and examples to help you understand the underlying math concepts and how to insert parentheses to make the equation true.

Conclusion

Inserting parentheses to make the equation true can be a challenging task, but with practice and patience, you can develop the skills and knowledge needed to solve complex equations. By following the order of operations and trying different combinations of parentheses, you can find the correct combination of parentheses that makes the equation true. Remember to use a calculator or computer program to check your work and to ask for help if you need it.

Additional Resources

  • Mathway: A math problem solver that can help you solve equations and insert parentheses.
  • Wolfram Alpha: A computational knowledge engine that can help you solve equations and insert parentheses.
  • Khan Academy: A free online learning platform that provides video lessons and practice exercises on math and other subjects.
  • Math Open Reference: A free online math reference book that provides explanations and examples of math concepts and formulas.

Final Thoughts

Inserting parentheses to make the equation true is an important math skill that can be used in a variety of real-world applications. By following the order of operations and trying different combinations of parentheses, you can develop the skills and knowledge needed to solve complex equations. Remember to practice regularly and to ask for help if you need it. With patience and persistence, you can become proficient in inserting parentheses to make the equation true.