Simplify The Expression. Write Your Answers Using Integers Or Improper Fractions. \frac{5}{2} G - 5\left(-5 G + \frac{3}{2}\right ]

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Introduction

In this article, we will simplify the given expression using integers or improper fractions. The expression involves addition and subtraction of fractions, as well as multiplication and division of fractions. We will use the rules of arithmetic operations to simplify the expression step by step.

The Given Expression

The given expression is:

52g−5(−5g+32)\frac{5}{2} g - 5\left(-5 g + \frac{3}{2}\right)

Step 1: Distribute the Negative Sign

To simplify the expression, we need to distribute the negative sign inside the parentheses. This means that we need to change the sign of each term inside the parentheses.

52g−5(−5g+32)=52g−(−5⋅−5g+(−5)⋅32)\frac{5}{2} g - 5\left(-5 g + \frac{3}{2}\right) = \frac{5}{2} g - (-5 \cdot -5 g + (-5) \cdot \frac{3}{2})

Step 2: Simplify the Terms Inside the Parentheses

Now, we need to simplify the terms inside the parentheses. We will multiply the terms inside the parentheses.

52g−(−5⋅−5g+(−5)⋅32)=52g−(25g−152)\frac{5}{2} g - (-5 \cdot -5 g + (-5) \cdot \frac{3}{2}) = \frac{5}{2} g - (25 g - \frac{15}{2})

Step 3: Combine Like Terms

Now, we need to combine like terms. We will combine the terms with the same variable.

52g−(25g−152)=52g−25g+152\frac{5}{2} g - (25 g - \frac{15}{2}) = \frac{5}{2} g - 25 g + \frac{15}{2}

Step 4: Simplify the Expression

Now, we need to simplify the expression by combining the like terms.

52g−25g+152=52g−502g+152\frac{5}{2} g - 25 g + \frac{15}{2} = \frac{5}{2} g - \frac{50}{2} g + \frac{15}{2}

Step 5: Combine the Fractions

Now, we need to combine the fractions by finding a common denominator.

52g−502g+152=5−50+152g\frac{5}{2} g - \frac{50}{2} g + \frac{15}{2} = \frac{5 - 50 + 15}{2} g

Step 6: Simplify the Numerator

Now, we need to simplify the numerator by combining the terms.

5−50+152g=−302g\frac{5 - 50 + 15}{2} g = \frac{-30}{2} g

Step 7: Simplify the Fraction

Now, we need to simplify the fraction by dividing the numerator and denominator by their greatest common divisor.

−302g=−302g=−15g\frac{-30}{2} g = -\frac{30}{2} g = -15 g

Conclusion

In this article, we simplified the given expression using integers or improper fractions. We used the rules of arithmetic operations to simplify the expression step by step. The final simplified expression is:

−15g-15 g

Key Takeaways

  • To simplify the expression, we need to distribute the negative sign inside the parentheses.
  • We need to simplify the terms inside the parentheses by multiplying the terms.
  • We need to combine like terms by combining the terms with the same variable.
  • We need to simplify the expression by combining the like terms.
  • We need to combine the fractions by finding a common denominator.
  • We need to simplify the numerator by combining the terms.
  • We need to simplify the fraction by dividing the numerator and denominator by their greatest common divisor.

Final Answer

The final simplified expression is:

Introduction

In our previous article, we simplified the given expression using integers or improper fractions. In this article, we will provide a Q&A guide to help you understand the steps involved in simplifying the expression.

Q: What is the first step in simplifying the expression?

A: The first step in simplifying the expression is to distribute the negative sign inside the parentheses. This means that we need to change the sign of each term inside the parentheses.

Q: How do I simplify the terms inside the parentheses?

A: To simplify the terms inside the parentheses, we need to multiply the terms inside the parentheses. This will help us to combine the like terms.

Q: What is the next step in simplifying the expression?

A: The next step in simplifying the expression is to combine like terms. We need to combine the terms with the same variable.

Q: How do I combine like terms?

A: To combine like terms, we need to add or subtract the coefficients of the terms with the same variable. For example, if we have two terms with the same variable, we can combine them by adding or subtracting their coefficients.

Q: What is the next step in simplifying the expression?

A: The next step in simplifying the expression is to simplify the expression by combining the like terms. We need to combine the terms with the same variable.

Q: How do I simplify the expression?

A: To simplify the expression, we need to combine the like terms and then simplify the resulting expression. We can do this by combining the fractions and then simplifying the numerator and denominator.

Q: What is the final step in simplifying the expression?

A: The final step in simplifying the expression is to simplify the fraction by dividing the numerator and denominator by their greatest common divisor.

Q: What is the final simplified expression?

A: The final simplified expression is:

−15g-15 g

Frequently Asked Questions

  • Q: What is the difference between a like term and a unlike term? A: A like term is a term with the same variable, while a unlike term is a term with a different variable.
  • Q: How do I simplify a fraction? A: To simplify a fraction, we need to divide the numerator and denominator by their greatest common divisor.
  • Q: What is the greatest common divisor (GCD)? A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder.

Conclusion

In this article, we provided a Q&A guide to help you understand the steps involved in simplifying the expression. We covered topics such as distributing the negative sign, simplifying the terms inside the parentheses, combining like terms, and simplifying the expression. We also answered frequently asked questions to help you better understand the concepts.

Key Takeaways

  • To simplify the expression, we need to distribute the negative sign inside the parentheses.
  • We need to simplify the terms inside the parentheses by multiplying the terms.
  • We need to combine like terms by combining the terms with the same variable.
  • We need to simplify the expression by combining the like terms.
  • We need to combine the fractions by finding a common denominator.
  • We need to simplify the numerator by combining the terms.
  • We need to simplify the fraction by dividing the numerator and denominator by their greatest common divisor.

Final Answer

The final simplified expression is:

−15g-15 g