Evaluate The Expression And Simplify If Possible:${ -10 \frac{4}{7} - (3) }$

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Introduction

In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Evaluating an expression involves substituting values for variables and performing the operations in the correct order. Simplifying an expression, on the other hand, involves rewriting it in a more compact or easier-to-understand form. In this article, we will evaluate the expression −1047−(3)-10 \frac{4}{7} - (3) and simplify it if possible.

Understanding the Expression

The given expression is −1047−(3)-10 \frac{4}{7} - (3). This expression consists of two parts: a mixed number and a negative integer. The mixed number is −1047-10 \frac{4}{7}, which represents a combination of a whole number and a fraction. The negative integer is −3-3.

Evaluating the Expression

To evaluate the expression, we need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate the expression inside the parentheses.
  2. Exponents: Evaluate any exponential expressions.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

In this case, we only have a subtraction operation, so we can proceed to evaluate it.

Subtracting the Negative Integer

To subtract a negative integer, we need to add its positive counterpart. Therefore, we can rewrite the expression as:

−1047+3-10 \frac{4}{7} + 3

Converting the Mixed Number to an Improper Fraction

To simplify the expression, we need to convert the mixed number to an improper fraction. To do this, we multiply the whole number by the denominator and add the numerator:

−1047=−70+47=−667-10 \frac{4}{7} = \frac{-70 + 4}{7} = \frac{-66}{7}

Adding the Positive Integer

Now that we have converted the mixed number to an improper fraction, we can add the positive integer:

−667+3\frac{-66}{7} + 3

Finding a Common Denominator

To add the improper fraction and the positive integer, we need to find a common denominator. The least common multiple of 7 and 1 is 7, so we can rewrite the positive integer as:

3=2173 = \frac{21}{7}

Adding the Improper Fraction and the Positive Integer

Now that we have a common denominator, we can add the improper fraction and the positive integer:

−667+217=−457\frac{-66}{7} + \frac{21}{7} = \frac{-45}{7}

Simplifying the Expression

The expression −457\frac{-45}{7} is already in its simplest form, so we cannot simplify it further.

Conclusion

In this article, we evaluated the expression −1047−(3)-10 \frac{4}{7} - (3) and simplified it if possible. We followed the order of operations, converted the mixed number to an improper fraction, and added the positive integer. The final simplified expression is −457\frac{-45}{7}.

Frequently Asked Questions

  • Q: What is the order of operations? A: The order of operations is PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
  • Q: How do I convert a mixed number to an improper fraction? A: To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator.
  • Q: How do I add an improper fraction and a positive integer? A: To add an improper fraction and a positive integer, find a common denominator and add the numerators.

Further Reading

References

Introduction

In our previous article, we evaluated the expression −1047−(3)-10 \frac{4}{7} - (3) and simplified it if possible. In this article, we will answer some frequently asked questions related to evaluating and simplifying expressions.

Q&A

Q: What is the order of operations?

A: The order of operations is PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I evaluate an expression with multiple operations?

A: To evaluate an expression with multiple operations, follow the order of operations. First, evaluate any expressions inside parentheses. Then, evaluate any exponential expressions. Next, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an expression?

A: To simplify an expression, look for any opportunities to combine like terms. Combine any terms that have the same variable and coefficient. Also, look for any opportunities to rewrite the expression in a more compact or easier-to-understand form.

Q: What is a like term?

A: A like term is a term that has the same variable and coefficient. For example, 2x and 4x are like terms because they both have the variable x and the coefficient 2 and 4 respectively.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the terms. For example, 2x + 4x = 6x.

Q: What is an improper fraction?

A: An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, 5/2 is an improper fraction.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. For example, 2 1/2 = (2 x 2) + 1 = 5/2.

Q: How do I add an improper fraction and a positive integer?

A: To add an improper fraction and a positive integer, find a common denominator and add the numerators. For example, 5/2 + 3 = (5 + 6)/2 = 11/2.

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers. A decimal is a way of expressing a fraction as a number with a point separating the whole number part from the fractional part.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, divide the numerator by the denominator. For example, 1/2 = 0.5.

Q: How do I convert a decimal to a fraction?

A: To convert a decimal to a fraction, express the decimal as a ratio of two numbers. For example, 0.5 = 1/2.

Conclusion

In this article, we answered some frequently asked questions related to evaluating and simplifying expressions. We covered topics such as the order of operations, simplifying expressions, like terms, improper fractions, and converting between fractions and decimals.

Frequently Asked Questions

  • Q: What is the order of operations? A: The order of operations is PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
  • Q: How do I simplify an expression? A: To simplify an expression, look for any opportunities to combine like terms and rewrite the expression in a more compact or easier-to-understand form.
  • Q: What is a like term? A: A like term is a term that has the same variable and coefficient.
  • Q: How do I combine like terms? A: To combine like terms, add or subtract the coefficients of the terms.

Further Reading

References