Evaluate The Expression:$\[ -5 \frac{1}{4} \times (-4) \\]

Introduction

In mathematics, evaluating expressions is a fundamental concept that involves simplifying mathematical statements to obtain a final value. When dealing with expressions that involve fractions and negative numbers, it's essential to understand the rules of arithmetic operations to arrive at the correct solution. In this article, we will evaluate the expression $-5 \frac{1}{4} \times (-4)$, which involves multiplying a mixed number by a negative integer.

Understanding the Expression

The given expression is $-5 \frac{1}{4} \times (-4)$. To evaluate this expression, we need to understand the concept of mixed numbers and how to multiply them by negative integers. A mixed number is a combination of a whole number and a fraction, represented as $a \frac{b}{c}$. In this case, the mixed number is $-5 \frac{1}{4}$, where $-5$ is the whole number part and $\frac{1}{4}$ is the fractional part.

Multiplying Mixed Numbers by Negative Integers

When multiplying a mixed number by a negative integer, we need to follow the rules of arithmetic operations. The product of two negative numbers is positive, and the product of a negative number and a positive number is negative. In this case, we have a negative mixed number being multiplied by a negative integer.

Step-by-Step Solution

To evaluate the expression $-5 \frac{1}{4} \times (-4)$, we can follow these steps:

1. Convert the mixed number to an improper fraction: To make the multiplication easier, we can convert the mixed number $-5 \frac{1}{4}$ to an improper fraction. To do this, we multiply the whole number part by the denominator and add the numerator: $-5 \times 4 + 1 = -20 + 1 = -19$. So, the mixed number $-5 \frac{1}{4}$ is equivalent to the improper fraction $-\frac{19}{4}$.
2. Multiply the improper fraction by the negative integer: Now that we have the mixed number in improper fraction form, we can multiply it by the negative integer $-4$. When multiplying a fraction by a negative integer, we multiply the numerator by the negative integer and keep the denominator the same: $-\frac{19}{4} \times (-4) = \frac{19 \times (-4)}{4}$.
3. Simplify the expression: To simplify the expression, we can multiply the numerator and denominator by $-1$ to get rid of the negative sign in the numerator: $\frac{19 \times (-4)}{4} = \frac{-19 \times 4}{4} = -19$.

Conclusion

In conclusion, the expression $-5 \frac{1}{4} \times (-4)$ can be evaluated by converting the mixed number to an improper fraction, multiplying the improper fraction by the negative integer, and simplifying the expression. The final value of the expression is $-19$.

Frequently Asked Questions

• Q: What is the product of a negative mixed number and a negative integer? A: The product of a negative mixed number and a negative integer is positive.
• 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 part by the denominator and add the numerator.
• Q: What is the final value of the expression $-5 \frac{1}{4} \times (-4)$? A: The final value of the expression $-5 \frac{1}{4} \times (-4)$ is $-19$.

Final Answer

The final answer is $\boxed{-19}$.

Introduction

In our previous article, we evaluated the expression $-5 \frac{1}{4} \times (-4)$, which involved multiplying a mixed number by a negative integer. In this article, we will answer some frequently asked questions related to evaluating expressions with mixed numbers and negative integers.

Q&A

Q: What is the product of a positive mixed number and a negative integer?

A: The product of a positive mixed number and a negative integer is negative. For example, $3 \frac{1}{4} \times (-2) = -6 \frac{1}{2}$.

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 part by the denominator and add the numerator. For example, $2 \frac{3}{4} = 2 \times 4 + 3 = 11$. So, the mixed number $2 \frac{3}{4}$ is equivalent to the improper fraction $\frac{11}{4}$.

Q: What is the product of two negative mixed numbers?

A: The product of two negative mixed numbers is positive. For example, $-3 \frac{1}{4} \times (-2 \frac{1}{2}) = 7 \frac{1}{4}$.

Q: How do I simplify an expression with a negative mixed number?

A: To simplify an expression with a negative mixed number, convert the mixed number to an improper fraction and then simplify the expression. For example, $-2 \frac{1}{4} \times 3 = -\frac{9}{4} \times 3 = -\frac{27}{4}$.

Q: What is the final value of the expression $-3 \frac{1}{2} \times (-2 \frac{1}{4})$?

A: To evaluate this expression, we need to convert the mixed numbers to improper fractions and then multiply them. $-3 \frac{1}{2} = -\frac{7}{2}$ and $-2 \frac{1}{4} = -\frac{9}{4}$. So, the expression becomes $-\frac{7}{2} \times -\frac{9}{4} = \frac{63}{8}$.

Q: How do I evaluate an expression with a negative mixed number and a fraction?

A: To evaluate an expression with a negative mixed number and a fraction, convert the mixed number to an improper fraction and then multiply it by the fraction. For example, $-2 \frac{1}{4} \times \frac{3}{4} = -\frac{9}{4} \times \frac{3}{4} = -\frac{27}{16}$.

Conclusion

In conclusion, evaluating expressions with mixed numbers and negative integers requires a clear understanding of the rules of arithmetic operations. By converting mixed numbers to improper fractions and simplifying expressions, we can arrive at the correct solution. We hope this Q&A article has provided you with a better understanding of how to evaluate expressions with mixed numbers and negative integers.

Frequently Asked Questions

• Q: What is the product of a negative mixed number and a fraction? A: The product of a negative mixed number and a fraction is negative.
• Q: How do I convert a mixed number to a decimal? A: To convert a mixed number to a decimal, divide the numerator by the denominator and add the whole number part.
• Q: What is the final value of the expression $-4 \frac{1}{2} \times (-3 \frac{1}{4})$? A: The final value of the expression $-4 \frac{1}{2} \times (-3 \frac{1}{4})$ is $13 \frac{1}{8}$.

Final Answer

The final answer is $\boxed{13 \frac{1}{8}}$.