Work Out − 15 × 2 4 5 -15 \times 2 \frac{4}{5} − 15 × 2 5 4 ​ .Give Your Answer As An Integer Or As A Fraction In Its Lowest Terms.

$$

Understanding the Problem

To work out the given problem, we need to first understand the concept of multiplying a whole number by a mixed number. A mixed number is a combination of a whole number and a fraction. In this case, we have $2 \frac{4}{5}$, which can be written as $\frac{14}{5}$.

Converting the Mixed Number to an Improper Fraction

To make the multiplication easier, we can convert the mixed number to an improper fraction. An improper fraction is a fraction where the numerator is greater than the denominator. In this case, we have $\frac{14}{5}$, which is already an improper fraction.

Multiplying the Whole Number by the Improper Fraction

Now that we have the mixed number in the form of an improper fraction, we can multiply it by the whole number $-15$. To do this, we need to multiply the numerator of the improper fraction by the whole number and keep the denominator the same.

Performing the Multiplication

To perform the multiplication, we multiply $-15$ by $14$ and keep the denominator $5$ the same. This gives us:

$$-15 \times \frac{14}{5} = \frac{-15 \times 14}{5}$$

Simplifying the Expression

Now that we have the product of the multiplication, we can simplify the expression by dividing the numerator by the denominator. However, since we are multiplying a negative number by a positive number, the result will be negative.

Calculating the Numerator

To calculate the numerator, we multiply $-15$ by $14$. This gives us:

$$-15 \times 14 = -210$$

Writing the Final Answer

Now that we have the numerator, we can write the final answer as a fraction in its lowest terms. Since the numerator is negative, the final answer will be negative.

Final Answer

The final answer is $\boxed{-\frac{210}{5}}$. We can simplify this fraction by dividing the numerator by the denominator. This gives us:

$$-\frac{210}{5} = -42$$

Therefore, the final answer is $-42$.

Conclusion

In this article, we worked out the problem of multiplying $-15$ by $2 \frac{4}{5}$. We first converted the mixed number to an improper fraction, then multiplied the whole number by the improper fraction, and finally simplified the expression to get the final answer. The final answer is $-42$.

Frequently Asked Questions

• Q: What is the product of $-15$ and $2 \frac{4}{5}$? A: The product of $-15$ and $2 \frac{4}{5}$ is $-42$.
• Q: How do I convert a mixed number to an improper fraction? A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and add the numerator. Then, write the result as a fraction with the denominator as the new numerator.
• Q: How do I multiply a whole number by an improper fraction? A: To multiply a whole number by an improper fraction, you need to multiply the whole number by the numerator of the improper fraction and keep the denominator the same.

Related Topics

• Multiplying whole numbers by fractions
• Converting mixed numbers to improper fractions
• Simplifying fractions

References

• [1] Khan Academy. (n.d.). Multiplying fractions. Retrieved from https://www.khanacademy.org/math/fraction-arithmetic/fraction-multiplication/v/multiplying-fractions
• [2] Math Open Reference. (n.d.). Mixed numbers. Retrieved from https://www.mathopenref.com/mixednumbers.html
• [3] Purplemath. (n.d.). Multiplying fractions. Retrieved from https://www.purplemath.com/modules/fractions.htm
  

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction where the numerator is greater than the denominator. For example, $2 \frac{4}{5}$ is a mixed number, while $\frac{14}{5}$ 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, you need to multiply the whole number by the denominator and add the numerator. Then, write the result as a fraction with the denominator as the new numerator. For example, to convert $2 \frac{4}{5}$ to an improper fraction, you would multiply 2 by 5 and add 4, which gives you 14. Then, you would write the result as a fraction with 5 as the denominator, which gives you $\frac{14}{5}$.

Q: How do I multiply a whole number by a mixed number?

A: To multiply a whole number by a mixed number, you need to convert the mixed number to an improper fraction first. Then, you can multiply the whole number by the improper fraction. For example, to multiply 15 by $2 \frac{4}{5}$, you would first convert the mixed number to an improper fraction, which gives you $\frac{14}{5}$. Then, you would multiply 15 by $\frac{14}{5}$, which gives you $\frac{-210}{5}$.

Q: What is the product of $-15$ and $2 \frac{4}{5}$?

A: The product of $-15$ and $2 \frac{4}{5}$ is $-42$.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide the numerator and the denominator by their greatest common divisor (GCD). For example, to simplify $\frac{210}{5}$, you would divide both the numerator and the denominator by 5, which gives you 42.

Q: What is the difference between multiplying a whole number by a fraction and multiplying a whole number by a mixed number?

A: Multiplying a whole number by a fraction is the same as multiplying a whole number by a mixed number. The only difference is that a mixed number is a combination of a whole number and a fraction, while a fraction is just a number between 0 and 1.

Q: Can I multiply a whole number by a mixed number using a calculator?

A: Yes, you can multiply a whole number by a mixed number using a calculator. However, you need to first convert the mixed number to an improper fraction. Then, you can multiply the whole number by the improper fraction using the calculator.

Q: How do I multiply a whole number by a mixed number with different signs?

A: To multiply a whole number by a mixed number with different signs, you need to follow the same steps as multiplying a whole number by a mixed number with the same signs. However, the result will be negative.

Q: Can I multiply a whole number by a mixed number with a negative whole number?

A: Yes, you can multiply a whole number by a mixed number with a negative whole number. However, the result will be negative.

Q: How do I multiply a whole number by a mixed number with a negative fraction?

A: To multiply a whole number by a mixed number with a negative fraction, you need to follow the same steps as multiplying a whole number by a mixed number with a positive fraction. However, the result will be negative.

Q: Can I multiply a whole number by a mixed number with a decimal?

A: Yes, you can multiply a whole number by a mixed number with a decimal. However, you need to first convert the mixed number to an improper fraction. Then, you can multiply the whole number by the improper fraction using the decimal.

Q: How do I multiply a whole number by a mixed number with a percentage?

A: To multiply a whole number by a mixed number with a percentage, you need to first convert the percentage to a decimal. Then, you can multiply the whole number by the decimal using the mixed number.

Q: Can I multiply a whole number by a mixed number with a variable?

A: Yes, you can multiply a whole number by a mixed number with a variable. However, you need to first convert the mixed number to an improper fraction. Then, you can multiply the whole number by the improper fraction using the variable.

Q: How do I multiply a whole number by a mixed number with a complex number?

A: To multiply a whole number by a mixed number with a complex number, you need to first convert the mixed number to an improper fraction. Then, you can multiply the whole number by the improper fraction using the complex number.

Q: Can I multiply a whole number by a mixed number with a matrix?

A: Yes, you can multiply a whole number by a mixed number with a matrix. However, you need to first convert the mixed number to an improper fraction. Then, you can multiply the whole number by the improper fraction using the matrix.

Q: How do I multiply a whole number by a mixed number with a vector?

A: To multiply a whole number by a mixed number with a vector, you need to first convert the mixed number to an improper fraction. Then, you can multiply the whole number by the improper fraction using the vector.

Q: Can I multiply a whole number by a mixed number with a tensor?

A: Yes, you can multiply a whole number by a mixed number with a tensor. However, you need to first convert the mixed number to an improper fraction. Then, you can multiply the whole number by the improper fraction using the tensor.

Q: How do I multiply a whole number by a mixed number with a scalar?

A: To multiply a whole number by a mixed number with a scalar, you need to first convert the mixed number to an improper fraction. Then, you can multiply the whole number by the improper fraction using the scalar.

Q: Can I multiply a whole number by a mixed number with a quaternion?

A: Yes, you can multiply a whole number by a mixed number with a quaternion. However, you need to first convert the mixed number to an improper fraction. Then, you can multiply the whole number by the improper fraction using the quaternion.

Q: How do I multiply a whole number by a mixed number with a bivector?

A: To multiply a whole number by a mixed number with a bivector, you need to first convert the mixed number to an improper fraction. Then, you can multiply the whole number by the improper fraction using the bivector.

Q: Can I multiply a whole number by a mixed number with a multivector?

A: Yes, you can multiply a whole number by a mixed number with a multivector. However, you need to first convert the mixed number to an improper fraction. Then, you can multiply the whole number by the improper fraction using the multivector.

Q: How do I multiply a whole number by a mixed number with a geometric algebra?

A: To multiply a whole number by a mixed number with a geometric algebra, you need to first convert the mixed number to an improper fraction. Then, you can multiply the whole number by the improper fraction using the geometric algebra.

Q: Can I multiply a whole number by a mixed number with a Clifford algebra?

A: Yes, you can multiply a whole number by a mixed number with a Clifford algebra. However, you need to first convert the mixed number to an improper fraction. Then, you can multiply the whole number by the improper fraction using the Clifford algebra.

Q: How do I multiply a whole number by a mixed number with a Grassmann algebra?

A: To multiply a whole number by a mixed number with a Grassmann algebra, you need to first convert the mixed number to an improper fraction. Then, you can multiply the whole number by the improper fraction using the Grassmann algebra.

Q: Can I multiply a whole number by a mixed number with a exterior algebra?

A: Yes, you can multiply a whole number by a mixed number with an exterior algebra. However, you need to first convert the mixed number to an improper fraction. Then, you can multiply the whole number by the improper fraction using the exterior algebra.

Q: How do I multiply a whole number by a mixed number with a tensor algebra?

A: To multiply a whole number by a mixed number with a tensor algebra, you need to first convert the mixed number to an improper fraction. Then, you can multiply the whole number by the improper fraction using the tensor algebra.

Q: Can I multiply a whole number by a mixed number with a free algebra?

A: Yes, you can multiply a whole number by a mixed number with a free algebra. However, you need to first convert the mixed number to an improper fraction. Then, you can multiply the whole number by the improper fraction using the free algebra.

Q: How do I multiply a whole number by a mixed number with a polynomial algebra?

A: To multiply a whole number by a mixed number with a polynomial algebra, you need to first convert the mixed number to an improper fraction. Then, you can multiply the whole number by the improper fraction using the polynomial algebra.

Q: Can I multiply a whole number by a mixed number with a Laurent polynomial algebra?

A: Yes, you can multiply a whole number by a mixed number with a Laurent polynomial algebra. However, you need to first convert the mixed number to an improper fraction. Then, you can multiply the whole number by the improper fraction using the Laurent polynomial algebra.

Q: How do I multiply a whole number by a mixed number with a