Calculate 8 15 \frac{8}{15} 15 8 ​ Of 3. Give Your Answer As An Improper Fraction In Its Simplest Form.

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Understanding the Problem

To calculate $\frac{8}{15}$ of 3, we need to multiply $\frac{8}{15}$ by 3. This operation involves multiplying a fraction by a whole number, which is a fundamental concept in mathematics.

Multiplying a Fraction by a Whole Number

When we multiply a fraction by a whole number, we can multiply the numerator of the fraction by the whole number. In this case, we will multiply 8 by 3.

Calculating the Product

To calculate the product, we multiply 8 by 3.

8 × 3 = 24

Writing the Product as an Improper Fraction

Now that we have the product, we need to write it as an improper fraction in its simplest form. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Simplifying the Improper Fraction

To simplify the improper fraction, we need to divide the numerator by the denominator.

24 ÷ 15 = 1 with a remainder of 9

Writing the Simplified Improper Fraction

Now that we have the quotient and the remainder, we can write the simplified improper fraction.

$\frac{24}{15}$ = $\frac{1 \times 15 + 9}{15}$

Simplifying the Fraction Further

We can simplify the fraction further by dividing both the numerator and the denominator by their greatest common divisor (GCD).

The GCD of 15 and 9 is 3.

$\frac{15}{3}$ = 5

$\frac{9}{3}$ = 3

Writing the Final Answer

Now that we have simplified the fraction, we can write the final answer.

$\frac{24}{15}$ = $\frac{5 \times 3 + 3}{15}$

Conclusion

In conclusion, to calculate $\frac{8}{15}$ of 3, we multiplied $\frac{8}{15}$ by 3, which gave us 24. We then wrote the product as an improper fraction in its simplest form, which is $\frac{24}{15}$. We simplified the fraction further by dividing both the numerator and the denominator by their GCD, which is 3. The final answer is $\frac{8}{15}$ of 3 = $\frac{16}{15}$.

Final Answer

$\frac{8}{15}$ of 3 = $\frac{16}{15}$

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Frequently Asked Questions

Q: What is the meaning of $\frac{8}{15}$ of 3?

A: $\frac{8}{15}$ of 3 means that we need to multiply $\frac{8}{15}$ by 3. This operation involves multiplying a fraction by a whole number.

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

A: To multiply a fraction by a whole number, we can multiply the numerator of the fraction by the whole number. In this case, we will multiply 8 by 3.

Q: What is the product of 8 and 3?

A: The product of 8 and 3 is 24.

Q: How do I write the product as an improper fraction?

A: To write the product as an improper fraction, we need to write it in the form $\frac{a}{b}$, where $a$ is the product and $b$ is the denominator of the original fraction.

Q: How do I simplify the improper fraction?

A: To simplify the improper fraction, we need to divide the numerator by the denominator. If there is a remainder, we can write the fraction in the form $\frac{a \times b + c}{b}$, where $a$ is the quotient, $b$ is the denominator, and $c$ is the remainder.

Q: What is the simplified form of $\frac{24}{15}$?

A: The simplified form of $\frac{24}{15}$ is $\frac{8}{5}$.

Q: How do I check if the fraction is in its simplest form?

A: To check if the fraction is in its simplest form, we need to find the greatest common divisor (GCD) of the numerator and the denominator. If the GCD is 1, then the fraction is in its simplest form.

Q: What is the GCD of 24 and 15?

A: The GCD of 24 and 15 is 3.

Q: How do I simplify the fraction further?

A: To simplify the fraction further, we can divide both the numerator and the denominator by their GCD.

Q: What is the simplified form of $\frac{24}{15}$ after dividing by 3?

A: The simplified form of $\frac{24}{15}$ after dividing by 3 is $\frac{8}{5}$.

Q: What is the final answer to the problem?

A: The final answer to the problem is $\frac{8}{15}$ of 3 = $\frac{16}{15}$.

Conclusion

In conclusion, calculating $\frac{8}{15}$ of 3 involves multiplying $\frac{8}{15}$ by 3, which gives us 24. We then write the product as an improper fraction in its simplest form, which is $\frac{24}{15}$. We simplify the fraction further by dividing both the numerator and the denominator by their GCD, which is 3. The final answer is $\frac{8}{15}$ of 3 = $\frac{16}{15}$.

Final Answer

$\frac{8}{15}$ of 3 = $\frac{16}{15}$