Work Out 24 5 × 15 4 \frac{24}{5} \times \frac{15}{4} 5 24 ​ × 4 15 ​ .Give Your Answer As A Whole Number Or As A Fraction In Its Lowest Terms.

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Introduction

In this article, we will be working out the product of two fractions, $\frac{24}{5}$ and $\frac{15}{4}$. We will first multiply the numerators and denominators separately, and then simplify the resulting fraction to its lowest terms.

Multiplying the Numerators and Denominators

To multiply two fractions, we simply multiply the numerators together and the denominators together. In this case, we have:

$$\frac{24}{5} \times \frac{15}{4} = \frac{24 \times 15}{5 \times 4}$$

Calculating the Numerator and Denominator

Now, let's calculate the numerator and denominator separately.

Numerator

The numerator is the product of 24 and 15.

$$24 \times 15 = 360$$

Denominator

The denominator is the product of 5 and 4.

$$5 \times 4 = 20$$

Simplifying the Fraction

Now that we have the numerator and denominator, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).

Greatest Common Divisor (GCD)

To find the GCD of 360 and 20, we can use the Euclidean algorithm or simply list the factors of each number.

The factors of 360 are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

The factors of 20 are: 1, 2, 4, 5, 10, 20

The greatest common divisor of 360 and 20 is 20.

Simplifying the Fraction

Now that we have the GCD, we can simplify the fraction by dividing both the numerator and denominator by 20.

$$\frac{360}{20} = 18$$

$$\frac{20}{20} = 1$$

So, the simplified fraction is $\frac{18}{1}$, which is equal to the whole number 18.

Conclusion

In this article, we worked out the product of two fractions, $\frac{24}{5}$ and $\frac{15}{4}$. We first multiplied the numerators and denominators separately, and then simplified the resulting fraction to its lowest terms. The final answer is $\boxed{18}$.

Frequently Asked Questions

• What is the product of $\frac{24}{5}$ and $\frac{15}{4}$?
• How do you simplify a fraction?
• What is the greatest common divisor (GCD) of two numbers?

Step-by-Step Solution

1. Multiply the numerators together: $24 \times 15 = 360$
2. Multiply the denominators together: $5 \times 4 = 20$
3. Simplify the fraction by dividing both the numerator and denominator by their GCD (20)
4. The simplified fraction is $\frac{18}{1}$, which is equal to the whole number 18.

Related Topics

• Multiplying fractions
• Simplifying fractions
• Greatest common divisor (GCD)

Further Reading

• Wikipedia: Fraction
• Math Is Fun: Fractions
• Khan Academy: Fractions
  

Introduction

Multiplying fractions can be a bit tricky, but with the right techniques and understanding, it can be a breeze. In this article, we will answer some of the most frequently asked questions about multiplying fractions.

Q: What is the product of $\frac{24}{5}$ and $\frac{15}{4}$?

A: The product of $\frac{24}{5}$ and $\frac{15}{4}$ is $\frac{360}{20}$, which simplifies to $\frac{18}{1}$ or the whole number 18.

Q: How do you multiply fractions?

A: To multiply fractions, you simply multiply the numerators together and the denominators together. For example, to multiply $\frac{24}{5}$ and $\frac{15}{4}$, you would multiply the numerators (24 and 15) and the denominators (5 and 4) separately.

Q: What is the greatest common divisor (GCD) of two numbers?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder. For example, the GCD of 360 and 20 is 20.

Q: How do you simplify a fraction?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD. For example, to simplify $\frac{360}{20}$, you would divide both numbers by 20 to get $\frac{18}{1}$.

Q: What is the difference between multiplying fractions and adding fractions?

A: Multiplying fractions involves multiplying the numerators and denominators together, while adding fractions involves adding the numerators together and keeping the same denominator. For example, to add $\frac{1}{2}$ and $\frac{1}{2}$, you would add the numerators (1 + 1) and keep the same denominator (2) to get $\frac{2}{2}$, which simplifies to 1.

Q: Can you multiply a fraction by a whole number?

A: Yes, you can multiply a fraction by a whole number by multiplying the numerator of the fraction by the whole number. For example, to multiply $\frac{1}{2}$ by 3, you would multiply the numerator (1) by 3 to get $\frac{3}{2}$.

Q: What is the product of $\frac{1}{2}$ and $\frac{3}{4}$?

A: The product of $\frac{1}{2}$ and $\frac{3}{4}$ is $\frac{3}{8}$.

Q: How do you multiply mixed numbers?

A: To multiply mixed numbers, you need to convert the mixed numbers to improper fractions first. For example, to multiply 2 $\frac{1}{2}$ and 3 $\frac{1}{4}$, you would convert the mixed numbers to improper fractions (2 $\frac{1}{2}$ = $\frac{5}{2}$ and 3 $\frac{1}{4}$ = $\frac{13}{4}$) and then multiply the fractions together.

Q: Can you multiply a fraction by a decimal?

A: Yes, you can multiply a fraction by a decimal by converting the decimal to a fraction first. For example, to multiply $\frac{1}{2}$ by 0.5, you would convert the decimal to a fraction (0.5 = $\frac{1}{2}$) and then multiply the fractions together.

Q: What is the product of $\frac{1}{2}$ and 0.5?

A: The product of $\frac{1}{2}$ and 0.5 is $\frac{1}{2}$.

Conclusion

Multiplying fractions can be a bit tricky, but with the right techniques and understanding, it can be a breeze. We hope that this article has answered some of the most frequently asked questions about multiplying fractions and has provided you with a better understanding of the subject.

Related Topics

• Adding fractions
• Subtracting fractions
• Dividing fractions
• Greatest common divisor (GCD)
• Improper fractions
• Mixed numbers

Further Reading

• Wikipedia: Fraction
• Math Is Fun: Fractions
• Khan Academy: Fractions