Work Out 3 20 \frac{3}{20} 20 3 ​ Of 5. Give Your Answer As A Fraction In Its Simplest Form.

Introduction

Fractions are a fundamental concept in mathematics, and understanding how to work with them is crucial for solving various mathematical problems. In this article, we will focus on solving a specific problem involving fractions, which is to find $\frac{3}{20}$ of 5. We will break down the solution into simple steps and provide a clear explanation of each step.

Understanding the Problem

The problem requires us to find $\frac{3}{20}$ of 5. This means we need to multiply $\frac{3}{20}$ by 5. To solve this problem, we will use the concept of multiplying fractions.

Multiplying Fractions

When multiplying fractions, we simply multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom). The result is a new fraction.

Step 1: Multiply the Numerators

To multiply the numerators, we simply multiply 3 and 5.

3 × 5 = 15

Step 2: Multiply the Denominators

To multiply the denominators, we simply multiply 20 and 1 (since 5 can be written as $\frac{5}{1}$).

20 × 1 = 20

Step 3: Write the Result as a Fraction

Now that we have multiplied the numerators and denominators, we can write the result as a fraction.

$\frac{3}{20} \times 5 = \frac{15}{20}$

Simplifying the Fraction

The fraction $\frac{15}{20}$ can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD). The GCD of 15 and 20 is 5.

$\frac{15}{20} = \frac{15 ÷ 5}{20 ÷ 5} = \frac{3}{4}$

Conclusion

In this article, we solved the problem of finding $\frac{3}{20}$ of 5 by multiplying fractions. We broke down the solution into simple steps and provided a clear explanation of each step. We also simplified the resulting fraction to its simplest form.

Key Takeaways

• To multiply fractions, we multiply the numerators and multiply the denominators.
• The result of multiplying fractions is a new fraction.
• We can simplify a fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).

Practice Problems

Try solving the following problems on your own:

• Find $\frac{2}{3}$ of 9.
• Find $\frac{4}{5}$ of 12.
• Find $\frac{1}{2}$ of 8.

Answer Key

• $\frac{2}{3} \times 9 = \frac{18}{3} = 6$
• $\frac{4}{5} \times 12 = \frac{48}{5} = \frac{48 ÷ 5}{5 ÷ 5} = \frac{9.6}{1}$
• $\frac{1}{2} \times 8 = \frac{8}{2} = 4$

Final Thoughts

Q: What is the rule for multiplying fractions?

A: The rule for multiplying fractions is to multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom). The result is a new fraction.

Q: How do I multiply fractions with different denominators?

A: To multiply fractions with different denominators, you need to find the least common multiple (LCM) of the denominators. Then, multiply the numerators and denominators by the LCM.

Q: What is the least common multiple (LCM)?

A: The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers. For example, the LCM of 2 and 3 is 6.

Q: How do I find the LCM of two numbers?

A: To find the LCM of two numbers, you can list the multiples of each number and find the smallest number that appears in both lists.

Q: Can I simplify a fraction after multiplying it?

A: Yes, you can simplify a fraction after multiplying it by dividing both the numerator and denominator by their greatest common divisor (GCD).

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

A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder. For example, the GCD of 12 and 15 is 3.

Q: How do I find the GCD of two numbers?

A: To find the GCD of two numbers, you can list the factors of each number and find the largest number that appears in both lists.

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

A: Yes, you can multiply a fraction by a whole number by multiplying the numerator by the whole number.

Q: How do I multiply a fraction by a decimal?

A: To multiply a fraction by a decimal, you need to convert the decimal to a fraction and then multiply the fractions.

Q: Can I divide a fraction by a whole number?

A: Yes, you can divide a fraction by a whole number by inverting the fraction and multiplying it by the reciprocal of the whole number.

Q: How do I divide a fraction by a fraction?

A: To divide a fraction by a fraction, you need to invert the second fraction and multiply it by the first fraction.

Q: What are some common mistakes to avoid when multiplying fractions?

A: Some common mistakes to avoid when multiplying fractions include:

• Not multiplying the numerators and denominators correctly
• Not finding the least common multiple (LCM) of the denominators
• Not simplifying the resulting fraction
• Not inverting the fraction when dividing it by a whole number or another fraction

Conclusion

Multiplying fractions can be a challenging concept, but with practice and patience, you can become proficient in solving fraction problems. Remember to multiply the numerators and denominators, find the least common multiple (LCM of the denominators, and simplify the resulting fraction to its simplest form. By avoiding common mistakes and following the steps outlined in this article, you can become a master of multiplying fractions.