Understanding Fractions: What is 1/4 of 1 1/4?

In mathematics, understanding fractions is a fundamental skill. This article will break down the process of finding what 1/4 of 1 1/4 is, step-by-step. We will discuss the conversion from mixed numbers to improper fractions and how to multiply fractions to find the solution. By the end, you will be able to solve similar problems on your own.

Introduction to Fractions and Mixed Numbers

In mathematics, the word “of” is often used to imply multiplication. So, when we are asked to find 1/4 of 1 1/4, it translates to multiplying the fractions: 1/4 * 1 1/4. However, to simplify this process, it’s easier to first convert the mixed number to an improper fraction.

Converting Mixed Numbers to Improper Fractions

A mixed number, such as 1 1/4, can be converted to an improper fraction by following these steps: First, recognize that 1 whole can be written as a fraction with the same denominator as the fractional part: 1 4/4. Next, add the fraction part: 4/4 1/4 5/4. Thus, 1 1/4 is equivalent to 5/4. Now that we have converted the mixed number to an improper fraction, we can proceed to the next step in solving the problem: finding 1/4 of 1 1/4.

Multiplying Fractions

To find 1/4 of 1 1/4, we now need to multiply the fractions 1/4 and 5/4. The process of multiplying fractions is straightforward: Multiply the numerators: 1 * 5 5 Multiply the denominators: 4 * 4 16 Therefore, 1/4 * 5/4 5/16

Step-by-Step Solution

Let's break down the problem into more detailed steps, making it easy to follow and understand.

Step-by-Step Solution #1

1. Convert 1 1/4 to an improper fraction: 1 1/4 5/4 2. Multiply 1/4 by the improper fraction 5/4: 1/4 * 5/4 5/16 Therefore, 1/4 of 1 1/4 is 5/16.

Step-by-Step Solution #2

1. Rewrite the problem using improper fractions: 1/4 * 5/4 2. Multiply the fractions: 1 * 5 5 and 4 * 4 16 3. The result is 5/16 Thus, 1/4 of 1 1/4 is 5/16.

Alternative Methods

Let's explore two additional methods to find the solution.

Method 1: Convert to Decimals

1. Convert the fraction 1/4 to a decimal: 1/4 0.25 2. Convert the mixed number 1 1/4 to a decimal: 1 1/4 1.25 3. Multiply the decimals: 1.25 * 0.25 0.3125 4. Convert 0.3125 back to a fraction: 5/16 So, 1/4 of 1 1/4 is 5/16.

Method 2: High Common Factor (HCF) Reduction

1. Convert 1 1/4 to an improper fraction: 1 1/4 5/4 2. Multiply 5/4 by 1/4: 5/4 * 1/4 5/16 3. Since 5 and 16 have no common factors other than 1, the fraction 5/16 cannot be reduced further. Thus, 1/4 of 1 1/4 is 5/16.

Conclusion

In conclusion, understanding the concept of fractions, converting mixed numbers to improper fractions, and multiplying fractions are crucial skills for solving problems involving fractions. By following these steps, you can confidently find the solution to any similar problem. The key takeaway is that “of” in math typically means multiplication, and converting mixed numbers to improper fractions simplifies the process of fraction multiplication.

Frequently Asked Questions

Q: How do you convert a mixed number to an improper fraction?

To convert a mixed number to an improper fraction, first, write the whole number part as a fraction with the same denominator as the fractional part. Then add this fraction to the fractional part.

Q: How do you multiply fractions?

To multiply fractions, multiply the numerators together and the denominators together.

Q: How can you convert a decimal to a fraction?

Decimals can be converted to fractions by recognizing the decimal place value. For example, 0.25 is 25/100, which simplifies to 1/4.