Problem 27 - Fundamentals of Mathematics

Question

Convert each improper fraction to a mixed number. $$ \frac{5}{4} $$

Step-by-Step Solution

Answer

The mixed number is \( 1\frac{1}{4} \).

Step 1: Understand the Improper Fraction

An improper fraction is when the numerator (top part) is greater than or equal to the denominator (bottom part). In this case, \( \frac{5}{4} \) is an improper fraction because 5 is greater than 4.

Step 2: Divide the Numerator by the Denominator

To convert an improper fraction to a mixed number, divide the numerator by the denominator. Here we divide 5 by 4, which gives us 1 as the whole number part and a remainder of 1, because 5 divided by 4 equals 1 with a remainder of 1.

Step 3: Express the Remainder as a Fraction

The remainder (1) becomes the numerator of the fraction part of the mixed number, while the denominator remains the same (4). This gives us the fraction \( \frac{1}{4} \).

Step 4: Combine the Whole Number and Fraction

Combine the whole number part from Step 2 with the fraction from Step 3 to form the mixed number. So, for \( \frac{5}{4} \), the mixed number is \( 1\frac{1}{4} \).

Key Concepts

mixed numbers

Mixed numbers are a unique way to express a number that lies between whole numbers. When dealing with improper fractions, converting them into mixed numbers can provide clarity.
Imagine you have a pie that is cut into four pieces and you have five such pieces. To understand how many whole pies and additional slices you have, a mixed number is helpful.
A mixed number consists of two parts:

• A whole number
• A proper fraction (where the numerator is smaller than the denominator)

So, in our example where we converted the improper fraction \(\frac{5}{4}\), it becomes the mixed number \(1\frac{1}{4}\). This tells us we have one whole pie and one additional piece out of four.

numerator and denominator

To start understanding any fraction, it's essential to know the roles played by the numerator and the denominator. In the fraction \(\frac{a}{b}\),
- the numerator \(a\) represents how many parts we have.- the denominator \(b\) tells us into how many parts the whole is divided.
In improper fractions, such as \(\frac{5}{4}\), the numerator (5) is larger than the denominator (4), indicating more parts than a single whole, which is why conversion is required to better understand the quantity.

division process

Converting an improper fraction often requires the division process. This step is vital as it breaks down the number into comprehensible segments, namely whole numbers and a remaining fraction part.
Here's how it works:

• Divide the numerator by the denominator: For \(\frac{5}{4}\), you divide 5 by 4.
• Find the quotient: The quotient is 1, which forms the whole number part of the mixed number.
• Determine the remainder: The remainder is 1, which tells us how much more we have to account for in a fraction.

Understanding this division helps in writing down a mixed number correctly and confidently.

fractions conversion steps

The conversion of improper fractions to mixed numbers is a methodical process that ensures clarity and accuracy. Here are the steps simplified:
1. **Identify the Improper Fraction**: First, identify your improper fraction. Here, it’s \(\frac{5}{4}\).2. **Carry Out the Division**: Divide the numerator (5) by the denominator (4). The result is 1 with a remainder of 1.3. **Construct the Fraction Part**: The remainder (1) forms the numerator of the new fractional part, while the denominator remains the same, making it \(\frac{1}{4}\).4. **Combine Into Mixed Number**: Finally, combine the whole number (1) and the fraction \(\frac{1}{4}\) to find \(1\frac{1}{4}\).
Following these steps ensures that you achieve precision in conversion and master the concept over time.