Which Improper Fraction is equal to the mixed number 3 3/8
The Correct Answer and Explanation is :
To convert the mixed number ( 3 \frac{3}{8} ) into an improper fraction, follow these steps:
Step 1: Understand the Components of the Mixed Number
A mixed number consists of two parts:
- The whole number: ( 3 )
- The fractional part: ( \frac{3}{8} )
Step 2: Convert the Whole Number to a Fraction
To convert the whole number ( 3 ) into a fraction with the same denominator as the fractional part, multiply the whole number by the denominator of the fraction.
- The denominator of the fractional part is ( 8 ), so:
[
3 = \frac{3 \times 8}{8} = \frac{24}{8}
]
Thus, the whole number ( 3 ) becomes ( \frac{24}{8} ).
Step 3: Add the Fractional Part
Now, add the fractional part ( \frac{3}{8} ) to the whole number fraction ( \frac{24}{8} ):
[
\frac{24}{8} + \frac{3}{8} = \frac{24 + 3}{8} = \frac{27}{8}
]
Final Answer:
The improper fraction equivalent of the mixed number ( 3 \frac{3}{8} ) is ( \frac{27}{8} ).
Explanation:
An improper fraction is a fraction where the numerator (the top number) is equal to or greater than the denominator (the bottom number). In the case of the mixed number ( 3 \frac{3}{8} ), we converted the whole number into a fraction with the same denominator as the fractional part. After combining the whole and fractional parts, we obtained the improper fraction ( \frac{27}{8} ).
This process of converting a mixed number to an improper fraction is useful in mathematical operations, particularly when adding or subtracting fractions, as it’s easier to work with improper fractions than mixed numbers.