Which of the following is equivalent to 2 2/5 ?
The Correct Answer and Explanation is:
To convert the mixed fraction ( 2 \frac{2}{5} ) to an improper fraction or a decimal, follow these steps:
Step 1: Understand the mixed number
A mixed number consists of a whole number part and a fractional part. In this case, ( 2 \frac{2}{5} ) has:
- Whole number: 2
- Fractional part: ( \frac{2}{5} )
Step 2: Convert the mixed number to an improper fraction
To convert a mixed number into an improper fraction, you need to multiply the whole number by the denominator of the fractional part and then add the numerator. The formula for this conversion is:
[
\text{Improper fraction} = \left( \text{Whole number} \times \text{Denominator} \right) + \text{Numerator}
]
For ( 2 \frac{2}{5} ):
- Multiply the whole number (2) by the denominator (5):
[
2 \times 5 = 10
] - Then, add the numerator (2) to this result:
[
10 + 2 = 12
] - So, ( 2 \frac{2}{5} = \frac{12}{5} ).
Thus, the improper fraction equivalent of ( 2 \frac{2}{5} ) is ( \frac{12}{5} ).
Step 3: Convert the improper fraction to a decimal
To convert ( \frac{12}{5} ) to a decimal, divide the numerator by the denominator:
[
\frac{12}{5} = 12 \div 5 = 2.4
]
So, ( 2 \frac{2}{5} ) is equivalent to ( 2.4 ) in decimal form.
Conclusion
The mixed number ( 2 \frac{2}{5} ) can be expressed as:
- Improper fraction: ( \frac{12}{5} )
- Decimal: 2.4
This process of converting mixed numbers to improper fractions and decimals is helpful in various mathematical applications, such as when performing arithmetic operations or making comparisons.