Change the mixed fraction 1 1/5 to a percent
The Correct Answer and Explanation is :
To convert the mixed fraction (1 \frac{1}{5}) to a percentage:
- Convert the mixed fraction to an improper fraction:
- (1 \frac{1}{5} = \frac{6}{5}).
- Convert the improper fraction to a decimal:
- Divide the numerator (6) by the denominator (5):
(6 \div 5 = 1.2).
- Convert the decimal to a percentage:
- Multiply the decimal by 100:
(1.2 \times 100 = 120\%).
Thus, (1 \frac{1}{5}) is equal to 120%.
Explanation:
Percentages are a way of expressing a number as a fraction of 100. The steps to convert a mixed fraction to a percentage involve three main conversions:
Step 1: Mixed Fraction to Improper Fraction
A mixed fraction consists of a whole number and a proper fraction. To simplify calculations, it’s converted to an improper fraction. For (1 \frac{1}{5}):
[
1 + \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5}.
]
Step 2: Improper Fraction to Decimal
Fractions are converted to decimals by dividing the numerator by the denominator. Dividing 6 by 5 gives:
[
6 \div 5 = 1.2.
]
Step 3: Decimal to Percentage
To express a decimal as a percentage, multiply it by 100. Since percentages are fractions out of 100, this operation scales the decimal appropriately:
[
1.2 \times 100 = 120\%.
]
This process works for any fraction or mixed number. In real-life scenarios, percentages are often used to express proportions, growth rates, or comparisons, making it essential to understand these conversions. For instance, (1 \frac{1}{5}) or 120% could represent a 20% increase beyond a whole unit.