115% is equal to which of these fractions?
23/20
Converting Percentage to Fraction Explained
To convert a percentage into a fraction, we use the fact that 'percent' means 'out of 100'. So, any percentage \(P\%\) can be written as the fraction \(\frac{P}{100}\).
In this question, we need to convert 115% into a fraction. Following the rule, we write 115% as:
\(115\% = \frac{115}{100}\)
Now, we have the fraction \(\frac{115}{100}\). This fraction might not be in its simplest form. To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator (115) and the denominator (100) and divide both by it.
Let's find common factors for 115 and 100:
- 115 ends in 5, so it is divisible by 5.
- 100 ends in 0, so it is divisible by 5.
Since both numbers are divisible by 5, we can divide both the numerator and the denominator by 5:
Numerator: \(115 \div 5 = 23\)
Denominator: \(100 \div 5 = 20\)
So, the simplified fraction is:
\(\frac{115}{100} = \frac{115 \div 5}{100 \div 5} = \frac{23}{20}\)
The fraction equivalent of 115% is \(\frac{23}{20}\).
Let's compare this result with the given options:
| Option | Fraction | Matches \(\frac{23}{20}\)? |
|---|---|---|
| 1 | \(\frac{20}{3}\) | No |
| 2 | \(\frac{23}{20}\) | Yes |
| 3 | \(\frac{20}{23}\) | No |
| 4 | \(\frac{3}{20}\) | No |
The fraction \(\frac{23}{20}\) matches Option 2.
Revision Table: Percentage to Fraction Conversion
| Concept | Explanation | Example |
|---|---|---|
| Percentage Definition | A percentage represents a part per hundred. \(P\% = \frac{P}{100}\) | \(75\% = \frac{75}{100}\) |
| Simplifying Fractions | Divide the numerator and denominator by their greatest common divisor (GCD). | \(\frac{75}{100} = \frac{75 \div 25}{100 \div 25} = \frac{3}{4}\) |
Additional Information: Types of Fractions
Fractions can be classified based on their numerator and denominator:
- Proper Fraction: The numerator is less than the denominator (e.g., \(\frac{3}{4}\), \(\frac{7}{10}\)). These represent values less than 1.
- Improper Fraction: The numerator is greater than or equal to the denominator (e.g., \(\frac{5}{4}\), \(\frac{7}{7}\), \(\frac{23}{20}\)). These represent values greater than or equal to 1.
- Mixed Number: A combination of a whole number and a proper fraction (e.g., \(1 \frac{1}{4}\)). Improper fractions can be converted to mixed numbers, and vice versa. For \(\frac{23}{20}\), it can be written as \(1 \frac{3}{20}\) because 23 divided by 20 is 1 with a remainder of 3.
The fraction \(\frac{23}{20}\) is an example of an improper fraction, which makes sense as 115% is greater than 100% (which equals 1).
Important Questions from Percentage
Radha saves 25% of her income. If her expenditure increases by 20% and her income increases by 29%, then her savings increase by;
The income of A is 45% more than the income of B and the income of C is 60% less than the sum of the incomes of A and B. The income of D is 20% more than that of C. If the difference between the incomes of B and D is Rs. 13200, then the income (in Rs.) of C is:
The price of cooking oil increased by 25%. Find by how much percentage a family must reduce its consumption in order to maintain the same budget.
The population of a city increased by 30% in the first year and decreased by 15% in the next year. If the present population is 11,050 then population 2 years ago was:
The income of A is 30% less than the income of B and the income of B is 137.5% more than that of C. If the income of A is Rs. 28500 less than that of B, then the income (in Rs.) of C is:
