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
A number p increased by p% of 99 equals 99 increased by 99% of p. What is (p + 51)% of 928 + 72?
Amina saves 16% of her income. Now her income is increased by 20% but she still saves the same amount as before. What is the percentage increase in her expenditure?
What is 12% of 4% of 7% of 2 × 10 6 ?
Vignesh spends 42% of his monthly salary on food, 16% on house rent, 11% on entertainment and 7% on conveyance. But due to some family function, he has to borrow Rs. 12,000 from a money leader to meet the expenses of Rs. 18,000 What is his monthly salary?
If X is 12.25% more than Y. then Y is approximately_____ less than X.
