In his career, a tennis player won 5 matches lost 12 matches and had 3 matches as draw. The fraction of the match he lost in his career is:
3/5
Calculating Tennis Match Fractions
This question asks us to determine the fraction of matches lost by a tennis player based on his career statistics. To find the fraction of lost matches, we need to know the total number of matches played and the number of matches lost.
Understanding the Given Tennis Career Data
We are provided with the following information about the tennis player's career matches:
- Matches Won: 5
- Matches Lost: 12
- Matches Drawn: 3
Calculating the Total Number of Matches Played
The total number of matches played in the player's career is the sum of matches won, matches lost, and matches drawn.
Total Matches = Matches Won + Matches Lost + Matches Drawn
Let $W$ be the number of matches won, $L$ be the number of matches lost, and $D$ be the number of matches drawn. The Total Matches $(T)$ is:
$$T = W + L + D$$
Substituting the given values:
$$T = 5 + 12 + 3$$
$$T = 20 \text{ matches}$$
So, the tennis player played a total of 20 matches in his career.
Determining the Fraction of Lost Matches
The fraction of matches lost is calculated by dividing the number of matches lost by the total number of matches played.
Fraction of Lost Matches = $$\frac{\text{Matches Lost}}{\text{Total Matches}}$$
Using the values we have:
Fraction of Lost Matches = $$\frac{12}{20}$$
Simplifying the Fraction
The fraction $$\frac{12}{20}$$ can be simplified by finding the greatest common divisor (GCD) of the numerator (12) and the denominator (20). Both 12 and 20 are divisible by 4.
- Divide the numerator by 4: $12 \div 4 = 3$
- Divide the denominator by 4: $20 \div 4 = 5$
So, the simplified fraction is $$\frac{3}{5}$$
The fraction of the match he lost in his career is $$\frac{3}{5}$$.
Comparing with Options
Let's compare our calculated fraction with the given options:
| Option | Fraction | Matches Our Calculation? |
|---|---|---|
| 1 | 12/5 | No |
| 2 | 3/5 | Yes |
| 3 | 1/5 | No |
| 4 | 2/5 | No |
Our calculated fraction, $$\frac{3}{5}$$, matches Option 2.
Revision Table: Key Concepts
| Concept | Description | Formula/Example |
|---|---|---|
| Fraction | Represents a part of a whole. Written as Numerator/Denominator. | E.g., 3/5 (3 parts out of 5 total parts) |
| Total Number | The sum of all individual parts or categories. | Total = Part 1 + Part 2 + ... |
| Calculating Fraction of a Part | Divide the number of the specific part by the total number. | Fraction = $$\frac{\text{Number of Part}}{\text{Total Number}}$$ |
| Simplifying Fractions | Dividing both the numerator and denominator by their greatest common divisor (GCD). | $$\frac{12}{20} = \frac{12 \div 4}{20 \div 4} = \frac{3}{5}$$ |
Additional Information on Fractions and Statistics
Fractions are used in many real-world situations, including sports statistics. They help us understand proportions or ratios. In this case, the fraction 3/5 tells us that for every 5 matches played, the player lost 3 of them.
- Ratio: The relationship between two numbers, often expressed as a fraction. The ratio of lost matches to total matches is 12:20, which simplifies to 3:5.
- Percentage: Fractions can be converted to percentages to make them easier to compare. To convert a fraction to a percentage, you multiply by 100%. For example, $$\frac{3}{5} \times 100\% = 0.6 \times 100\% = 60\%$$. This means the player lost 60% of his career matches.
- Other Fractions: We could also calculate the fraction of matches won ($\frac{5}{20} = \frac{1}{4}$) or drawn ($\frac{3}{20}$) using the same method.
Understanding how to calculate fractions from raw data is a fundamental skill in mathematics and data analysis.
Important Questions from Fractions
If three-fifths of a number is 54, what is two-ninth of it?
Sunila had \(9\frac{1}{4}\) kg of flour to make bread with. If the recipe says that she needs \(1\frac{1}{8}\) kg to make one loaf of bread, how many loafs can she make? Estimate to the nearest whole number.
The value of \(\frac{{11}}{5} - \left( {\frac{2}{3}of\frac{3}{5} - \frac{1}{5}} \right) + \left( {\frac{6}{5} \div \frac{4}{5}} \right)\) is:
Simplify:
\(62\div 5 - \left(\frac{8}{9}\times \frac{18}{7}\right)\times \frac{7}{5}+\frac{5}{4}\times \frac{16}{25}\)
The value of 8 + \((\frac{1}{2} + \frac{1}{4})\) × 16 is:
