Answer :
- Find a common denominator: Convert $\frac{1}{5}$ to $\frac{3}{15}$.
- Subtract the fractions: $\frac{13}{15} - \frac{3}{15} = \frac{10}{15}$.
- Simplify the fraction: $\frac{10}{15} = \frac{2}{3}$.
- The simplified result is $\boxed{\frac{2}{3}}$.
### Explanation
1. Understanding the Problem
We are given two fractions, $\frac{13}{15}$ and $\frac{1}{5}$, and we need to subtract the second fraction from the first and simplify the result.
2. Finding a Common Denominator
To subtract fractions, we need to have a common denominator. The least common multiple (LCM) of 15 and 5 is 15. So, we will convert $\frac{1}{5}$ to an equivalent fraction with a denominator of 15.
3. Converting to Equivalent Fractions
To convert $\frac{1}{5}$ to a fraction with a denominator of 15, we multiply both the numerator and the denominator by 3:$$\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}$$
4. Subtracting the Fractions
Now that both fractions have the same denominator, we can subtract them:$$\frac{13}{15} - \frac{3}{15} = \frac{13 - 3}{15} = \frac{10}{15}$$
5. Simplifying the Result
Finally, we simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 5:$$\frac{10}{15} = \frac{10 \div 5}{15 \div 5} = \frac{2}{3}$$
6. Final Answer
Therefore, the simplified result of the subtraction is $\boxed{\frac{2}{3}}$.
### Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a pizza. For example, if you have $\frac{13}{15}$ of a cup of flour and you use $\frac{1}{5}$ of a cup, this problem shows you how to calculate how much flour you have left. Understanding fractions helps in managing resources and quantities in various real-world scenarios.
- Subtract the fractions: $\frac{13}{15} - \frac{3}{15} = \frac{10}{15}$.
- Simplify the fraction: $\frac{10}{15} = \frac{2}{3}$.
- The simplified result is $\boxed{\frac{2}{3}}$.
### Explanation
1. Understanding the Problem
We are given two fractions, $\frac{13}{15}$ and $\frac{1}{5}$, and we need to subtract the second fraction from the first and simplify the result.
2. Finding a Common Denominator
To subtract fractions, we need to have a common denominator. The least common multiple (LCM) of 15 and 5 is 15. So, we will convert $\frac{1}{5}$ to an equivalent fraction with a denominator of 15.
3. Converting to Equivalent Fractions
To convert $\frac{1}{5}$ to a fraction with a denominator of 15, we multiply both the numerator and the denominator by 3:$$\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}$$
4. Subtracting the Fractions
Now that both fractions have the same denominator, we can subtract them:$$\frac{13}{15} - \frac{3}{15} = \frac{13 - 3}{15} = \frac{10}{15}$$
5. Simplifying the Result
Finally, we simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 5:$$\frac{10}{15} = \frac{10 \div 5}{15 \div 5} = \frac{2}{3}$$
6. Final Answer
Therefore, the simplified result of the subtraction is $\boxed{\frac{2}{3}}$.
### Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a pizza. For example, if you have $\frac{13}{15}$ of a cup of flour and you use $\frac{1}{5}$ of a cup, this problem shows you how to calculate how much flour you have left. Understanding fractions helps in managing resources and quantities in various real-world scenarios.
