Answer :
- Find a common denominator for the fractions $\frac{14}{15}$ and $\frac{2}{3}$, which is 15.
- Convert $\frac{2}{3}$ to an equivalent fraction with a denominator of 15: $\frac{2}{3} = \frac{10}{15}$.
- Subtract the fractions: $\frac{14}{15} - \frac{10}{15} = \frac{4}{15}$.
- The final answer is $\boxed{\frac{4}{15}}$.
### Explanation
1. Finding a Common Denominator
We are asked to subtract two fractions: $\frac{14}{15}$ and $\frac{2}{3}$. To do this, we need to find a common denominator.
2. Identifying the LCM
The least common multiple (LCM) of 15 and 3 is 15. So, we will use 15 as the common denominator.
3. Converting to a Common Denominator
We need to rewrite the fraction $\frac{2}{3}$ with the denominator 15. To do this, we multiply both the numerator and the denominator of $\frac{2}{3}$ by 5: $\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}$.
4. Subtracting the Fractions
Now we can subtract the two fractions: $\frac{14}{15} - \frac{10}{15} = \frac{14 - 10}{15} = \frac{4}{15}$.
5. Simplifying the Result
The resulting fraction is $\frac{4}{15}$. We check if this fraction can be simplified. The factors of 4 are 1, 2, and 4. The factors of 15 are 1, 3, 5, and 15. The only common factor is 1, so the fraction is already in its simplest form.
6. Final Answer
Therefore, the final answer is $\boxed{\frac{4}{15}}$.
### Examples
Fractions are used in everyday life, such as when baking a cake. If a recipe calls for $\frac{14}{15}$ of a cup of flour and you only have $\frac{2}{3}$ of a cup, you need to calculate the difference to know how much more flour you need to add. This subtraction of fractions helps you determine the exact amount required to complete the recipe successfully.
- Convert $\frac{2}{3}$ to an equivalent fraction with a denominator of 15: $\frac{2}{3} = \frac{10}{15}$.
- Subtract the fractions: $\frac{14}{15} - \frac{10}{15} = \frac{4}{15}$.
- The final answer is $\boxed{\frac{4}{15}}$.
### Explanation
1. Finding a Common Denominator
We are asked to subtract two fractions: $\frac{14}{15}$ and $\frac{2}{3}$. To do this, we need to find a common denominator.
2. Identifying the LCM
The least common multiple (LCM) of 15 and 3 is 15. So, we will use 15 as the common denominator.
3. Converting to a Common Denominator
We need to rewrite the fraction $\frac{2}{3}$ with the denominator 15. To do this, we multiply both the numerator and the denominator of $\frac{2}{3}$ by 5: $\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}$.
4. Subtracting the Fractions
Now we can subtract the two fractions: $\frac{14}{15} - \frac{10}{15} = \frac{14 - 10}{15} = \frac{4}{15}$.
5. Simplifying the Result
The resulting fraction is $\frac{4}{15}$. We check if this fraction can be simplified. The factors of 4 are 1, 2, and 4. The factors of 15 are 1, 3, 5, and 15. The only common factor is 1, so the fraction is already in its simplest form.
6. Final Answer
Therefore, the final answer is $\boxed{\frac{4}{15}}$.
### Examples
Fractions are used in everyday life, such as when baking a cake. If a recipe calls for $\frac{14}{15}$ of a cup of flour and you only have $\frac{2}{3}$ of a cup, you need to calculate the difference to know how much more flour you need to add. This subtraction of fractions helps you determine the exact amount required to complete the recipe successfully.
