Answer :
To solve the problem of combining and simplifying the fractions [tex]\(\frac{14}{15} - \frac{41}{45}\)[/tex], follow these steps:
1. Find a common denominator:
The denominators of the fractions are 15 and 45. To combine these fractions, they need to have the same denominator. The least common multiple (LCM) of 15 and 45 is 45.
2. Convert each fraction to have the common denominator:
- The first fraction is [tex]\(\frac{14}{15}\)[/tex]. To convert it to a denominator of 45, multiply both the numerator and the denominator by 3:
[tex]\[
\frac{14}{15} = \frac{14 \times 3}{15 \times 3} = \frac{42}{45}
\][/tex]
- The second fraction is already [tex]\(\frac{41}{45}\)[/tex], so it does not need to be changed.
3. Subtract the fractions:
Now that both fractions have the same denominator, subtract the numerators:
[tex]\[
\frac{42}{45} - \frac{41}{45} = \frac{42 - 41}{45} = \frac{1}{45}
\][/tex]
4. Simplify the result:
The fraction [tex]\(\frac{1}{45}\)[/tex] cannot be simplified further, as 1 is the smallest natural number.
Therefore, the simplified result of [tex]\(\frac{14}{15} - \frac{41}{45}\)[/tex] is [tex]\(\frac{1}{45}\)[/tex].
1. Find a common denominator:
The denominators of the fractions are 15 and 45. To combine these fractions, they need to have the same denominator. The least common multiple (LCM) of 15 and 45 is 45.
2. Convert each fraction to have the common denominator:
- The first fraction is [tex]\(\frac{14}{15}\)[/tex]. To convert it to a denominator of 45, multiply both the numerator and the denominator by 3:
[tex]\[
\frac{14}{15} = \frac{14 \times 3}{15 \times 3} = \frac{42}{45}
\][/tex]
- The second fraction is already [tex]\(\frac{41}{45}\)[/tex], so it does not need to be changed.
3. Subtract the fractions:
Now that both fractions have the same denominator, subtract the numerators:
[tex]\[
\frac{42}{45} - \frac{41}{45} = \frac{42 - 41}{45} = \frac{1}{45}
\][/tex]
4. Simplify the result:
The fraction [tex]\(\frac{1}{45}\)[/tex] cannot be simplified further, as 1 is the smallest natural number.
Therefore, the simplified result of [tex]\(\frac{14}{15} - \frac{41}{45}\)[/tex] is [tex]\(\frac{1}{45}\)[/tex].
