Answer :
To simplify the expression [tex]\(\frac{1}{15} + \frac{2}{3} + \frac{14}{15}\)[/tex] and express it as an improper fraction, follow these steps:
1. Find a common denominator:
The denominators in the fractions are 15 and 3. The least common denominator (LCD) of these numbers is 15.
2. Convert [tex]\(\frac{2}{3}\)[/tex] to have the common denominator of 15:
Since [tex]\(\frac{2}{3}\)[/tex] needs to be expressed with a denominator of 15, we can convert it as follows:
- Multiply the numerator and the denominator of [tex]\(\frac{2}{3}\)[/tex] by 5 to maintain the equal value:
[tex]\[
\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}
\][/tex]
3. Add the fractions:
Now we can add the fractions with the same denominator:
[tex]\[
\frac{1}{15} + \frac{10}{15} + \frac{14}{15} = \frac{1 + 10 + 14}{15} = \frac{25}{15}
\][/tex]
4. Simplify the resulting fraction:
To simplify [tex]\(\frac{25}{15}\)[/tex], find the greatest common divisor (GCD) of 25 and 15, which is 5. Divide both the numerator and the denominator by the GCD:
[tex]\[
\frac{25 \div 5}{15 \div 5} = \frac{5}{3}
\][/tex]
Therefore, the simplified result is [tex]\(\frac{5}{3}\)[/tex].
1. Find a common denominator:
The denominators in the fractions are 15 and 3. The least common denominator (LCD) of these numbers is 15.
2. Convert [tex]\(\frac{2}{3}\)[/tex] to have the common denominator of 15:
Since [tex]\(\frac{2}{3}\)[/tex] needs to be expressed with a denominator of 15, we can convert it as follows:
- Multiply the numerator and the denominator of [tex]\(\frac{2}{3}\)[/tex] by 5 to maintain the equal value:
[tex]\[
\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}
\][/tex]
3. Add the fractions:
Now we can add the fractions with the same denominator:
[tex]\[
\frac{1}{15} + \frac{10}{15} + \frac{14}{15} = \frac{1 + 10 + 14}{15} = \frac{25}{15}
\][/tex]
4. Simplify the resulting fraction:
To simplify [tex]\(\frac{25}{15}\)[/tex], find the greatest common divisor (GCD) of 25 and 15, which is 5. Divide both the numerator and the denominator by the GCD:
[tex]\[
\frac{25 \div 5}{15 \div 5} = \frac{5}{3}
\][/tex]
Therefore, the simplified result is [tex]\(\frac{5}{3}\)[/tex].
