To solve the expression [tex]\( 1 \cdot \frac{5}{12} + \frac{1}{4} + \frac{1}{18} \)[/tex], we need to find a common denominator for the fractions so that we can add them together. Here is the step-by-step solution:
1. Identify the fractions:
The fractions involved are [tex]\(\frac{5}{12}\)[/tex], [tex]\(\frac{1}{4}\)[/tex], and [tex]\(\frac{1}{18}\)[/tex].
2. Find a common denominator:
The denominators are 12, 4, and 18. We need to find the least common multiple (LCM) of these numbers.
[tex]\[
\text{LCM of 12, 4, and 18} = 36
\][/tex]
3. Convert each fraction to have the common denominator 36:
[tex]\[
\frac{5}{12} = \frac{5 \cdot 3}{12 \cdot 3} = \frac{15}{36}
\][/tex]
[tex]\[
\frac{1}{4} = \frac{1 \cdot 9}{4 \cdot 9} = \frac{9}{36}
\][/tex]
[tex]\[
\frac{1}{18} = \frac{1 \cdot 2}{18 \cdot 2} = \frac{2}{36}
\][/tex]
4. Add the fractions:
Now that all fractions have the same denominator, we can add them easily.
[tex]\[
\frac{15}{36} + \frac{9}{36} + \frac{2}{36} = \frac{15 + 9 + 2}{36} = \frac{26}{36}
\][/tex]
5. Simplify the fraction:
The fraction [tex]\(\frac{26}{36}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2.
[tex]\[
\frac{26 \div 2}{36 \div 2} = \frac{13}{18}
\][/tex]
6. Convert the fraction to a decimal:
By performing the division [tex]\(\frac{13}{18}\)[/tex], we get the decimal equivalent.
[tex]\[
\frac{13}{18} \approx 0.7222222222222223
\][/tex]
Hence, the detailed solution proceeds as follows, and the final result is [tex]\( \approx 0.7222222222222223 \)[/tex].
