To find the sum of the fractions [tex]\( \frac{1}{6}, \frac{2}{3}, \)[/tex] and [tex]\( \frac{1}{4} \)[/tex] and select the best match from the given choices, let's follow these steps:
1. Convert each fraction to a decimal:
- [tex]\(\frac{1}{6} = 0.16666666666666666 \)[/tex]
- [tex]\(\frac{2}{3} = 0.6666666666666666 \)[/tex]
- [tex]\(\frac{1}{4} = 0.25 \)[/tex]
2. Add these decimal values:
- [tex]\(0.16666666666666666 + 0.6666666666666666 + 0.25 = 1.0833333333333333\)[/tex]
3. Convert the sum of decimals back to a fraction:
- The decimal [tex]\( 1.0833333333333333 \)[/tex] converts to the fraction [tex]\( \frac{13}{12} \)[/tex].
4. Match the fraction sum to the given choices:
- Choice A: [tex]\( \frac{13}{12} \)[/tex] or [tex]\(1 \frac{1}{12} \)[/tex]
- Choice B: [tex]\( \frac{11}{12} \)[/tex]
- Choice C: [tex]\( \frac{2}{72} \)[/tex] or [tex]\( \frac{1}{36} \)[/tex]
- Choice D: [tex]\( \frac{4}{12} \)[/tex] or [tex]\( \frac{1}{3} \)[/tex]
Therefore, the sum of [tex]\( \frac{1}{6}, \frac{2}{3}, \)[/tex] and [tex]\( \frac{1}{4} \)[/tex] is [tex]\( \frac{13}{12} \)[/tex], which corresponds to Choice A. Hence, the best answer is:
A. [tex]\( \frac{13}{12} \)[/tex], or [tex]\(1 \frac{1}{12} \)[/tex]
