To add the fractions [tex]\( \frac{2}{3} \)[/tex] and [tex]\( \frac{1}{6} \)[/tex], follow these steps:
### Step 1: Find the Least Common Denominator (LCD)
The denominators of the two fractions are 3 and 6. The least common denominator (LCD) of 3 and 6 is 6.
### Step 2: Convert Fractions to Equivalent Fractions with the LCD
Next, we need to convert each fraction to an equivalent fraction with the denominator of 6:
- For [tex]\( \frac{2}{3} \)[/tex]:
- Multiply the numerator and the denominator by 2 (since [tex]\( 6 \div 3 = 2 \)[/tex]).
- [tex]\[ \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \][/tex]
- For [tex]\( \frac{1}{6} \)[/tex]:
- The denominator is already 6, so the fraction remains the same.
- [tex]\[ \frac{1 \times 1}{6 \times 1} = \frac{1}{6} \][/tex]
### Step 3: Add the Numerators
Now that both fractions have the same denominator, we can add the numerators:
- Numerator of [tex]\( \frac{4}{6} \)[/tex] is 4.
- Numerator of [tex]\( \frac{1}{6} \)[/tex] is 1.
- [tex]\[ 4 + 1 = 5 \][/tex]
### Step 4: Write the Resulting Fraction
The resulting fraction will have the same denominator (6) and the sum of the numerators (5):
- [tex]\[ \frac{4}{6} + \frac{1}{6} = \frac{5}{6} \][/tex]
### Final Answer
The sum of the fractions [tex]\( \frac{2}{3} \)[/tex] and [tex]\( \frac{1}{6} \)[/tex] is [tex]\( \frac{5}{6} \)[/tex].
