Final answer:
To add 3/4 and 1/6, find a common denominator, which is 12, convert each fraction to an equivalent fraction with the common denominator, and then add the numerators. The sum of 3/4 and 1/6 is 11/12.
Step-by-step explanation:
Understanding Addition of Fractions
To add fractions like 3/4 and 1/6, we need to have a common denominator. The least common denominator (LCD) of 4 and 6 is 12. To convert fractions to have the same denominator, we find an equivalent fraction for each that has 12 as the denominator.
For 3/4, we multiply the numerator and the denominator by 3 to get 9/12. For 1/6, we multiply the numerator and the denominator by 2 to get 2/12. The new fractions are equivalent to the originals but have the same denominator, so we can add them directly:
(3/4) → (3*3)/(4*3) = 9/12
(1/6) → (1*2)/(6*2) = 2/12
Now we add the numerators and keep the denominator the same:
9/12 + 2/12 = (9+2)/12 = 11/12
The sum of 3/4 and 1/6 is 11/12.