Final answer:
To solve the equation a +3 1/4 = 5 2/9, convert the mixed numbers to improper fractions and then solve for a by isolating it on one side of the equation.
Step-by-step explanation:
To solve the equation a +3 1/4 = 5 2/9, we need to find the value of a. First, we need to convert the mixed numbers into improper fractions. 3 1/4 can be written as 13/4 and 5 2/9 can be written as 47/9. Now we can rewrite the equation as a + 13/4 = 47/9. To solve for a, we need to isolate it on one side of the equation. Subtracting 13/4 from both sides gives us a = 47/9 - 13/4. To subtract fractions, we need a common denominator. The least common multiple of 4 and 9 is 36, so we can rewrite the equation with a common denominator: a = (47/9) * (4/4) - (13/4) * (9/9). Simplifying the equation gives us a = (188/36) - (117/36). Subtracting the fractions gives us a = 71/36. Therefore, the answer is a = 71/36.