Add. Express the answer in simplest form. 2\frac{2}{3} 4\frac{5}{12}
To add 2\frac{2}{3} and 4\frac{5}{12}, you first need to convert the mixed numbers into improper fractions. Here's how you can do that:
For 2\frac{2}{3}:
- Multiply the whole number (2) by the denominator of the fraction (3): 2 * 3 = 6.
- Add the result to the numerator (2) of the fraction: 6 + 2 = 8.
- Write the sum (8) over the original denominator (3): 8/3.
For 4\frac{5}{12}:
- Multiply the whole number (4) by the denominator of the fraction (12): 4 * 12 = 48.
- Add the result to the numerator (5) of the fraction: 48 + 5 = 53.
- Write the sum (53) over the original denominator (12): 53/12.
Now that you have both fractions, you can add them together:
2\frac{2}{3} + 4\frac{5}{12} = 8/3 + 53/12.
To add these fractions, you need to find a common denominator. In this case, the least common multiple (LCM) of 3 and 12 is 12. To ensure that both fractions have a denominator of 12, multiply the first fraction by 4/4 (which is equivalent to 1) and the second fraction by 1/1:
(8/3) * (4/4) + (53/12) * (1/1) = 32/12 + 53/12.
Now that both fractions have the same denominator, you can add the numerators to get the final sum:
32/12 + 53/12 = (32 + 53)/12 = 85/12.
The answer, expressed in simplest form, is 85/12.