The sum of 2/9 and 2 5/9 in simplest form is
The Correct Answer and Explanation is:
To find the sum of 29\frac{2}{9}92 and 2592 \frac{5}{9}295, we first need to convert the mixed number 2592 \frac{5}{9}295 into an improper fraction.
Step 1: Convert the mixed number into an improper fraction
A mixed number consists of a whole number and a fraction. To convert it into an improper fraction, multiply the whole number by the denominator and add the numerator. Here’s the calculation for 2592 \frac{5}{9}295:259=(2×9)+59=18+59=2392 \frac{5}{9} = \frac{(2 \times 9) + 5}{9} = \frac{18 + 5}{9} = \frac{23}{9}295=9(2×9)+5=918+5=923
So, 259=2392 \frac{5}{9} = \frac{23}{9}295=923.
Step 2: Add the fractions
Now that both terms are in the form of fractions with the same denominator, we can add them directly. The fractions are:29 and 239\frac{2}{9} \text{ and } \frac{23}{9}92 and 923
Since they have the same denominator, we add the numerators:29+239=2+239=259\frac{2}{9} + \frac{23}{9} = \frac{2 + 23}{9} = \frac{25}{9}92+923=92+23=925
Step 3: Simplify the fraction (if needed)
In this case, 259\frac{25}{9}925 is already in its simplest form because 25 and 9 have no common factors (other than 1).
Step 4: Convert to a mixed number (if desired)
If we want to express the result as a mixed number, we divide 25 by 9:25÷9=2 remainder 725 \div 9 = 2 \text{ remainder } 725÷9=2 remainder 7
Thus, 259=279\frac{25}{9} = 2 \frac{7}{9}925=297.
Final Answer
The sum of 29\frac{2}{9}92 and 2592 \frac{5}{9}295 is 259\frac{25}{9}925, or as a mixed number, 2792 \frac{7}{9}297.
