Final answer:
Fractions are added or subtracted by finding a common denominator, combining numerators and simplifying. For 2/5 + 2/7, the answer is 24/35. For 4/28 - 7/9, the answer simplifies to -40/63. Lastly, 3 1/3 + 4 7/8 results in 8 5/24.
Step-by-step explanation:
To add or subtract fractions, we need a common denominator. When we find it, we can combine the numerators while keeping the denominator the same.
- For 2/5+ 2/7, find the least common denominator, which is 35. So we rewrite the fractions as (2×5)+(2×7) over 35, which simplifies to 14/35 + 10/35 = 24/35.
- For 4/28 - 7/9, the least common denominator is 252. We rewrite the fractions as (4×9) - (7×28) over 252, simplifying to 36/252 - 196/252, which further simplifies to -160/252. This can be reduced by dividing both the numerator and the denominator by the greatest common factor, 4, giving a final answer of -40/63.
- For 3 1/3 + 4 7/8, convert mixed numbers to improper fractions, getting 10/3 and 39/8. Using a common denominator of 24, rewrite them as 80/24 + 117/24. The sum is 197/24, which is equivalent to 8 5/24.
To check the answer, verify that the fractions are fully simplified and that the sum or difference is reasonable by comparing it to the original fractions.