(2/25 +13/25) - (2/5 - 14/15)
17/25 + 8/15
91/75
(2/25 +13/25) - (2/5 - 14/15)
= 15/25 - (-4/25)
= (15+4)/25
= 19/25
(2/25 +13/25) - (2/5 - 14/15)
= 15/25 - (-8/15)
= 15/25 + 8/15
(45+40)/75
= 85/75
= 17/15
To solve this expression, we need to simplify each fraction separately and then perform the necessary operations to find the final result.
Let's simplify each fraction step by step:
1) Simplify the first fraction: (2/25 + 13/25)
The denominators in both fractions are the same (25), so we can directly add the numerators:
2 + 13 = 15
The fraction becomes 15/25. However, we can simplify this further by dividing both the numerator and denominator by their greatest common divisor, which in this case is 5:
15 ÷ 5 = 3
25 ÷ 5 = 5
So, the first fraction simplifies to 3/5.
2) Simplify the second fraction: (2/5 - 14/15)
To simplify the subtraction of fractions with different denominators (5 and 15), we need to find a common denominator. The least common multiple of 5 and 15 is 15, so we need to rewrite both fractions with a denominator of 15:
(2/5) × (3/3) = 6/15
(14/15) × (1/1) = 14/15
Now that both fractions have the same denominator, we can perform the subtraction:
6/15 - 14/15 = (-8)/15
Combining the two simplified fractions:
3/5 - (-8)/15
To subtract fractions, we need to find a common denominator. The least common multiple of 5 and 15 is 15, so we will convert both fractions to have a denominator of 15:
(3/5) × (3/3) = 9/15
((-8)/15) × (1/1) = (-8)/15
Now, we can subtract the fractions:
9/15 - (-8)/15 = 9/15 + 8/15 = (9 + 8)/15 = 17/15
Thus, the expression (2/25 + 13/25) - (2/5 - 14/15) simplifies to 17/15.