Question

1)3 1/5-(-4 1/7) 2)2/9-1/3

Answer 1

To solve the given arithmetic expressions, let's simplify each one step by step:

1. 3 1/5 - (-4 1/7):

First, let's convert the mixed numbers into improper fractions: 3 1/5 = (3 * 5 + 1) / 5 = 16/5 -4 1/7 = (-4 * 7 + 1) / 7 = -29/7

Now, we can rewrite the expression: 16/5 - (-29/7)

To subtract a negative number, we can change it to addition: 16/5 + 29/7

To add these fractions, we need a common denominator, which is the least common multiple (LCM) of 5 and 7, which is 35.

Converting both fractions to have a denominator of 35: (16/5) * (7/7) = 112/35 (29/7) * (5/5) = 145/35

Now, we can add the fractions: 112/35 + 145/35 = 257/35

Therefore, the solution is 257/35.

2. 2/9 - 1/3:

To subtract fractions, we need a common denominator. In this case, the least common multiple (LCM) of 9 and 3 is 9.

Converting both fractions to have a denominator of 9: (2/9) * (1/1) = 2/9 (1/3) * (3/3) = 3/9

Now, we can subtract the fractions: 2/9 - 3/9 = -1/9

Therefore, the solution is -1/9.