Question

2 4/7 + 4 1/8 : 2 3/4 ;2 1/9

Answer 1

To solve this expression, we'll break it down step by step:

1. Start with the division: 4 1/8 ÷ 2 3/4

First, convert both mixed numbers into improper fractions: 33/8 ÷ 11/4

2. Invert and multiply: 33/8 * 4/11

3. Simplify by canceling common factors: (33 * 4) / (8 * 11) = 132/88

4. Simplify the fraction: Divide both the numerator and denominator by their greatest common factor, which is 44: (132 ÷ 44) / (88 ÷ 44) = 3/2

Now we have the division result as 3/2.

2 4/7 + (3/2) * 2 1/9

5. Convert the mixed numbers to improper fractions: 2 4/7 = 18/7 2 1/9 = 19/9

6. Multiply the fractions: (3/2) * (19/9) = (3 * 19) / (2 * 9) = 57/18

7. Simplify the fraction: Divide both the numerator and denominator by their greatest common factor, which is 3: (57 ÷ 3) / (18 ÷ 3) = 19/6

8. Add the fractions: 18/7 + 19/6

To add these fractions, you need a common denominator, which is the least common multiple (LCM) of 7 and 6, which is 42.

9. Convert both fractions to have a denominator of 42: (18/7) * (6/6) = 108/42 (19/6) * (7/7) = 133/42

10. Add the fractions with the common denominator: 108/42 + 133/42 = (108 + 133) / 42 = 241/42

So, 2 4/7 + (3/2) * 2 1/9 = 241/42.