Question

4) 3 5\6- 1 4\5 5) 12 1\4- (3 5\12+ 5 1\6)

Answer 1

4) 3 5\6- 1 4\5= 23/6-9/5=115/30-54/30=61/30=2 1/30

5) 12 1\4- (3 5\12+ 5 1\6)= 3 2/3

3 5\12+ 5 1\6=41/12+31/6=41/12+62/12=103/12
12 1/4-103/12=49/4-103/12=147/12-103/12=44/12=3 2/3

Answer 2

Let's solve the expressions step by step:

4. 3 5/6 - 1 4/5

To subtract mixed numbers, we first need to convert them to improper fractions and then perform the subtraction.

Step 1: Convert the mixed numbers to improper fractions: 3 5/6 = (6 * 3 + 5) / 6 = 23 / 6 1 4/5 = (5 * 1 + 4) / 5 = 9 / 5

Step 2: Subtract the fractions: (23/6) - (9/5)

To subtract fractions, we need to find a common denominator, which in this case is 30 (LCM of 6 and 5).

Step 3: Convert both fractions to have a common denominator of 30: (23/6) * (5/5) = 115/30 (9/5) * (6/6) = 54/30

Step 4: Subtract the fractions: (115/30) - (54/30) = (115 - 54) / 30 = 61/30

The result is 2 1/30.

5. 12 1/4 - (3 5/12 + 5 1/6)

Step 1: Convert the mixed numbers to improper fractions: 12 1/4 = (4 * 12 + 1) / 4 = 49 / 4 3 5/12 = (12 * 3 + 5) / 12 = 41 / 12 5 1/6 = (6 * 5 + 1) / 6 = 31 / 6

Step 2: Perform the operations inside the parentheses first: (41/12) + (31/6)

Step 3: Convert both fractions to have a common denominator of 12: (41/12) * (1/1) = 41/12 (31/6) * (2/2) = 62/12

Step 4: Add the fractions inside the parentheses: (41/12) + (62/12) = (41 + 62) / 12 = 103/12

Step 5: Subtract the result from the first mixed number: (49/4) - (103/12)

To subtract fractions, we need to find a common denominator, which in this case is 12 (LCM of 4 and 12).

Step 6: Convert both fractions to have a common denominator of 12: (49/4) * (3/3) = 147/12 (103/12) * (1/1) = 103/12

Step 7: Subtract the fractions: (147/12) - (103/12) = (147 - 103) / 12 = 44/12

Step 8: Simplify the fraction: 44/12 can be reduced to 11/3

The final result is 11/3 or 3 2/3.