Question

(1) 2 3/4 - 1 5/6 (2) 4 2/5 + 3 5/6 (3) 7 5/12 - ( 1 5/8 + 2 1/24

Answer 1

1)

2 3/4 - 1 5/6 = 2 9/12 - 1 10/12 = 1 21/12 - 1 10/12 = 11/12,

2)

4 2/5 + 3 5/6 = 4 12/30 + 3 25/30 = 7 37/30 = 8 7/30,

3)

7 5/12 - (1 5/8 + 2 1/24) = 7 5/12 - 1 5/8 - 2 1/24 = 7 10/24 - 1 15/24 - 2 1/24 =

= 6 34/24 - 1 15/24 - 2 1/24 = 3 18/24 = 3 3/4

Answer 2

1) 2 3/4 - 1 5/6 = 11/4 - 11/6 = 11/12
2) 4 2/5 + 3 5/6 = 22/5 + 23/6 = 247/30
3) 7 5/12 - (1 5/8 + 2 1/24) = 89/12 - 11/3 = 45/12 = 15/4

Answer 3

Let's solve the given arithmetic expressions step-by-step:

(1) 2 3/4 - 1 5/6

Step 1: Convert both mixed numbers into improper fractions. 2 3/4 = (2 * 4 + 3) / 4 = 11 / 4 1 5/6 = (1 * 6 + 5) / 6 = 11 / 6

Step 2: Subtract the fractions. 11 / 4 - 11 / 6

Step 3: Find a common denominator, which is the least common multiple (LCM) of 4 and 6, which is 12.

Step 4: Convert both fractions to have a denominator of 12. 11 / 4 = (11 * 3) / (4 * 3) = 33 / 12 11 / 6 = (11 * 2) / (6 * 2) = 22 / 12

Step 5: Subtract the fractions. 33 / 12 - 22 / 12 = (33 - 22) / 12 = 11 / 12

So, the result of the first expression is 11/12.

(2) 4 2/5 + 3 5/6

Step 1: Convert both mixed numbers into improper fractions. 4 2/5 = (4 * 5 + 2) / 5 = 22 / 5 3 5/6 = (3 * 6 + 5) / 6 = 23 / 6

Step 2: Add the fractions. 22 / 5 + 23 / 6

Step 3: Find a common denominator, which is the least common multiple (LCM) of 5 and 6, which is 30.

Step 4: Convert both fractions to have a denominator of 30. 22 / 5 = (22 * 6) / (5 * 6) = 132 / 30 23 / 6 = (23 * 5) / (6 * 5) = 115 / 30

Step 5: Add the fractions. 132 / 30 + 115 / 30 = (132 + 115) / 30 = 247 / 30

Step 6: If possible, simplify the fraction. 247 / 30 cannot be simplified further.

So, the result of the second expression is 247/30.

(3) 7 5/12 - (1 5/8 + 2 1/24)

Step 1: Convert all mixed numbers into improper fractions. 7 5/12 = (7 * 12 + 5) / 12 = 89 / 12 1 5/8 = (1 * 8 + 5) / 8 = 13 / 8 2 1/24 = (2 * 24 + 1) / 24 = 49 / 24

Step 2: Add the fractions inside the parentheses first. 13 / 8 + 49 / 24

Step 3: Find a common denominator, which is the least common multiple (LCM) of 8 and 24, which is 24.

Step 4: Convert both fractions to have a denominator of 24. 13 / 8 = (13 * 3) / (8 * 3) = 39 / 24 49 / 24 remains the same.

Step 5: Add the fractions. 39 / 24 + 49 / 24 = (39 + 49) / 24 = 88 / 24

Step 6: If possible, simplify the fraction. 88 / 24 = (88 / 8) / (24 / 8) = 11 / 3

Now, subtract the result from step 6 from 89/12:

89 / 12 - 11 / 3

Step 7: Find a common denominator, which is the least common multiple (LCM) of 12 and 3, which is 12.

Step 8: Convert both fractions to have a denominator of 12. 89 / 12 remains the same. 11 / 3 = (11 * 4) / (3 * 4) = 44 / 12

Step 9: Subtract the fractions. 89 / 12 - 44 / 12 = (89 - 44) / 12 = 45 / 12

Step 10: If possible, simplify the fraction. 45 / 12 = (45 / 3) / (12 / 3) = 15 / 4

So, the result of the third expression is 15/4.