Question

(2 13/48-(-2 5/12)):(-3 3/4)+9 3/4:(-13)

Answer 1

1) 2 13/48 - (-2 5/12) = 109/48 + 29/12 = 109/48 + 116/48 = 225/48

2) 225/48 : (-3 3/4) = 225/48 : (-15/4) = 225/48 * (- 4/15) = - 15/12

3) 9 3/4 : (-13) = 39/4 * (-1/13) = - 3/4

4) -15/12 + (-3/4) = -15/12 - 9/12 = -24/12 = - 2

Answer 2

To simplify the given expression, let's convert the mixed numbers to improper fractions and apply the order of operations (PEMDAS/BODMAS).

Given expression:

(2 13/48 - (-2 5/12)) : (-3 3/4) + 9 3/4 : (-13)

First, let's simplify the subtraction inside the parentheses: 2 13/48 - (-2 5/12)

To subtract mixed numbers, we need to convert them to improper fractions.

2 13/48 can be written as (2 * 48 + 13) / 48 = 109/48

(-2 5/12) can be written as (-2 * 12 + 5) / 12 = (-24 + 5) / 12 = -19/12

Now, the subtraction becomes:

(109/48) - (-19/12)

To subtract fractions, we need a common denominator, which is the least common multiple (LCM) of 48 and 12, which is 48.

(109/48) - (-19/12) = (109/48) + (19/12)

Now that the fractions have a common denominator, we can add them:

(109/48) + (19/12) = (109/48) + (19/12) = (109 + 19) / 48 = 128/48

Next, let's simplify the division (-3 3/4) :

(-3 3/4) can be written as (-3 * 4 + 3) / 4 = (-12 + 3) / 4 = -9/4

Now, we have:

(128/48) : (-9/4) + 9 3/4 : (-13)

To divide fractions, we multiply by the reciprocal of the divisor:

(128/48) : (-9/4) = (128/48) * (-4/9) = -512/432

Simplifying -512/432, we can divide both the numerator and denominator by their greatest common divisor, which is 16:

-512/432 = (-512/16) / (432/16) = -32/27

Now, the expression becomes:

-32/27 + 9 3/4 : (-13)

Let's simplify the addition 9 3/4:

9 3/4 can be written as (9 * 4 + 3) / 4 = (36 + 3) / 4 = 39/4

Now we have:

-32/27 + 39/4 : (-13)

To divide fractions, we multiply by the reciprocal of the divisor:

39/4 : (-13) = 39/4 * (-1/13) = -39/52

Now the expression becomes:

-32/27 + (-39/52)

To add fractions, we need a common denominator, which is the least common multiple (LCM) of 27 and 52, which is 1404.

-32/27 + (-39/52) = (-32/27) * (52/52) + (-39/52) * (27/27)

= (-32 * 52) / (27 * 52) + (-39 * 27) / (52 * 27)

= -1664/1404 + (-1053/1404)

Now that the fractions have a common denominator, we can add them:

-1664/1404 + (-1053/1404) = (-1664 - 1053) / 1404 = -2717/1404

The simplified expression is -2717/1404.