Question

(2 13/48+2 2/15):3 3/4-9 3/4:12

Answer 1

1) 2 13/48 + 2 2/15 = 2 65/240 + 2 32/240 = 4 97/240

2) 4 97/240 : 3 3/4 = 1057/240 : 15/4 = 1057/240 * 4/15 = 1057/900 = 1 157/900

3) 9 3/4 : 12 = 39/4 * 1/12 = 39/48 = 13/16

4) 1 157/900 - 13/16 = 1 628/3600 -  2925/3600 = 1303/3600

Answer 2

To solve the expression (2 13/48 + 2 2/15) : (3 3/4 - 9 3/4 : 12), follow these steps:

Step 1: Convert mixed numbers to improper fractions. 2 13/48 can be converted to an improper fraction as (2 * 48 + 13) / 48 = 109/48. 2 2/15 can be converted to an improper fraction as (2 * 15 + 2) / 15 = 32/15. 3 3/4 can be converted to an improper fraction as (3 * 4 + 3) / 4 = 15/4. 9 3/4 can be converted to an improper fraction as (9 * 4 + 3) / 4 = 39/4.

Step 2: Perform the operations inside the brackets first. (109/48 + 32/15) : (15/4 - 39/4 : 12)

Step 3: Perform the addition and subtraction inside the brackets. To add 109/48 and 32/15, we need a common denominator. The least common multiple of 48 and 15 is 240. So, we convert both fractions to have a denominator of 240. (109/48 * 5/5) + (32/15 * 16/16) = 545/240 + 512/240 = 1057/240.

To subtract 39/4 from 15/4, we need a common denominator, which is 4. (15/4 - 39/4) = -24/4 = -6.

Now, the expression becomes: (1057/240) : (-6 : 12)

Step 4: Perform the division (-6 : 12). To divide -6 by 12, we get: (-6) / 12 = -1/2.

Finally, the result of the expression is: 1057/240 : (-1/2) = 1057/240 * (-2/1) = -2114/240 = -1763/160.

So, (2 13/48 + 2 2/15) : (3 3/4 - 9 3/4 : 12) equals -1763/160.