Question

67 4/17+12 13/17-(1/6+29 1/8-28 1/3+3/8)-75

Answer 1

1)1/6+29 1/8=4/24+29 3/24=29 7/24
2) 29 7/24-28 1/3= 29 7/24-28 8/24= 28 31/24-28 8/24= 23/24
3)23/24+3/8=23/24+9/24=32/24=1 8/24=1 1/3
4)67 4/17+ 12 13/17= 79 17/17=80
5)80-1 1/3= 79 3/3-1 1/3= 78 2/3
6) 78 2/3-75=3 2/3

Answer 2

To simplify the given expression, let's follow the order of operations (PEMDAS/BODMAS):

P - Parentheses E - Exponents (none in this expression) MD - Multiplication and Division AS - Addition and Subtraction

The expression is:

67 4/17 + 12 13/17 - (1/6 + 29 1/8 - 28 1/3 + 3/8) - 75

Step 1: Simplify the expressions inside the parentheses first.

1/6 + 29 1/8 - 28 1/3 + 3/8

To add/subtract mixed fractions, we need to find a common denominator. The common denominator here is 24.

1/6 = (1/6) * (4/4) = 4/24 29 1/8 = 29 + 1/8 = 29 * 24/24 + 3/24 = 696/24 + 3/24 = 699/24 28 1/3 = 28 + 1/3 = 28 * 8/8 + 8/24 = 224/24 + 8/24 = 232/24 3/8 = 3/8

Now, the expression inside the parentheses becomes:

4/24 + 699/24 - 232/24 + 3/8

Now, add and subtract the fractions:

(4/24 + 699/24 - 232/24) = 471/24 = 19 11/24

So, the expression inside the parentheses becomes:

19 11/24 + 3/8

To add these mixed fractions, we again find a common denominator, which is 24.

3/8 = 3/8

Now, the expression inside the parentheses becomes:

19 11/24 + 3/8 = 19 * 24/24 + 11/24 + 3/8 = 456/24 + 11/24 + 9/24 = 476/24 = 19 22/24

Step 2: Substitute the simplified expression back into the original expression:

67 4/17 + 12 13/17 - (19 22/24) - 75

Step 3: Add and subtract the mixed fractions:

67 + 12 = 79

4/17 + 13/17 = 17/17 = 1 (common denominator is 17)

19 22/24 - 75

To subtract mixed fractions, find a common denominator. The common denominator here is 24.

19 22/24 = 19 * 24/24 + 22/24 = 456/24 + 22/24 = 478/24

Now, subtract:

478/24 - 75 = 478/24 - 1800/24 = (478 - 1800)/24 = -1322/24 = -551/12

Step 4: Final answer:

79 + 1 - 551/12

To add the whole number and the fraction, convert the whole number 79 to a fraction with the same denominator (which is 12).

79 = 79 * 12/12 = 948/12

Now, add:

948/12 + 1 - 551/12 = (948 + 1 - 551)/12 = 398/12 = 33 2/12 = 33 1/6

So, the simplified expression is 33 1/6.