What is 12 8/15(as in fractions) − 7 + 7/15 + 15? Simplify your answer.
To simplify the expression, we need to convert all the mixed numbers to improper fractions and then perform the operations.
12 8/15 can be written as (12 * 15 + 8)/15 = 188/15
7 can be written as 7/1
So the expression becomes:
188/15 - 7/1 + 7/15 + 15
To add or subtract fractions, we need a common denominator. The common denominator for 15 and 1 is 15, so we need to convert 7/1 to have a denominator of 15:
7/1 * 15/15 = 105/15
Now the expression becomes:
188/15 - 105/15 + 7/15 + 15
To combine the fractions:
(188 - 105 + 7)/15 + 15 = 90/15 + 15
To simplify further, we can divide both the numerator and denominator of 90/15 by 15:
(90/15) ÷ (15/15) + 15 = 6 + 15
And finally:
6 + 15 = 21
Therefore, the simplified answer is 21.
To simplify the expression 12 8/15 - 7 + 7/15 + 15, we need to convert the mixed number 12 8/15 into an improper fraction.
12 8/15 can be converted to an improper fraction as follows:
12 * 15 + 8 = 168 (numerator)
15 (denominator)
So, 12 8/15 is equivalent to the improper fraction 168/15.
Now we can rewrite the expression with the improper fraction:
168/15 - 7 + 7/15 + 15
To add or subtract fractions, we need to have a common denominator. The common denominator between 15 and 1 is 15. So, let's convert all the fractions to have a denominator of 15:
(168/15) - (7 * 15/15) + (7/15) + (15 * 15/15)
Now, let's simplify each term:
168/15 - 105/15 + 7/15 + 225/15
Now that all the fractions have the same denominator, we can combine them:
(168 - 105 + 7 + 225)/15
Simplifying the numerator gives us:
295/15
So, the simplified answer is 295/15.