What is 12 8/15 − 7 + 7 1/5 + 15? Simplify your answer.
To simplify the expression 12 8/15 − 7 + 7 1/5 + 15, we first need to convert the mixed numbers to improper fractions.
12 8/15 can be written as (12 * 15 + 8)/15 = 188/15.
7 1/5 can be written as (7 * 5 + 1)/5 = 36/5.
Now we can rewrite the expression as:
188/15 - 7 + 36/5 + 15.
To add or subtract fractions, they must have a common denominator. In this case, the common denominator is 15.
Rewriting each fraction with the common denominator:
(188 - 7) / 15 + (36/5 * 3/3) + (15 * 5/5)
= 181/15 + 108/15 + 75/5.
Now that all fractions have the same denominator, we can combine them:
181/15 + 108/15 + 75/5 = (181 + 108 + 225)/15.
= 514/15.
So the simplified expression is 514/15.
To simplify the expression 12 8/15 − 7 + 7 1/5 + 15, we need to add and subtract the terms and fractions.
First, let's convert the whole numbers to improper fractions:
12 = 12/1
15 = 15/1
7 = 7/1
5 = 5/1
Next, find a common denominator to add and subtract the fractions:
For the fractions 8/15 and 1/5, the least common denominator (LCD) is 15.
Now, let's convert the mixed numbers to improper fractions:
12 8/15 = (12 * 15 + 8)/15 = 188/15
7 1/5 = (7 * 5 + 1)/5 = 36/5
Now we can simplify the expression:
188/15 − 7/1 + 36/5 + 15/1
To add the fractions, we need to find a common denominator, which is 15 for the first two fractions and 5 for the third fraction:
(188/15) − (7/1) + (36/5) + (15/1)
Now, let's add the fractions:
(188/15) − (7/1) + (36/5) + (15/1) = (188/15) − (105/15) + (72/15) + (75/15)
Now we can add the numerators and keep the denominator the same:
(188 − 105 + 72 + 75)/15 = 230/15
Finally, we can simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 5:
230/15 = (230 ÷ 5)/(15 ÷ 5) = 46/3
Therefore, the simplified answer is 46/3 or 15 1/3.