What is 12 8/15 -7 +7/15 +15
To solve this expression, we follow the order of operations (PEMDAS/BODMAS).
First, let's simplify the mixed number 12 8/15 to an improper fraction:
12 8/15 = 12 + 8/15 = (12 × 15 + 8) / 15 = 184/15
The expression now becomes:
184/15 - 7 + 7/15 + 15
Next, we add or subtract the fractions and the whole numbers separately.
Adding the fractions:
184/15 + 7/15 = (184 + 7) / 15 = 191/15
Now the expression becomes:
191/15 - 7 + 15
To subtract a whole number from a fraction, we need to convert the whole number into a fraction with a common denominator:
191/15 - 7/1 + 15/1
To have a common denominator for all fractions, we multiply the denominator of the first fraction by 1 (15/1), and multiply the denominator of the second fraction by 15 (1 * 15 = 15):
191/15 - 7 * 15/15 + 15/1
Simplifying the expression:
= 191/15 - 105/15 + 15/1
Now that all fractions have the same denominator (15), we can add or subtract them directly:
= (191 - 105 + 15)/15
Calculating the numerator:
191 - 105 + 15 = 101
The final result is:
101/15
To solve this, follow these steps:
Step 1: Convert the mixed number 12 8/15 into an improper fraction:
To convert the mixed number to an improper fraction, multiply the whole number (12) by the denominator (15). Then add the numerator (8) to the product. Place the sum over the denominator to get 192/15.
Step 2: Add all the fractions together:
Combine the fractions 192/15, 7/15, and 15/1 by finding a common denominator, which is 15.
192/15 + 7/15 + 15/1 = (192 + 7 + 225) / 15
Step 3: Simplify the numerator:
192 + 7 + 225 = 424
So, the equation becomes:
424/15 + 15/1
Step 4: Find a common denominator:
To add fractions with different denominators, find a common denominator. In this case, the common denominator is 15.
Step 5: Add the fractions:
Combine the fractions 424/15 and 15/1, by placing them over the common denominator:
(424/15) + (15/1) = (424 + 225) / 15
Step 6: Simplify the numerator:
424 + 225 = 649
So, the equation becomes:
649/15
Therefore, 12 8/15 - 7 + 7/15 + 15 = 649/15 as a fraction.