What is 12 8/15 − 7 + 7/15 + 15 in simplest form?
To solve this expression, we need to find a common denominator for all the fractions involved.
Since the denominator of 8/15 is 15, we convert 12 to an equivalent fraction with a denominator of 15: 12 = 12/1 = (12*15)/(1*15) = 180/15.
Now we can perform the arithmetic:
180/15 − 7 + 7/15 + 15 = (180 − 7 + 7 + 15)/15
= 195/15
= 13.
Therefore, 12 8/15 − 7 + 7/15 + 15 simplifies to 13 in simplest form.
To simplify the expression 12 8/15 - 7 + 7/15 + 15, we can follow these steps:
1. Convert the mixed number 12 8/15 to an improper fraction.
12 8/15 = (12 * 15 + 8) / 15 = 188/15
2. Add the fractions together.
188/15 - 7 + 7/15 + 15 = 188/15 + 15/1 + 7/15
3. Find a common denominator for the fractions.
The common denominator for 15 and 1 is 15.
188/15 + 15/1 + 7/15 = 188/15 + 225/15 + 7/15
4. Add the numerators together and keep the common denominator.
188/15 + 225/15 + 7/15 = (188 + 225 + 7) / 15 = 420/15
5. Simplify the fraction by reducing it.
The greatest common divisor of 420 and 15 is 15. Divide both the numerator and the denominator by 15.
420/15 = (420 ÷ 15) / (15 ÷ 15) = 28/1
6. Convert the improper fraction to a mixed number if necessary.
Since 28 divided by 1 is still 28, the simplified form is 28.
Therefore, 12 8/15 - 7 + 7/15 + 15, when simplified, is equal to 28.