What is 12 8/15 - 7 + 7 1/5 + 15
in simplest form?
To simplify the expression 12 8/15 - 7 + 7 1/5 + 15, we need to convert all the mixed fractions 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 the expression becomes:
188/15 - 7 + 36/5 + 15
To add the fractions together, we need to find a common denominator. The least common multiple (LCM) of 15 and 5 is 15.
(188/15) - (7 * 15/15) + (36/5 * 3/3) + (15 * 15/15)
= 188/15 - 105/15 + 108/15 + 225/15
Now that all the fractions have the same denominator, we can combine them:
= (188 - 105 + 108 + 225) / 15
= 416/15
So, 12 8/15 - 7 + 7 1/5 + 15 in simplest form is 416/15.
To find the sum in simplest form, we need to convert all the mixed numbers to improper fractions and then perform the calculation.
Step 1: Convert the mixed numbers to improper fractions.
12 8/15 can be rewritten as (12 * 15 + 8)/15 = 188/15
7 1/5 can be rewritten as (7 * 5 + 1)/5 = 36/5
Step 2: Perform the calculation.
188/15 - 7 + 36/5 + 15
First, let's find a common denominator for the fractions. The least common multiple of 15 and 5 is 15. So we can rewrite the fractions with a common denominator of 15:
(188/15) - (7 * 15/15) + (36/5 * 3/3) + (15 * 15/15)
Step 3: Simplify the fraction.
188/15 - 105/15 + 108/15 + 225/15
Now that the fractions have the same denominator, we can add/subtract the numerators:
(188 - 105 + 108 + 225)/15 = 416/15
So, the sum 12 8/15 - 7 + 7 1/5 + 15 in simplest form is 416/15.