Answer:35 or 34 11/15.
Explanation:
To find the value of the expression 12 8/15 − 7 + 71/5 + 15, we can use the order of operations, which states that we should perform any calculations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.
Let's break down the expression step by step:
1. We have 12 8/15, which can be written as a mixed number. To do this, we multiply the whole number (12) by the denominator (15) and add the numerator (8), then write the result over the denominator.
12 * 15 + 8 = 180 + 8 = 188
So 12 8/15 is equivalent to 188/15.
2. Now let's substitute this value back into the original expression:
188/15 − 7 + 71/5 + 15
3. Next, let's simplify the addition and subtraction. To add or subtract fractions, the denominators must be the same. In this case, the denominators are 15 and 5, so we need to find a common denominator. The least common multiple of 15 and 5 is 15.
To convert the fractions to have a common denominator of 15:
188/15 − 7 * 15/15 + 71/5 * 3/3 + 15 * 15/15
= 188/15 − 105/15 + 213/15 + 225/15
4. Now that the denominators are the same, we can add the numerators:
188 − 105 + 213 + 225 = 521
5. The denominator remains 15, so the final result is:
521/15
Using the given use value of 21, we can divide the numerator by the denominator to find the whole number and the remainder:
521 ÷ 15 = 34 remainder 11
Therefore, the simplified value of the expression is 34 11/15.