Write the algebraic expressions for the following.
12 more than the sum of two-thirds of a number a and four-fifths.

Options

A. `12+(2a)/(3) - (4)/(5)`
B. `12+(2a)/(3)+(5)/(4)`
C. `12+(2a)/(3)+(4)/(5)`
D. `12-(2a)/(3)+(4)/(5)`

Answer

To write the algebraic expression for the statement "12 more than the sum of two-thirds of a number a and four-fifths," we can follow these steps:

### Step 1: Identify the components of the expression
The statement consists of two main parts:
- "two-thirds of a number a"
- "four-fifths"

### Step 2: Write the expression for "two-thirds of a number a"
Two-thirds of a number \( a \) can be expressed as:
\[ \frac{2}{3}a \]

### Step 3: Write the expression for "four-fifths"
Four-fifths can be expressed as:
\[ \frac{4}{5} \]

### Step 4: Find the sum of the two expressions
Now, we need to find the sum of the two expressions from Steps 2 and 3:
\[ \frac{2}{3}a + \frac{4}{5} \]

### Step 5: Add 12 to the sum
The statement mentions "12 more than" the sum we calculated in Step 4. Therefore, we add 12 to the sum:
\[ 12 + \left(\frac{2}{3}a + \frac{4}{5}\right) \]

### Step 6: Write the final expression
The final algebraic expression is:
\[ 12 + \frac{2}{3}a + \frac{4}{5} \]

### Summary
The algebraic expression for "12 more than the sum of two-thirds of a number a and four-fifths" is:
\[ 12 + \frac{2}{3}a + \frac{4}{5} \]

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