Divide `13.2` in the ratio ` 4:7.`

Answer

To divide `13.2` in the ratio `4:7`, we can follow these steps:

### Step 1: Set up the equation
Let the parts of the ratio be represented as `4x` and `7x`. Therefore, we can write the equation:
\[ 4x + 7x = 13.2 \]

### Step 2: Combine like terms
Combine the terms on the left side:
\[ 11x = 13.2 \]

### Step 3: Solve for x
To find the value of `x`, divide both sides of the equation by `11`:
\[ x = \frac{13.2}{11} \]

### Step 4: Remove the decimal for easier calculation
To simplify the division, we can remove the decimal by multiplying the numerator and denominator by `10`:
\[ x = \frac{132}{110} \]

### Step 5: Simplify the fraction
Now, divide `132` by `11`:
\[ x = 12 \]

### Step 6: Calculate the parts
Now that we have `x`, we can find the two parts:
1. For `4x`:
\[ 4x = 4 \times 12 = 48 \]
2. For `7x`:
\[ 7x = 7 \times 12 = 84 \]

### Step 7: Convert to decimal
Since we initially multiplied by `10` to remove the decimal, we need to divide by `10` to convert back:
1. For `4x`:
\[ 4x = \frac{48}{10} = 4.8 \]
2. For `7x`:
\[ 7x = \frac{84}{10} = 8.4 \]

### Conclusion
Thus, `13.2` divided in the ratio `4:7` gives us:
- The first part (4x) = **4.8**
- The second part (7x) = **8.4**

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