Divide `10.4` into the ratio `3:5.`

Answer

To divide 10.4 into the ratio of 3:5, we will follow these steps:

### Step 1: Understand the Ratio
The ratio 3:5 means that for every 3 parts of one quantity, there are 5 parts of another quantity. The total parts in the ratio is 3 + 5 = 8 parts.

### Step 2: Let the Common Multiple be x
Let the common multiple be \( x \). Therefore, we can express the two parts as:
- First part = \( 3x \)
- Second part = \( 5x \)

### Step 3: Set Up the Equation
Since the total of the two parts must equal 10.4, we can write the equation:
\[ 3x + 5x = 10.4 \]

### Step 4: Combine Like Terms
Combine the terms on the left side:
\[ 8x = 10.4 \]

### Step 5: Solve for x
To find \( x \), divide both sides of the equation by 8:
\[ x = \frac{10.4}{8} \]

### Step 6: Perform the Division
Now, let's perform the division:
- 8 goes into 10 once (1), leaving a remainder of 2.
- Bring down the 4 to make it 24.
- 8 goes into 24 three times (3).

Thus, \( x = 1.3 \).

### Step 7: Calculate Each Part
Now we can find each part:
- First part (3x):
\[ 3x = 3 \times 1.3 = 3.9 \]

- Second part (5x):
\[ 5x = 5 \times 1.3 = 6.5 \]

### Final Answer
Thus, when dividing 10.4 into the ratio of 3:5, we get:
- First part = 3.9
- Second part = 6.5