Solve, using properties/ methods that simplify the calculations:
`314xx15`

Answer

To solve the multiplication \( 314 \times 15 \) using properties that simplify calculations, we can break down the numbers into simpler parts. Here’s a step-by-step solution:

### Step 1: Break down the numbers
We can express \( 314 \) and \( 15 \) as:
- \( 314 = 300 + 14 \)
- \( 15 = 10 + 5 \)

### Step 2: Use the distributive property
Now we can use the distributive property to multiply:
\[ 314 \times 15 = (300 + 14) \times (10 + 5) \]

### Step 3: Apply the distributive property
Now we will multiply each part:
1. \( 300 \times 10 = 3000 \)
2. \( 300 \times 5 = 1500 \)
3. \( 14 \times 10 = 140 \)
4. \( 14 \times 5 = 70 \)

### Step 4: Add all the products together
Now we add all the results from the multiplications:
\[ 3000 + 1500 + 140 + 70 \]

### Step 5: Perform the addition
Now, let's add these values step by step:
1. \( 3000 + 1500 = 4500 \)
2. \( 4500 + 140 = 4640 \)
3. \( 4640 + 70 = 4710 \)

### Final Answer
Thus, the product \( 314 \times 15 = 4710 \).

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