Mutiply 185 by 215.

Answer

To multiply 185 by 215 using a shortcut method, we can break down the numbers into simpler components. Here’s a step-by-step solution:

### Step 1: Break down 215
We can express 215 as the sum of 200 and 15:
\[ 215 = 200 + 15 \]

### Step 2: Set up the multiplication
Now, we can rewrite the multiplication:
\[ 185 \times 215 = 185 \times (200 + 15) \]

### Step 3: Distribute the multiplication
Using the distributive property, we can separate the multiplication:
\[ 185 \times 215 = 185 \times 200 + 185 \times 15 \]

### Step 4: Calculate \( 185 \times 200 \)
To calculate \( 185 \times 200 \):
\[ 185 \times 200 = 37000 \]

### Step 5: Break down 15
Next, we can break down 15 into 10 and 5:
\[ 15 = 10 + 5 \]

### Step 6: Calculate \( 185 \times 15 \)
Using the same distributive property:
\[ 185 \times 15 = 185 \times (10 + 5) \]
\[ = 185 \times 10 + 185 \times 5 \]

### Step 7: Calculate \( 185 \times 10 \)
Calculating \( 185 \times 10 \):
\[ 185 \times 10 = 1850 \]

### Step 8: Calculate \( 185 \times 5 \)
Now, calculate \( 185 \times 5 \):
\[ 185 \times 5 = 925 \]

### Step 9: Add the results of \( 185 \times 15 \)
Now, we can add the two results from step 7 and step 8:
\[ 1850 + 925 = 2775 \]

### Step 10: Combine all parts
Now, we combine the results from step 4 and step 9:
\[ 37000 + 2775 = 39775 \]

### Final Result
Thus, the product of 185 and 215 is:
\[ 185 \times 215 = 39775 \]

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