Question

a. Multiply 12 and 36 by rewriting 36 as \(30+6,\) and use the distributive property to obtain the result. b. Multiply 12 and 36 vertically.

Short answer

Answer: The two multiplication methods used to multiply 12 and 36 are the distributive property method and the vertical multiplication method. The product of 12 and 36 is 432.

Step-by-step solution

Part a: Using the Distributive Property

First, rewrite the given number 36 as the sum of 30 and 6. Now, we have to multiply 12 by \((30+6)\). Using the distributive property, we get the following: \(12 \times (30+6) = 12 \times 30 + 12 \times 6\) Now, multiply each term: \(12 \times 30 = 360\) \(12 \times 6 = 72\) Finally, add the results: \(360 + 72 = 432\) So, \(12 \times 36 = 432\) using the distributive property.

Part b: Vertical Multiplication Method

Now, let's multiply 12 and 36 using the vertical multiplication method. Write down the numbers one below the other with proper alignment, like this: ``` 12 x 36 ``` Step 1: Multiply the ones place of both numbers (2 and 6): \(2 \times 6 = 12\) Write 12 down and carry over the 1 (tens place) to the next step. ``` 12 x 36 ----- 72 ``` Step 2: Multiply the ones place of the first number (2) by the tens place of the second number (3) and add the carry-over (1): \((2 \times 3) + 1 = 7\) Write 7 to the left of the previous result. ``` 12 x 36 ----- 72 7 ``` Step 3: Multiply the tens place of the first number (1) by the ones place of the second number (6) and write the result below the previous step, but shifted one place to the left: \((1 \times 6) = 6\) ``` 12 x 36 ----- 72 7 6 ``` Step 4: Multiply the tens places of both numbers (1 and 3): \((1 \times 3) = 3\) Write 3 to the left of the previous result. ``` 12 x 36 ----- 72 7 36 ``` Step 5: Add the results: ``` 12 x 36 ----- 72 7 36 ----- 432 ``` So, \(12 \times 36 = 432\) using the vertical multiplication method.