To understand two-digit multiplication, we first need to master place values.Let's break down the number twenty-three. In the tens place, we have 2, which represents twenty.In the ones place, we have 3, which represents three ones.So twenty-three can be broken down as twenty plus three.When writing numbers vertically for multiplication, proper alignment is crucial.Let's write twenty-three times twelve vertically. We'll align the numbers carefully.Notice how each digit lines up in its proper place value column.The tens digits go in the tens column, and the ones digits go in the ones column.Keeping these columns straight will be essential for our multiplication process.Now that we understand place values and proper alignment, we're ready to begin multiplication.Now let's solve twenty-three times twelve step by step.First, we multiply the ones digits. Three times two equals six.Next, we multiply three by the tens digit, one. Three times one is three.Now we multiply twenty by two. Twenty times two equals forty.Finally, we multiply twenty by ten, which gives us two hundred.Notice how we position each number carefully based on its place value.These partial products are now ready to be added together.Now that we have our partial products, let's add them together to find the final answer.We have two rows to add: forty-six from multiplying by two, and two hundred thirty from multiplying by ten.Let's add column by column, starting from the right with the ones place.In the ones column, we have six plus zero, which equals six.Moving to the tens column, we add four plus three to get seven.Finally, in the hundreds column, we add zero plus two to get two.Our final answer is two hundred seventy-six. We can verify this makes sense because twenty-three times twelve should be more than twenty times ten, which is two hundred.
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