Understand the Problem
The image appears to show a diagram or mind map centered around the concept of 'partial products', with sections labeled for examples. It likely relates to a math concept used in multiplication.
Answer
The product of $23$ and $45$ is $1035$.
Answer for screen readers
The final answer to $23 \times 45$ is $1035$.
Steps to Solve
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Understanding Partial Products Partial products are used in multiplication to break down numbers into simpler parts. For example, when multiplying two numbers, you can separate them into tens and units.
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Decomposing the Numbers For example, to multiply $23 \times 45$, decompose each number:
- $23 = 20 + 3$
- $45 = 40 + 5$
- Creating Partial Products Multiply each part:
- $20 \times 40 = 800$
- $20 \times 5 = 100$
- $3 \times 40 = 120$
- $3 \times 5 = 15$
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Adding the Partial Products Now, add all the partial products together: $$ 800 + 100 + 120 + 15 $$
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Calculating the Final Sum Calculate the total: $$ 800 + 100 = 900 $$ $$ 900 + 120 = 1020 $$ $$ 1020 + 15 = 1035 $$
The final answer to $23 \times 45$ is $1035$.
More Information
Partial products make multiplication easier, especially for larger numbers, by breaking them down into simpler calculations. This method is particularly useful for students learning multiplication concepts.
Tips
Common mistakes include:
- Forgetting to decompose both numbers fully.
- Incorrectly multiplying parts, leading to wrong partial products.
- Failing to add up all the partial products.
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