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Chapter 1: Problem 2

$$ \begin{array}{r} 87 \\ \times \quad 4 \\ \hline \end{array} $$

Short Answer

Expert verified
348

Step by step solution

01

Multiply the Units

Multiply the units digit of 87 (which is 7) by 4. This gives us: \[ 7 \times 4 = 28 \] Place the 8 in the units place of the answer and carry over the 2 to the tens place.
02

Multiply the Tens with Carry Over

Next, multiply the tens digit of 87 (which is 8) by 4. Then add the carry over from the previous step. \[ 8 \times 4 = 32 \] Adding the carry over 2, we get: \[ 32 + 2 = 34 \] Place 34 in the tens and hundreds places of the answer.
03

Combine and Write the Final Answer

Combine the results from steps 1 and 2 to get the final answer: The answer is \[ 348 \].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

units place
The units place in a number is the digit farthest to the right. This digit represents the number of ones in the number. For example, in the number 87, the units place is 7. When multiplying, we often start with the units place. In our exercise, we multiplied 7 (the units digit of 87) by 4. This step is crucial because it lays the foundation for the next steps. When we multiply these digits, we get 28, where 8 from 28 is placed in the units place of the answer.
carry over
Carry over, or regrouping, is a basic arithmetic technique used when a product or sum in a column exceeds 9. In our multiplication example, when we multiplied the units place (7) by 4, the result was 28. We put the 8 in the units place of the answer, but 2 has to be carried over to the next higher place (the tens place). Carrying over ensures that each place value is appropriately accommodated, and it is essential for accurate calculations. In step 2, when multiplying the tens place, we add this carried-over value to the intermediate product.
basic arithmetic
Basic arithmetic involves simple operations such as addition, subtraction, multiplication, and division. These operations form the building blocks for more complex math problems. In our example, we focused on multiplication, which is essentially repeated addition. Basic arithmetic principles also include recognizing the position of digits and properly handling carry-over values to maintain accuracy. Understanding these principles helps build a strong foundation in mathematics.
multiplication steps
To solve multiplication problems, follow a step-by-step process: Start with the units place, multiply it by the other number, and write down the result, remembering to carry over any excess to the next higher place. In the given exercise:
  • Step 1: Multiply the units digit of 87 (7) by 4 to get 28. Write down 8 and carry over 2.
  • Step 2: Multiply the tens digit of 87 (8) by 4 to get 32. Add the carry-over 2 to get 34. Write down 34 next to the units place.
  • Step 3: Combine the results from steps 1 and 2 to get the final answer, which is 348.
By following these systematic steps, any multiplication problem can be solved effectively.

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