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Chapter 1: Problem 36

Multiply. $$\begin{array}{r} 105 \\ \times 9 \\ \hline \end{array}$$

Short Answer

Expert verified
105 multiplied by 9 equals 945.

Step by step solution

01

Multiply the Ones Place

First, multiply the digit in the ones place of 105 (which is 5) by 9.\(5 \times 9 = 45\). Write down 5 and carry over 4.
02

Multiply the Tens Place

Next, multiply the digit in the tens place of 105 (which is 0) by 9, then add the carry-over value from the previous step.\(0 \times 9 + 4 = 4\). Write down 4.
03

Multiply the Hundreds Place

Finally, multiply the digit in the hundreds place of 105 (which is 1) by 9.\(1 \times 9 = 9\). Write down 9.
04

Combine the Results

Now, combine all the digits from steps 1-3. The digits are 945. Therefore, 105 multiplied by 9 equals 945.

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Key Concepts

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

place value
Understanding place value is essential for multiplication. Each digit in a number has a specific place value depending on its position. For example, in the number 105:
  • 5 is in the ones place.
  • 0 is in the tens place.
  • 1 is in the hundreds place.
When multiplying, it's important to handle each digit according to its place value. This ensures that the multiplication process is accurate and the resulting product is correct. Knowledge of place value makes complex calculations more manageable as it breaks the process into smaller, easier steps.
carrying over
Carrying over is a technique used during multiplication when a product of two digits exceeds 9. For example, in our exercise:
  • When multiplying 5 (ones place of 105) by 9, we get 45.
Here, 5 is written in the ones place and 4 is carried over to the next place value (tens place). Carrying over helps maintain the structure of place values and ensures no part of the number is overlooked. It's a critical part of accurate multiplication.
step-by-step solution
Breaking down multiplication into a step-by-step solution can make it simpler:
  1. First step: Multiply the ones place of 105 (which is 5) by 9. This gives us 45. Write down 5 and carry over 4.
  2. Second step: Multiply the tens place of 105 (which is 0) by 9 and then add the carry-over value (4). This results in 4.
  3. Third step: Multiply the hundreds place of 105 (which is 1) by 9. This gives us 9.
  4. Final step: Combine the results to form the final product, 945.
Using a step-by-step approach clarifies each part of the multiplication process and ensures accuracy.
basic arithmetic
Multiplication is one of the basic arithmetic operations. It's essentially repeated addition. In our exercise, multiplying 105 by 9 means adding 105 to itself 9 times. Understanding the basic idea behind arithmetic operations lets you tackle more complex problems with confidence. Strong arithmetic skills form the foundation for all higher-level math and practical problem-solving in daily life.

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