Multiplying by Three-Digit Numbers

Steps for Multiplying by a Three-Digit Number

1. Understand the Structure:

   • A three-digit number can be expressed as: (abc) (where (a), (b), and (c) are digits).

2. Break Down the Multiplication:

   • Multiply the number by each digit of the three-digit number separately.
   • Remember to adjust for the place value of each digit (hundreds, tens, units).

3. Steps to Multiply:

   • Example: Multiply (N) by (abc)
     • (N \times c) (multiply by the unit’s place)
     • (N \times b) (multiply by the ten’s place) and shift left (add a zero)
     • (N \times a) (multiply by the hundred’s place) and shift left (add two zeros)

4. Adding the Results:

   • Add all the partial results together.

Example Calculation

1. Example Problem: (234 \times 456)

   • Step 1: Multiply (234 \times 6) (units)
   • Step 2: Multiply (234 \times 5) (tens), shift left to give (1170)
   • Step 3: Multiply (234 \times 4) (hundreds), shift left to give (93600)

2. Adding Partial Results:

   • (1404) (from 6)
   • (1170) (from 50)
   • (93600) (from 400)
   • Total: (106584)

Tips for Multiplication

• Use the distributive property to simplify calculations.
• Align numbers vertically for clarity when adding.
• Practice with different three-digit numbers to build speed and confidence.

Common Mistakes

• Forgetting to shift for place value.
• Misaligning numbers when adding the partial products.
• Falling into simple arithmetic errors during multiplication.

Practice Problems

1. (123 \times 456)
2. (234 \times 789)
3. (345 \times 654)

By mastering these steps, you can multiply any number by a three-digit number efficiently.

Multiplying by Three-Digit Numbers

• A three-digit number is represented as (abc), where (a), (b), and (c) are digits.
• Multiplying by a three-digit number involves breaking down the multiplication into three separate steps, one for each digit of the three-digit number.
• Each step requires multiplying the number by the corresponding digit and adjusting for its place value.
• To multiply by the unit’s place (c), multiply directly.
• To multiply by the ten’s place (b), add a zero to the right before multiplying to shift the result one place to the left.
• To multiply by the hundred’s place (a), add two zeros to the right before multiplying, shifting the result two places to the left.
• After multiplying, align the partial results by their place values and sum them to get the final answer.
• Example: To multiply (234 \times 456), one would first multiply (234 \times 6) (units).
• Then multiply (234 \times 5) (tens) and shift the result to the left, adding a zero to get (1170).
• Finally, multiply (234 \times 4) (hundreds) and shift it two places to the left by adding two zeros, yielding (93600).
• Adding the partial results (1404), (1170), and (93600) together results in the final answer, (106584).
• Tips: Use the distributive property to simplify calculations, align numbers vertically for clarity when adding, and practice multiplying with different three-digit numbers to gain speed and confidence.
• Common Mistakes: Forgetting to shift for place value, misaligning numbers when adding partial products, and making arithmetic errors during multiplication.

Practice Problems

• (123 \times 456)
• (234 \times 789)
• (345 \times 654)

This quiz covers the steps for multiplying a number by a three-digit number. It includes understanding the structure of a three-digit number, breaking down the multiplication process, and adding the partial results. Test your skills with examples and practice problems.