Multi-Digit Multiplication

Multiplying by One Digit

When you multiply a multi-digit number by a single digit, work from right to left and remember to carry!

Example: $23 \times 4$

Written Steps:

1. Multiply ones: $3 \times 4 = 12$ (write 2, carry 1)
2. Multiply tens: $2 \times 4 = 8$, plus carried 1 = $9$
3. Result: $92$

Multiplying by Two Digits

When multiplying by a two-digit number, you multiply twice and then add the results.

Example: $34 \times 26$

Written Steps:

1. Multiply by the ones digit: $34 \times 6 = 204$
2. Multiply by the tens digit: $34 \times 2 = 68$ (shifted one place left = 680)
3. Add the two products: $204 + 680 = 884$

The Standard Algorithm

Key steps to remember:

1. Start from the right - Always begin with the ones place
2. Carry when needed - If a product is 10 or more, carry to the next place
3. Shift for place value - When multiplying by tens, shift one place left
4. Add all partial products - Sum up all the rows to get your final answer

Tips to Remember

• Line up your numbers carefully - Keep digits in the correct columns
• Remember to shift - When multiplying by the tens place, shift one position left
• Check your work - Use estimation to see if your answer makes sense
• Practice regrouping - Carrying is essential for accuracy!

Real-World Applications

Multiplication helps us solve everyday problems:

• Shopping: If one toy costs $24 and you buy 15 toys, how much total?

  • $24 \times 15 = 360$ (so $360)

• Area: A rectangle is 18 feet long and 12 feet wide. What's the area?

  • $18 \times 12 = 216$ square feet

• Groups: If each class has 28 students and there are 4 classes, how many students?

  • $28 \times 4 = 112$ students