Multiplication:

Multiplication is a mathematical operation that involves adding a number to itself several times. For example, $3\times 4$ means adding 3 four times (3 + 3 + 3 + 3). Fluently multiplying within 100 means quickly and accurately multiplying numbers where the product is 100 or less, using strategies that help solve these problems efficiently.

Strategies for Multiplying Within 100:

1. Using Known Multiplication Facts: memorize multiplication tables to recall answers quickly.
2. Skip Counting: Repeat the count by a number to reach the product (e.g., for 3×4, count "3, 6, 9, 12").
3. Using the Distributive Property: Break down larger problems into smaller parts (e.g., 6×8 as $+6\times 3$).
4. Commutative Property of Multiplication: Recognize that the order of factors doesn’t matter ($4\times 3$).
5. Using Arrays: Visualizes multiplication by arranging objects in rows and columns.

Example 1:

Simple Multiplication Using Skip Counting. Find the product of 4×5.

Solution Using Skip Counting:

1. Count by 4 five times: 4, 8, 12, 16, 20.
2. Final solution: 4×5=20

Example 2:

Using the Distributive Property: Find 6×8 by breaking it down.

Solution Using Distributive Property:

1. Break down 8 as 5 + 3.
2. Rewrite 6×8 as 6×(5+3).
3. Use the distributive property: $+6\times 3$.
   • 6×5=30.
   • 6×3=18.
4. Add the two results: 30 + 18 = 48.
5. Final solution: 30+18=48.

Example 3:

Memorizing a One-Digit Product: What is 9×7?

Solution using memorization:

1. Recall from memory or previous practice that 9×7=63.
2. Final solution: $63$.

Example 4: 2-Digit by 1-Digit Multiplication Using Standard Algorithm Calculate 9×23.

Solution:

1. Write the numbers vertically and multiply each place separately

23
× 9
-----

• Multiply the ones place:
  • 9×3=27. Write down 7 in the one's place and carry over 2 to the tens.
• Multiply the tens place:
  • 9×2=18.
  • Add the carried-over 2: 18 + 2 = 20.
• Write the final product:

23
× 9
-----
207

Final solution:  $9\times 23=207$.

Example 4:

Multiplying two 2-digit numbers: calculate 13×15.

Solution Using the Distributive Property:

1. Break down both numbers:
   • 13=10+3 and $15=10+5$.
2. Apply the distributive property:
   • $13\times 15=(10+3)\times (10+5)$.
   • Distribute each term:
     • 10×10=100
     • 10×5=50
     • 3×10=30
     • 3×5=15
3. Add the products together:
   • 100+50+30+15=195

Final solution: 13×15=195.

Let's practice solving Place values, and stay tuned with us for more content