a × b = Product

Example: 5 × 3 = 15

(5 + 5 + 5 = 15)

Factors: Numbers being multiplied (e.g., in 5 × 3, both 5 and 3 are factors)

Product: The result of multiplication (e.g., 5 × 3 = 15, product is 15)

Multiplicand: The first number (being multiplied)

Multiplier: The second number (what you multiply by)

Partial Product: Intermediate results when multiplying multi-digit numbers

Step 1: Write numbers vertically, aligning the rightmost digits

Step 2: Multiply each digit of the bottom number by the top number

Step 3: Start with the ones place, then tens, hundreds, etc.

Step 4: For each new digit, shift one place to the left (add a zero)

Step 5: Add all partial products to get the final answer

Problem: Multiply 234 × 7

Problem: Multiply 43 × 26

Problem: Multiply 124 × 26

Steps to Multiply with Zeros:

1. Multiply the non-zero digits

2. Count total zeros in both numbers

3. Add those zeros to your product

Problem: Multiply 300 × 40

Problem: Multiply 250 × 8

Problem: Multiply 6,000 × 500

Quick Tip: When multiplying by 10, 100, or 1000, just add that many zeros!

Example: 45 × 100 = 4,500 (add 2 zeros)

The order of factors doesn't change the product

a × b = b × a

Example: 7 × 5 = 5 × 7 = 35

The grouping of factors doesn't change the product

(a × b) × c = a × (b × c)

Example: (2 × 3) × 4 = 2 × (3 × 4) = 24

Multiplicative Identity: Any number multiplied by 1 equals itself

a × 1 = 1 × a = a

Example: 25 × 1 = 25

Zero Property: Any number multiplied by 0 equals 0

a × 0 = 0 × a = 0

Example: 1,000 × 0 = 0

a × (b + c) = (a × b) + (a × c)

Example: 3 × (4 + 5) = (3 × 4) + (3 × 5)

3 × 9 = 12 + 15 = 27

Step 1: Round each factor to its highest place value

Step 2: Multiply the rounded numbers

Step 3: Use mental math for the calculation

• If digit is 0-4: Round DOWN

• If digit is 5-9: Round UP

• Round to nearest 10, 100, or 1000

Problem: Estimate 47 × 32

Problem: Estimate 678 × 849

Problem: Estimate a range for 45 × 67

• Times

• Product

• Each

• Per

• Total (when groups are equal)

• At this rate

• Twice, triple, quadruple

Problem: A movie theater has 24 rows of seats. Each row has 18 seats. How many seats are there in total?

Problem: A warehouse stores 500 boxes on each floor. If there are 30 floors, how many boxes can the warehouse store?

Problem: A school has 15 classrooms. Each classroom has 8 rows of desks with 4 desks in each row. How many desks are in the school?

Problem: A bookstore sells about 89 books per day. Estimate how many books they sell in 31 days.

✓ Align digits properly when multiplying vertically

✓ Start multiplying from the rightmost digit

✓ Carry when products are 10 or more

✓ Shift left (add zero) for each new digit in multiplier

✓ Multiplying by 10, 100, 1000: just add zeros!

✓ Order doesn't matter: 3 × 5 = 5 × 3 (commutative)

✓ Estimate first to check if your answer makes sense

✓ Any number × 1 = itself

✓ Any number × 0 = 0

✓ Check your work with estimation or division

Multiplication Steps:

"Right to Left, Bottom to Top!" (multiply from right, work through each digit)

Numbers Ending in Zeros:

"Multiply what's not zero, then add the zeros!"

300 × 40 = (3 × 4) + (000) = 12,000

Commutative Property:

"Flip the factors, same result!"

Estimating:

"Round 'em up, Round 'em down, Multiply and you're homeward bound!"

Zero Property:

"Anything times zero = zero, no exceptions, my hero!"

Check Your Work:

Estimate first, calculate, then check: Does it make sense?