Multiply Whole Numbers

Lesson 1 – Prime Factorization Prime factorization is breaking down a composite number into its prime factors. To find the prime factorization of a number, use a factor tree. Example: 18 ↓ ↓ 6 x 3 ↓ ↓ ↓ 3 x 2 x 3 The prime factorization of 18 is 2 x 3 x 3 ( 2 x 3 ²).

Lesson 3 – Powers and Exponents 3 ⁴ 3 is the base4 is the exponent The base is the number that is being multiplied. The exponent tells you how many times you multiply the base. Example: 3 ⁴ = 3 x 3 x 3 x 3 ↓ 9 x 9 = 81

Lesson 4 – Multiplication Patterns With powers of 10 and other large numbers, you can use mental math to solve. Example:450 x 10³ ↓ 450 x 1,000 (the exponent tells you how many zeros to add) 1. Multiply the numbers that are not zeros. 450 x 1, x 1 = Count the number of zeros in the product. Put that many zeros in your answer. 450 x 1,000 ↓ ↓ 1 zero + 3 zeros = 4 zeros in answer 450 x 1,000 = 450,000

Lesson 5 – Problem-Solving Strategy: Make a Table Janice is training for a marathon. She begins by running 2 miles the first week. Each week she runs double the amount of miles. How many miles will she run during week 4? Double = x 2 starting # x 2 x 2 x 2 Janice will run 16 miles during week 4. Week1234 Miles24816

Lesson 7 – The Distributive Property You can use the Distributive Property to break numbers into smaller ones that you can easily multiply. Example: 8 x 12 ↓ ↓ 10 2 Break the digit down into tens and ones Multiply and add the sums. (8 x 10) + (8 x 2) = 96

Lesson 8 – Estimate Products 1. Round numbers all the way to the left. Use the rules for rounding. 92 → round down x 12 → x – round up 2. Multiply the non-zero numbers. Count the zeros x 1 = 9 x 10 1 zero + 1 zero = 2 zeros 900

Lesson 9 – Multiply by One-Digit Numbers 1. Multiply the ones.873 x Multiply the tens. Bring the digit in the tens place over to the next number x Multiply the hundreds. Add the number you carried over x 2 1,746

Lesson 10 – Multiply by Two-Digit Numbers 1. Multiply the ones.4 56 x Erase any markings. Add a zero to the next row. 3. Multiply the tens. 56 x Add the columns. 952