Chapter 2 Multiply Whole Numbers Lesson 1 Prime

Chapter 2 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 ( 2 x 3²).

Lesson 3 – Powers and Exponents � 3⁴ 3 is the base 4 is the exponent �The base is the number that is being multiplied. �The exponent tells you how many times you multiply the base. �Example: 3⁴=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, 000 45 x 1 = 45 2. 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 Week Miles 1 2 starting # x 2 2 3 4 4 8 16 x 2 Janice will run 16 miles during week 4.

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) 80 + 16 = 96

Lesson 8 – Estimate Products 1. Round numbers all the way to the left. Use the rules for rounding. 92 → 90 x 12 → x 10 0 1 2 3 4 - round down 5 6 7 8 9 – round up 2. Multiply the non-zero numbers. Count the zeros. 90 x 10 900 9 x 1=9 1 zero + 1 zero = 2 zeros

Lesson 9 – Multiply by One-Digit Numbers 1. Multiply the ones. 873 x 2 6 2. Multiply the tens. Bring the digit in the tens place over to the next number. 1 873 x 2 46 3. Multiply the hundreds. Add the number you carried over. 1 873 x 2 1, 746

Lesson 10 – Multiply by Two-Digit Numbers 1. Multiply the ones. 4 56 x 17 392 2. Erase any markings. Add a zero to the next row. 3. Multiply the tens. 56 x 17 392 + 560 4. Add the columns. 952