3 Chapter Whole Numbers and Their Operations

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Presentation transcript:

3 Chapter Whole Numbers and Their Operations Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

3-4 Algorithms for Whole-Number Multiplication and Division Multiplication Algorithms Division Algorithms Division by a Two-Digit Divisor Multiplication and Division in Different Bases Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Algorithms for Whole-Number Multiplication and Division They select appropriate methods and apply them accurately to estimate products or calculate them mentally, depending on the context and numbers involved. They develop fluency with efficient procedures, including the standard algorithm, for multiplying whole numbers, understand why the procedures work (on the basis of place value and properties of operations), and use them to solve problems. NCTM grade 4 Focal Points, p. 16 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Properties of Exponents Definition of an for whole numbers If a, the base and n, the exponent, are whole numbers and n  0, then Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Properties of Exponents Theorem 3-9 For any whole number a and natural numbers m and n: Theorem 3-10 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Properties of Exponents Theorem 3-11 For any whole number a and natural numbers m and n: Theorem 3-12 If a, m, and n are natural numbers with m > n, then Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. Example 3-4 Write each of the following with only one exponent. a. b. a. b. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Multiplication Algorithms Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Multiplication Algorithms Multiplication by 10n To multiply by 10, replace each piece with a base-ten piece that represents the next higher power of 10. Replace each unit with a long, and replace each long with a flat. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Multiplication Algorithms Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Multiplication Algorithms Multiplication using expanded addition Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Multiplication Algorithms Multiplication with Two-Digit Factors Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Multiplication Algorithms Lattice Multiplication Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. Division Algorithms Using Repeated Subtraction to Develop the Standard Division Algorithm or Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. Division Algorithms or Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. Division Algorithms Using Base-Ten Blocks to Develop the Standard Division Algorithm 1. Represent 726 with base-ten blocks. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. 2. Determine how many sets of 6 flats (hundreds) there are. There is one set of 6 flats with 1 flat, 2 longs, and 6 units left over. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. 3. Convert the one leftover flat to 10 longs. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. 4. Determine how many sets of 6 longs there are in the 12 longs. There are 2 set of 6 longs and 6 units left over. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. 5. Now determine how many sets of 6 units there are. There is 1 set of 6 units with no units left over. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Division Algorithms Short Division Decide where to start. Divide the hundreds. Write the remainder by the tens. Divide the tens. Write the remainder by the ones. Divide the ones. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Division by a Two-Digit Divisor Four step method: 1. Estimate 2. Multiply 3. Subtract 4. Compare (check) Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Division by a Two-Digit Divisor Divide 1. Estimate the quotient. The quotient is between 10 and 100. 2. Find the number of tens in the quotient. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. 3. Find the number of units in the quotient. 4. Check. 32 · 81 + 26 = 2618 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Multiplication and Division in Different Bases Base-Five Multiplication Table Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Multiplication and Division in Different Bases Multiply 21five · 3five. Fives Ones 2 1  3 → → → Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Multiplication and Division in Different Bases Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. Example 3-4a Multiply: Copyright © 2013, 2010, and 2007, Pearson Education, Inc.