38 Chapter 1 Whole Numbers 3. Multiplying Many-Digit Whole Numbers When multiplying numbers with several digits, it is sometimes necessary to carry. To see why, consider the product 3 29. By writing the factors in expanded form, we can apply the distributive property. In this way, we see that 3 is multiplied by both 20 and 9. 3 29 3120 92 13 202 13 92 60 27 6 tens 2 tens 7 ones 8 tens 7 ones Now we will multiply in vertical form. Multiply Write the 7 in the ones column and carry the 2. 3 2 tens 6 tens. Multiply Add the carry: Write the 8 in the tens place. Multiplying a Many-Digit Number by a One-Digit Number Multiply. 368 5 Solution: Using the distributive property, we have 51300 60 82 1500 300 40 1840 This can be written vertically as: The numbers 40, 300, and 1500 are called partial products. The product of 386 and 5 is found by adding the partial products. The product is 1840. The solution to Example 4 can also be found by using a shorter form of multiplication. We outline the procedure: Multiply 5 8 40. Write the 0 in the ones place and carry the 4. 4 8 36 5 0 368 5 40 300 1500 1840 Multiply 5 8. Multiply 5 60. Multiply 5 300. Add. Example 4 6 tens 2 tens 8 tens. 2 2 9 3 8 7 3 9 27. 2 2 9 3 7 29 3 87 Skill Practice Multiply. 8. 247 3 Answer 8. 741
miller_prealgebra_2e_ch1_3
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