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Multiplying and Dividing Decimals by Whole Numbers

Learn to convert decimals to fractions, multiply by 10, perform division, and solve using area models. Explore number sentences, strategies, and the relationship between multiplication, division, and fractions.

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Multiplying and Dividing Decimals by Whole Numbers

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  1. Multiplying and Dividing Decimals by Whole Numbers • 67.9 9.7 x 7 = 9 + 0.7 • 9 x 7 = 63 Change the decimal to a fraction, multiply. Multiply the decimal by 10, multiply, then divide the product by 10. OR • 7 x 7 x = • 49 x = • 49 ÷ 10 = 4.9 • 7 x 0.7 = • 7 x = • = 4 ones + 9 tenths = 4.9 • 63 + 4.9 = 67.9 Place Value 29, Multiplication Division 26, Fractions Decimals 26

  2. Multiplying and Dividing Decimals by Whole Numbers Multiply the number by 10, multiply, then divide the product by 10 97 x 7 = 9 + 07 97 x 7 = 9 + 07 • 67.9 9.7 x 7 = 9 + 0.7 Using the area model OR 9.7 x 7 = 9.7 x 7 = 7 x 9.7 x 10 ÷ 10 9.7 x 7 = 7 x 97 ÷ 10 x 90 + 7 7 630 49 630 + 49 = 679 679 ÷ 10 = 67.9 9 x 7 = 63 7 x 7 x = 49 x = 49 ÷ 10 = 4.9 63 + 4.9 = 67.9 Place Value 29, Multiplication Division 26, Fractions Decimals 26

  3. Multiplying and Dividing Decimals by Whole Numbers • 32 ÷ 4 = 8 x 32 = 8 • 8.925 35.7 ÷ 4 = 32 + 3.7 3.6 + 0.1 Change the decimal to a fraction, divide. Multiply the decimal by 10, divide, then divide the product by 10. OR • 3.6 ÷ 4 = 0.9 x 3.6 = 0.9 • 0.1 ÷ 4 = x 0.1 = • ÷ 4 = x = • ÷ 4 = x = 0.1 ÷ 4 = x 0.1 = 1 ÷ 4 ÷ 10 = x 1 ÷ 10 = 0.25 ÷ 10 = 0.25 ÷ 10 = 0.25 ÷ 10 = 0.025 0.25 ÷ 10 = 0.025 8 + 0.9 + 0.025 = 8.925 Place Value 29, Multiplication Division 26, Fractions Decimals 26

  4. Multiplying and Dividing Decimals by Whole Numbers • 8.925 35.7 ÷ 4 = 32 + 3.7 3.6 + 0.1 357 ÷ 4 = x 357 = 300 + 57 300 + 57 40 + 17 40 + 17 16 + 1 16 + 1 300 ÷ 4 = 75 x 300 = 75 40 ÷ 4 = 10 x 40 = 10 16 ÷ 4 = 4 x 16 = 4 1 ÷ 4 = x 1 = 75 + 10 + 4 + = 89.25   89.25 ÷ 10 = 8.925 Divide the decimal by 10, divide, then divide the product by 10. Place Value 29, Multiplication Division 26, Fractions Decimals 26

  5. Multiplying and Dividing Decimals by Whole Numbers • What numbers did you select? • How could you record the number sentence? • How could you multiply / divide the numbers? • How could you record your solution strategy? • The numbers I selected are ... • I recorded my number sentence by ... • I multiplied / divided by ... • I recorded my strategy as ... What is multiplication? What is division? How are multiplication and division related? How are division and fractions related? How can we use properties and relationships to multiply and divide whole numbers and decimals? Place Value 29, Multiplication Division 26, Fractions Decimals 26

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