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Conceptual arithmetic methods with decimals

Conceptual arithmetic methods with decimals. Multiplication. Multiplication with decimals. The following three techniques will be covered in this presentation: Using upper and lower product bounds to correctly place the decimal point Converting to fractions Place value multiplication.

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Conceptual arithmetic methods with decimals

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  1. Conceptual arithmetic methods with decimals Multiplication

  2. Multiplication with decimals • The following three techniques will be covered in this presentation: • Using upper and lower product bounds to correctly place the decimal point • Converting to fractions • Place value multiplication

  3. Technique 1 Using upper and lower product bounds to correctly place the decimal point

  4. Example 1: Find the product of 3.8 and 0.52 1. Find upper and lower bounds for the factors:3 < 3.8 < 4 and 0.5 < 0.52 < 0.6 2. Find upper and lower bounds for the product:

  5. Example 1: Find the product of 3.8 and 0.52 3. Multiply the factors as if they were whole numbers: 4. Use the upper and lower bounds for the product to correctly place the decimal point. Answer:

  6. Example 2: Find the product of 72.3 and 8.201 1. 70 < 72.3 < 80 and 8 < 8.201 < 9 2. 3. Multiply the factors as if they were whole numbers: 4.Correctly place the decimal point using the bounds.Answer:

  7. Technique 2 Convert to fractions

  8. Example 3: Find the product of 1.2 and 0.03 • Convert each decimal to fraction form: • Multiply the fractions: • Rewrite in decimal form: 1.2 x 0.03 = 0.036 • If you have trouble seeing the decimal form, note that 36/1000 = 30/1000 + 6/1000 = 3/100 + 6/1000 = 0.03 + 0.006 = 0.036

  9. Example 4: Find the product of 0.025 and 0.08 • Convert each decimal to fraction form: • Multiply the fractions: • Rewrite in decimal form: 0.025 x 0.08 = 0.002

  10. Example 5: Find the product of34.23 and 0.011 • Convert each decimal to fraction form: • Multiply the fractions: • Rewrite in decimal form: 34.23 x 0.011 = 0.37653 • Note that the final digit of 3 in the numerator 37653 from step 2 must be in the 100,000ths (hundred thousandths) place.

  11. Technique 3 Place Value Multiplication

  12. Multiplication of decimals using place value • Use a place value chart to organize the factors and partial products. • The number of columns depends on the problems. Leave room to add more columns if necessary.

  13. Example 6: Find the product of 2.3 and 4.5 • Step 1: Enter the factors into a place value chart.

  14. Example 6: Find the product of 2.3 and 4.5 • Step 2: Find the partial products.

  15. Example 6: Find the product of 2.3 and 4.5 • Step 2: Find the partial products.

  16. Example 6: Find the product of 2.3 and 4.5 • Step 2: Find the partial products.

  17. Example 6: Find the product of 2.3 and 4.5 • Step 2: Find the partial products.

  18. Example 6: Find the product of 2.3 and 4.5 • Step 3: Sum the partial products to obtain the final product.

  19. Example 7: Find the product of.08 and .907 • Example: Find the product of .08 and .907 • Estimate practice: The answer should lie between

  20. 0.08 x 0.907 = 0.07256

  21. Example 8: Find the product of 2.305 and 70.89 • Find the product of 2.305 and 70.89. • Estimating, we see that our answer should be between2 x 70 = 140 and 3 x 71 = 213. We can use this as a check at the end.

  22. 70.89 x 2.305 = 163.40145

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