1 / 32

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.

field
Download Presentation

Conceptual arithmetic methods with decimals

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related