1.8: Estimating Products

Before you practice estimating products, look at the easy multiplication that can be done when the factors end in zeros.

You already know how to quickly multiply by 10, 100, 1000, and so on.

You can find the products in questions like these using regular multiplication, but here is a shortcut:

  1. Count all the zeros at the end of the numbers in both factors.
  2. Write down that many zeros at the end of the product.
  3. Multiply the other digits in the usual way and put them before the zeros.

Example A

[latex]30\times500=[/latex]

  1. How many zeros at the end of the factors? 3
  2. Write them down. 000
  3. Multiply the other digits and put them before the zeros. [latex]\boldsymbol{3 \times 5 = 15}[/latex]

[latex]30\times500=15\,000[/latex]

Example B

[latex]400\times3\,000=[/latex]

  1. How many zeros at the end of the factors? 5
  2. Write them down. 00000
  3. Multiply the other digits and put them before the zeros. [latex]\boldsymbol{4 \times 3 = 12}[/latex]

[latex]400\times3\,000=1\,200\,000[/latex]

Exercise 1

Find the products using the shortcut. Check your work using the answer key at the end of the exercise.

Example:     [latex]\begin{array}{rr}&300\\\times&20\\\hline&6000\end{array}[/latex]

 

  1. [latex]\begin{array}{rr}&6000\\\times&200\\\hline\\\end{array}[/latex]
  2. [latex]\begin{array}{rr}&210\\\times&20\\\hline\\\end{array}[/latex]
  3. [latex]\begin{array}{rr}&800\\\times&600\\\hline\\\end{array}[/latex]
  4. [latex]\begin{array}{rr}&400\\\times&500\\\hline\\\end{array}[/latex]
  5. [latex]\begin{array}{rr}&6000\\\times&90\\\hline\\\end{array}[/latex]
  6. [latex]\begin{array}{rr}&50000\\\times&6000\\\hline\\\end{array}[/latex]
  7. [latex]\begin{array}{rr}&80000\\\times&30\\\hline\\\end{array}[/latex]
  8. [latex]\begin{array}{rr}&5000\\\times&50\\\hline\\\end{array}[/latex]
  9. [latex]\begin{array}{rr}&70\\\times&80\\\hline\\\end{array}[/latex]
  10. [latex]\begin{array}{rr}&3000\\\times&700\\\hline\\\end{array}[/latex]
  11. [latex]\begin{array}{rr}&50000\\\times&900\\\hline\\\end{array}[/latex]
  12. [latex]\begin{array}{rr}&9000\\\times&8000\\\hline\\\end{array}[/latex]
  13. [latex]\begin{array}{rr}&60000\\\times&90\\\hline\\\end{array}[/latex]
  14. [latex]\begin{array}{rr}&90000\\\times&2000\\\hline\\\end{array}[/latex]
  15. [latex]\begin{array}{rr}&600\\\times&600\\\hline\\\end{array}[/latex]
  16. [latex]\begin{array}{rr}&40000\\\times&800\\\hline\\\end{array}[/latex]
  17. [latex]\begin{array}{rr}&2400\\\times&70\\\hline\\\end{array}[/latex]
  18. [latex]\begin{array}{rr}&390\\\times&40\\\hline\\\end{array}[/latex]
  19. [latex]\begin{array}{rr}&7200\\\times&5000\\\hline\\\end{array}[/latex]
  20. [latex]\begin{array}{rr}&7000\\\times&7000\\\hline\\\end{array}[/latex]
  21. [latex]\begin{array}{rr}&61000\\\times&400\\\hline\\\end{array}[/latex]
  22. [latex]\begin{array}{rr}&5200\\\times&300\\\hline\\\end{array}[/latex]
  23. [latex]\begin{array}{rr}&40\\\times&60\\\hline\\\end{array}[/latex]

Exercise 1 Answers

  1. 1 200 000
  2. 4 200
  3. 480 000
  4. 200 000
  5. 540 000
  6. 300 000 000
  7. 2 400 000
  8. 250 000
  9. 5 600
  10. 2 100 000
  11. 45 000 000
  12. 72 000 000
  13. 5 400 000
  14. 180 000 000
  15. 360 000
  16. 32 000 000
  17. 168 000
  18. 15 600
  19. 36 000 000
  20. 49 000 000
  21. 24 400 000
  22. 1 560 000
  23. 2 400

To find an estimated product, round the factors before you multiply. If a factor has only one digit, do not round it.

Example C

[latex]\begin{array}{rr}&6258\\\times&3\\\hline\end{array}[/latex]

6258 rounds to 6000. Leave 3 as is.

[latex]\begin{array}{rr}&6000\\\times&3\\\hline&18000\end{array}[/latex]

18000 is the estimated product.

Example D

[latex]\begin{array}{rr}&491\\\times&24\\\hline\end{array}[/latex]

491 rounds to 500. 24 rounds to 20.

[latex]\begin{array}{rr}&500\\\times&20\\\hline&10000\end{array}[/latex]

10000 is the estimated product.

1.8: Practice Questions

  1. Multiply these numbers.
    1. [latex]\begin{array}{rr}&600\\\times&70\\\hline\\\end{array}[/latex]
    2. [latex]\begin{array}{rr}&9000\\\times&30\\\hline\\\end{array}[/latex]
    3. [latex]\begin{array}{rr}&5000\\\times&600\\\hline\\\end{array}[/latex]
    4. [latex]\begin{array}{rr}&3000\\\times&500\\\hline\\\end{array}[/latex]
    5. [latex]\begin{array}{rr}&400\\\times&50\\\hline\\\end{array}[/latex]
    6. [latex]\begin{array}{rr}&8000\\\times&1000\\\hline\\\end{array}[/latex]

     

  2. Find an estimated product.
    1. [latex]\begin{array}{rr}&87\\\times&23\\\hline\\\end{array}[/latex]
    2. [latex]\begin{array}{rr}&268\\\times&25\\\hline\\\end{array}[/latex]
    3. [latex]\begin{array}{rr}&9421\\\times&75\\\hline\\\end{array}[/latex]
    4. [latex]\begin{array}{rr}&2632\\\times&49\\\hline\\\end{array}[/latex]
    5. [latex]\begin{array}{rr}&365\\\times&455\\\hline\\\end{array}[/latex]
    6. [latex]\begin{array}{rr}&7264\\\times&590\\\hline\\\end{array}[/latex]

1.8: Practice Answers

  1. Multiply these numbers.
    1. 42000
    2. 270000
    3. 3000000
    4. 1500000
    5. 20000
    6. 8000000

     

  2. Find an estimated product.
    1. [latex]90\times20=1\,800[/latex]
    2. [latex]300\times30=9\,000[/latex]
    3. [latex]9\,000\times80=720\,000[/latex]
    4. [latex]3\,000\times50=150\,000[/latex]
    5. [latex]400\times500=200\,000[/latex]
    6. [latex]7\,000\times600=4\,200\,000[/latex]

Attribution

This chapter has been adapted from Topic C: Estimating Products in Adult Literacy Fundamental Mathematics: Book 3 – 2nd Edition (BCcampus) by Wendy Tagami and Liz Girard (2023), which is under a CC BY 4.0 license.

License

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Intermediate PreAlgebra: Building Success Copyright © 2024 by Kim Tamblyn, TRU Open Press is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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