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1. Using a shorter method, find:
(a) 336 + 9999
(b) 8125 + 9999
(c) 1736 + 99999
(d) 1800 - 99
(e) 62939 - 9999
(f) 1739 x 9999

Answer :

To solve these problems, we can use a shorter method by recognizing patterns and using some simple arithmetic tricks. Let's look at each one:

  1. 336 + 9999

    When adding 336 to 9999, think of 9999 as 10000 - 1.

    [tex]336 + 9999 = 336 + (10000 - 1)[/tex]

    Simplify it:

    [tex]336 + 10000 = 10336[/tex]

    Then subtract 1:

    [tex]10336 - 1 = 10335[/tex]

  2. 8125 + 9999

    Again, use the trick: 9999 is 10000 - 1.

    [tex]8125 + 9999 = 8125 + (10000 - 1)[/tex]

    Simplify it:

    [tex]8125 + 10000 = 18125[/tex]

    Then subtract 1:

    [tex]18125 - 1 = 18124[/tex]

  3. 1736 + 99999

    Here, treat 99999 as 100000 - 1.

    [tex]1736 + 99999 = 1736 + (100000 - 1)[/tex]

    Simplify it:

    [tex]1736 + 100000 = 101736[/tex]

    Then subtract 1:

    [tex]101736 - 1 = 101735[/tex]

  4. 1800 - 99

    For subtraction, think of 99 as 100 - 1.

    [tex]1800 - 99 = 1800 - (100 - 1)[/tex]

    Simplify it:

    [tex]1800 - 100 = 1700[/tex]

    Then add 1:

    [tex]1700 + 1 = 1701[/tex]

  5. 62939 - 9999

    Again, consider 9999 as 10000 - 1.

    [tex]62939 - 9999 = 62939 - (10000 - 1)[/tex]

    Simplify it:

    [tex]62939 - 10000 = 52939[/tex]

    Then add 1:

    [tex]52939 + 1 = 52940[/tex]

  6. 1739 x 9999

    For multiplication, you can use the distributive property.

    [tex]1739 \times 9999 = 1739 \times (10000 - 1)[/tex]

    [tex]= 1739 \times 10000 - 1739 \times 1[/tex]

    Calculate it:

    [tex]1739 \times 10000 = 17390000[/tex]

    [tex]1739 \times 1 = 1739[/tex]

    Then subtract:

    [tex]17390000 - 1739 = 17388261[/tex]

This method helps streamline calculations by using common numerical tricks to simplify arithmetic operations.

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