High School

Find the product of 113 and 118.

Here, both the numbers are greater than 100 and the base here is 100. Taking the difference of the two numbers 113 and 118 from the base, we get +13 and +18 and write them as below.

113 -> +13
118 -> +18

Answer :

To find the product of 113 and 118 using the base method, follow these steps:

First, identify that both numbers are close to 100, which we consider as our base:

[tex]113 \rightarrow +13[/tex]
[tex]118 \rightarrow +18[/tex]

  1. Add the base deviations:

    Add the two deviations:[tex]+13 + (+18) = +31[/tex]

    Add this result to the base (100) to find the partial product:

    [tex]113 + 18 = 131[/tex] or [tex]118 + 13 = 131[/tex]

    In both cases, we add the deviation of one number to the other number.

  2. Multiply the deviations:

    Multiply the two deviations:

    [tex]+13 \times +18 = 234[/tex]

  3. Combine the results:

    Now, take the value obtained from adding the base deviations (131) and multiply it by the base number (100) and then add the product of the deviations to get the final result:

    [tex]131 \times 100 + 234 = 13100 + 234 = 13334[/tex]

Therefore, the product of 113 and 118 is [tex]13334[/tex].

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