High School

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------------------------------------------------ Using your observations in 5.1 to 5.4, determine how many 4s will be in the following calculation:

\[ 2222222222222 \times 11 \]

Number of 4s =

Answer :

To determine how many 4s appear in the product of the multiplication of the number consisting entirely of thirteens 2s by 11, we will follow these steps:

  1. Understand the Mathematical Expression: The expression is [tex]2222222222222 \times 11[/tex], which is a number written with thirteen 2s multiplied by 11.

  2. Apply the Multiplication by 11 Rule: When multiplying a number by 11, you can perform this operation by adding each pair of neighboring digits from left to right, starting with the first digit.

  3. Step-by-Step Multiplication:

    Let's label the digits of the number as follows:

    [tex]x[/tex] is the starting number = [tex]2222222222222[/tex]

    • Write down the first digit: 2
    • Add subsequent pairs: 2+2, 2+2, ..., until the second-to-last digit
    • Write down the last digit: 2

    So the sequence of adding pairs is:

    • First digit: 2
    • Next digits between first and last: all are 2+2=4
    • Last digit: 2

    Following this pattern brings the solution: 24444444444442.

  4. Count the Number of 4s:

    • From the sequence [tex]24444444444442[/tex], count how many 4s appear.
    • There are eleven 4s in result.

Thus, the number of 4s in the result is 11.

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