At a work place 153 of the 225 empolyees attened a meeting. Which statement shows values that are all equivalent to the fraction of employees who attened the meeting?

1 answer

To determine values equivalent to the fraction of employees who attended the meeting, we start with the fraction \(\frac{153}{225}\).

To find equivalent fractions, we can simplify this fraction or multiply the numerator and the denominator by the same integer.

  1. Simplifying the Fraction: We can check if we can simplify \(\frac{153}{225}\). We can find the greatest common divisor (GCD) of 153 and 225.

    The prime factorization of 153 is:

    • \(153 = 3 \times 51 = 3 \times 3 \times 17 = 3^2 \times 17\)

    The prime factorization of 225 is:

    • \(225 = 15 \times 15 = 3 \times 5 \times 3 \times 5 = 3^2 \times 5^2\)

    The GCD of 153 and 225 is \(9\) (which is \(3^2\)).

    Now we can divide both the numerator and denominator by their GCD:

    \[ \frac{153 \div 9}{225 \div 9} = \frac{17}{25} \]

  2. Creating Equivalent Fractions: Now that we have \(\frac{17}{25}\), we can create equivalent fractions by multiplying both the numerator and denominator by the same integer.

    For example:

    • If we multiply by 2: \(\frac{17 \times 2}{25 \times 2} = \frac{34}{50}\)
    • If we multiply by 3: \(\frac{17 \times 3}{25 \times 3} = \frac{51}{75}\)
    • If we multiply by 4: \(\frac{17 \times 4}{25 \times 4} = \frac{68}{100}\)

So, the equivalent fractions for the fraction of employees who attended the meeting are:

  • \(\frac{153}{225}\)
  • \(\frac{17}{25}\)
  • \(\frac{34}{50}\)
  • \(\frac{51}{75}\)
  • \(\frac{68}{100}\)

You can choose any of them to show values equivalent to \(\frac{153}{225}\).