High School

Reduce each fraction to its lowest terms by first factoring the numerator and denominator into the product of prime factors, and then dividing out any factors they have in common.

[tex]\frac{50}{75} = \square[/tex]

Answer :

To reduce the fraction [tex]\(\frac{50}{75}\)[/tex] to its lowest terms, follow these steps:

1. Factor the Numerator and Denominator:
- The numerator is [tex]\(50\)[/tex].
- Prime factorization: [tex]\(50 = 2 \times 5 \times 5\)[/tex].
- The denominator is [tex]\(75\)[/tex].
- Prime factorization: [tex]\(75 = 3 \times 5 \times 5\)[/tex].

2. Identify Common Factors:
- Both the numerator and the denominator have the common factors [tex]\(5 \times 5\)[/tex].

3. Divide Out the Common Factors:
- Cancel out the common factors from both the numerator and the denominator:
- After canceling [tex]\(5 \times 5\)[/tex], you are left with:
[tex]\[
\frac{2}{3}
\][/tex]

4. Conclusion:
- The fraction [tex]\(\frac{50}{75}\)[/tex] reduces to [tex]\(\frac{2}{3}\)[/tex] when expressed in its lowest terms.

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