Answer :

Sure! Let's determine whether the fractions [tex]\(\frac{-42}{-45}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex] are equivalent.

1. Identify the fractions:
- The first fraction is [tex]\(\frac{-42}{-45}\)[/tex].
- The second fraction is [tex]\(\frac{14}{15}\)[/tex].

2. Simplify the first fraction:
- [tex]\(\frac{-42}{-45}\)[/tex] simplifies to [tex]\(\frac{42}{45}\)[/tex] because dividing a negative number by a negative number results in a positive number.

3. Find the greatest common divisor (GCD) of the numerator and the denominator:
- The GCD of 42 and 45 is 3.

4. Simplify [tex]\(\frac{42}{45}\)[/tex] by dividing both the numerator and the denominator by the GCD:
- [tex]\(\frac{42 \div 3}{45 \div 3} = \frac{14}{15}\)[/tex].

5. Compare the two fractions:
- After simplification, [tex]\(\frac{42}{45}\)[/tex] becomes [tex]\(\frac{14}{15}\)[/tex].
- The fraction [tex]\(\frac{14}{15}\)[/tex] is already in its simplest form.

Since both fractions simplify to [tex]\(\frac{14}{15}\)[/tex], we conclude that [tex]\(\frac{-42}{-45}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex] are equivalent.

Final Answer: True

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