Answer :
To determine which of the provided fractions is equivalent to [tex]\(\frac{-84}{-90}\)[/tex] in its simplest form, let's simplify the fraction step-by-step.
1. Identify the original fraction:
The original fraction is [tex]\(\frac{-84}{-90}\)[/tex].
2. Recognize that a negative sign in both the numerator and the denominator cancels out:
Since both the numerator and denominator are negative, the fraction [tex]\(\frac{-84}{-90}\)[/tex] is the same as [tex]\(\frac{84}{90}\)[/tex].
3. Simplify the fraction:
To simplify [tex]\(\frac{84}{90}\)[/tex], we need to find the greatest common divisor (GCD) of 84 and 90.
The GCD of 84 and 90 is 6.
4. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{84}{90} = \frac{84 \div 6}{90 \div 6} = \frac{14}{15}
\][/tex]
5. Choose the equivalent fraction from the options:
The fraction [tex]\(\frac{14}{15}\)[/tex] is already given in the options. It matches the simplified form of the original fraction.
Therefore, [tex]\(\frac{14}{15}\)[/tex] is the equivalent fraction of [tex]\(\frac{-84}{-90}\)[/tex] in the least common terms. The correct choice is:
[tex]\[
\frac{14}{15}
\][/tex]
1. Identify the original fraction:
The original fraction is [tex]\(\frac{-84}{-90}\)[/tex].
2. Recognize that a negative sign in both the numerator and the denominator cancels out:
Since both the numerator and denominator are negative, the fraction [tex]\(\frac{-84}{-90}\)[/tex] is the same as [tex]\(\frac{84}{90}\)[/tex].
3. Simplify the fraction:
To simplify [tex]\(\frac{84}{90}\)[/tex], we need to find the greatest common divisor (GCD) of 84 and 90.
The GCD of 84 and 90 is 6.
4. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{84}{90} = \frac{84 \div 6}{90 \div 6} = \frac{14}{15}
\][/tex]
5. Choose the equivalent fraction from the options:
The fraction [tex]\(\frac{14}{15}\)[/tex] is already given in the options. It matches the simplified form of the original fraction.
Therefore, [tex]\(\frac{14}{15}\)[/tex] is the equivalent fraction of [tex]\(\frac{-84}{-90}\)[/tex] in the least common terms. The correct choice is:
[tex]\[
\frac{14}{15}
\][/tex]
