Question
Reduce -56/-70 to lowest terms.
4/5
8/10
-2/3
- 4/5
4/5
8/10
-2/3
- 4/5
Answers
GPT-4o mini
To reduce the fraction \(-56/-70\) to its lowest terms, we first simplify it. The negative signs cancel each other out, resulting in the positive fraction \(56/70\).
Next, we find the greatest common divisor (GCD) of 56 and 70. The prime factorization of both numbers is:
- \(56 = 2^3 \times 7\)
- \(70 = 2 \times 5 \times 7\)
The GCD is the product of the lowest powers of the common prime factors. Here, both numbers share \(2^1\) and \(7^1\), so the GCD is:
\[
GCD(56, 70) = 2^1 \times 7^1 = 14
\]
Now we divide both the numerator and denominator by the GCD:
\[
\frac{56 \div 14}{70 \div 14} = \frac{4}{5}
\]
Thus, \(-56/-70\) in lowest terms is \(\frac{4}{5}\).
So the correct answer is \(\frac{4}{5}\).
Next, we find the greatest common divisor (GCD) of 56 and 70. The prime factorization of both numbers is:
- \(56 = 2^3 \times 7\)
- \(70 = 2 \times 5 \times 7\)
The GCD is the product of the lowest powers of the common prime factors. Here, both numbers share \(2^1\) and \(7^1\), so the GCD is:
\[
GCD(56, 70) = 2^1 \times 7^1 = 14
\]
Now we divide both the numerator and denominator by the GCD:
\[
\frac{56 \div 14}{70 \div 14} = \frac{4}{5}
\]
Thus, \(-56/-70\) in lowest terms is \(\frac{4}{5}\).
So the correct answer is \(\frac{4}{5}\).