Reduce the fraction to lowest terms. Do not use spaces in answer.
-5jk
________=
35j^2k^2
Sure thing! Let's simplify the fraction -5jk divided by 35j^2k^2.
To simplify, let's first cancel out any common factors between the numerator (-5jk) and the denominator (35j^2k^2).
Both the numerator and denominator have a factor of 5, so we can cancel it out:
(-5jk / 5) / (35j^2k^2 / 5) = -jk / 7j^2k^2
Next, let's cancel out the common factor of j:
(-jk / 7j^2k^2) / (7j^2k^2 / 7j) = -k / 7j
So, the fraction -5jk / 35j^2k^2 reduced to lowest terms is -k / 7j.
To reduce the given fraction to its lowest terms, we need to find the greatest common factor (GCF) of the numerator and denominator and then divide both numerator and denominator by the GCF.
The numerator is -5jk and the denominator is 35j^2k^2.
First, let's factor the numerator and denominator:
-5jk = -1 * 5 * j * k
35j^2k^2 = 5 * 7 * j * j * k * k
Next, let's find the GCF of -1 * 5 * j * k and 5 * 7 * j * j * k * k:
The GCF is 5 * j * k.
Now, divide both the numerator and denominator by the GCF:
-5jk / 35j^2k^2 = (-1 * 5 * j * k) / (5 * j * k)
= (-1 * j * k) / (j * k)
= -1
Therefore, the given fraction -5jk / 35j^2k^2 reduces to -1 in its lowest terms.
To reduce the fraction -5jk / 35j^2k^2 to its lowest terms, we first need to find the greatest common factor (GCF) of the numerator and denominator.
Let's break down the numerator and denominator into their prime factors:
Numerator: -5jk
-5 = -1 * 5 (prime factors)
j = j (no prime factors)
k = k (no prime factors)
Denominator: 35j^2k^2
35 = 5 * 7 (prime factors)
j^2 = j * j (prime factors)
k^2 = k * k (prime factors)
Now let's cancel out the common factors between the numerator and denominator:
-5jk / 35j^2k^2 = (-1 * 5 * j * k) / (5 * 7 * j * j * k * k)
We can cancel out one instance of the prime factors in the numerator and denominator:
-5jk / 35j^2k^2 = (-1 * k) / (7 * j * k)
Since we cannot cancel out any more factors, we have reached the lowest terms. Therefore, the reduced fraction is:
-1k / 7jk