Certainly! Let's solve the problem step-by-step.
Given the problem:
[tex]\[
-\frac{51}{7} \div -7
\][/tex]
Step 1: Rewrite the division as multiplication by the reciprocal.
Dividing by a number is equivalent to multiplying by its reciprocal. The reciprocal of [tex]\(-7\)[/tex] is [tex]\(-\frac{1}{7}\)[/tex].
So, we get:
[tex]\[
-\frac{51}{7} \div -7 = -\frac{51}{7} \times -\frac{1}{7}
\][/tex]
Step 2: Multiply the fractions.
When multiplying fractions, we multiply the numerators together and the denominators together:
[tex]\[
-\frac{51}{7} \times -\frac{1}{7} = \frac{-51 \times -1}{7 \times 7} = \frac{51}{49}
\][/tex]
Step 3: Simplify the fraction.
Next, we check if the fraction can be simplified. We look for the greatest common divisor (GCD) of the numerator and the denominator. In this particular case:
[tex]\[
\text{GCD}(51, 49) = 1
\][/tex]
Since the GCD is 1, the fraction is already in its simplest form.
Thus:
[tex]\[
\frac{51}{49}
\][/tex]
Step 4: Convert to a mixed number if necessary.
The fraction [tex]\(\frac{51}{49}\)[/tex] can be expressed as a mixed number. Here’s how:
- Divide the numerator by the denominator:
[tex]\[
51 \div 49 = 1 \text{ (quotient)} \, \text{and} \, 2 \text{ (remainder)}
\][/tex]
So, we can write:
[tex]\[
\frac{51}{49} = 1 \frac{2}{49}
\][/tex]
To summarize, the division:
[tex]\[
-\frac{51}{7} \div -7
\][/tex]
results in:
[tex]\[
1 \frac{2}{49}
\][/tex]
So the final result, in simplest form, is:
[tex]\[
\boxed{1 \frac{2}{49}}
\][/tex]
