91Ó°ÊÓ

The multiplicative inverse, also called the reciprocal, of a number is what you multiply that number by to get 1.
If you have a number like 5, its multiplicative inverse is \(\frac{1}{5}\).
Why? Because 5 times \(\frac{1}{5}\) equals 1. Another way to say this is: \[5 \times \frac{1}{5} = 1 \]
The concept is simple, but it is very important in math. It is especially useful in solving fractions and equations.
In our exercise, the number given is \(-7\). To find the multiplicative inverse, we just divide 1 by \(-7\).
This gives us: \[ \frac{1}{-7} \]
Since there are no further simplifications needed, we can also write it as \(-\frac{1}{7}\).
So, the reciprocal or multiplicative inverse of \(-7\) is \(-\frac{1}{7}\).
Remember, the reciprocal of any non-zero number always exists and is unique!

Fraction simplification is all about making fractions easier to work with.
A fraction is simplified when the numerator (top number) and the denominator (bottom number) have no common factors other than 1.
Let's consider \(\frac{4}{8}\).
Both 4 and 8 can be divided by 4, giving us \(\frac{1}{2}\).
That is a simplified fraction.
In our exercise, we get \(\frac{1}{-7}\) or \(-\frac{1}{7}\).
This fraction is already in its simplest form because 1 and 7 have no common factors other than 1, and there's no simplification required.
The negative sign can stay either in the numerator or in front of the entire fraction, but the fraction itself is as simple as it gets.

Negative numbers are numbers less than zero.
They are often seen as numbers with a ‘minus’ (–) sign in front of them.
For example, \(-3, -7\), and \(-10\) are negative numbers.
When dealing with reciprocals of negative numbers, we handle the negative sign carefully.
For any negative number \-n\, its reciprocal is \(\frac{1}{-n}\), which is also written as \(-\frac{1}{n}\).
In our case, the negative number was \(-7\), and its reciprocal became \(\frac{1}{-7}\) or \(-\frac{1}{7}\).
Negative numbers follow specific rules in arithmetic:

• Adding a negative number is like subtracting its positive counterpart.
• Multiplying two negative numbers gives a positive result.
• Dividing two negative numbers also results in a positive number.

Understanding these rules helps in correctly handling negative numbers whether they are whole numbers or fractions.