Final answer:
Multiplying or dividing two quantities by the same number is called the property of equality and preserves the balance of an equation. It applies to both operations equally, ensuring the two sides remain equivalent when performed correctly, and it is also used in creating conversion factors and simplifying fractions in algebra and scientific notation.
Step-by-step explanation:
When you multiply or divide two quantities by the same number, it is known as using a multiplicative property called the property of equality. This property states that if you perform the same operation (either multiplication or division) on both sides of an equation, the two sides remain equal. For example, if you have an equation a = b, and you multiply both sides by a number n, you will get an = bn, which maintains the equality. Similarly, dividing both sides by the same number also maintains the equality. It's important to apply the operation to every term within an equation, enclosing multiple terms in small brackets if necessary, to ensure that the equality is preserved.
Furthermore, when dealing with conversion factors or simplifying fractions, if you have the same quantity in the numerator and the denominator, the fraction is equal to 1. This is because any number divided by itself is 1, which can be a useful concept in algebra and scientific notation calculations where numbers and units can cancel each other out.