Question

How do you simplify $\dfrac{45}{75}$ to lowest terms?

Answer 1

Hint: Firstly, we write the given fraction in simplified form and then express it in fractions to express it in the lowest form. Now write the numerator and denominator in factored form and then cancel the common factors. Now after we get a form where we cannot cancel any more common factors, convert it into decimal. This will be its lowest form.

Complete step by step solution:
The given fraction is, $\dfrac{45}{75}$
The first step is to write this fraction in simplified form.
A fraction is in simplest form if the top and bottom have no common factors other than 1. You might also hear the simplest form called "lowest terms”. You can divide the numerator and denominator by their Greatest common factor (GCF).
Now let us write the factors for the given integers in the numerator and the denominator.
We get,
$\Rightarrow \dfrac{3\times 3\times 5}{3\times 5\times 5}$
Now cancel the common terms in the numerator and the denominator.
Upon eliminating the common terms, we get,
$\Rightarrow \dfrac{3}{5}$
Now as we can see we cannot further simplify this fraction since the only common factor left for both of them is 1.
Now we shall write this in decimal form to express the lowest form.
Upon writing this in the decimal form we get,
$\Rightarrow 0.6$

Hence, when we simplify $\dfrac{45}{75}$ to the lowest terms we get 0.6

Note: Always check the number of decimal places (number of digits) after the decimal place to convert the decimal into a fraction. The number of digits is then written to the power of $10\;$ and then placed in the denominator and in the numerator, the number will be written the same as it is, but without the decimal point.