Question

How do you write fractions with a common denominator?

Answer 1

Hint: In this question, we have been asked how to write fractions with common denominators. First, we need to find the least common multiple of the two denominators. Then, we will multiply with the required numbers to make the denominators equal. We can only add or subtract with common denominators.

Complete step-by-step solution:
The denominator is the number in the bottom part of a fraction.
It reveals how many equal partitions the item is divided into.
When the denominators of two or more fractions are the equal, they are Common Denominators.
Before we can conduct addition or subtraction with fractions, the fractions need to have a common denominator.
That is the denominators must be the equal.
To make the denominators the same we can:
Let’s take the fractions $\dfrac{1}{3}$ and $\dfrac{1}{6}$
First thing to be done is finding the least common multiple,
Here is how to find out:
 $\dfrac{1}{3}$
List multiples of 3:
 \[\begin{array}{*{20}{l}}
  {3,{\text{ }}6,{\text{ }}9,{\text{ }}12,{\text{ }}15,{\text{ }}18,{\text{ }}21,{\text{ }}...}
\end{array}\]
 $\dfrac{1}{6}$
List multiples of 6:
 \[\begin{array}{*{20}{l}}
  {6,{\text{ }}12,{\text{ }}18,{\text{ }}24,{\text{ }}...}
\end{array}\]
Now find the smallest number that is the present in both:
multiples of 3:
 \[\begin{array}{*{20}{l}}
  {3,\;{\mathbf{6}},{\text{ }}9,{\text{ }}12,{\text{ }}15,{\text{ }}18,{\text{ }}21,{\text{ }}...}
\end{array}\]
multiples of 6:
\[\begin{array}{*{20}{l}}
  {\;{\mathbf{6}},{\text{ }}9,{\text{ }}12,{\text{ }}15,{\text{ }}18,{\text{ }}21,{\text{ }}...}
\end{array}\]
We can clearly see that the answer is 6, and that is the Least Common Denominator.
So let us try using it!
We want both fractions to have 6 parts:
When we multiply top and bottom of $\dfrac{1}{3}$ by 2 we get $\dfrac{2}{6}$
$\dfrac{1}{6}$ already has a denominator of 6
And our question now looks like:
$\dfrac{1}{3} = \dfrac{2}{6}$
$\dfrac{1}{6}$=$\dfrac{1}{6}$

Note: The numerator, found at the top of a fraction, tells us how many parts are available, while the denominator, found at the bottom of a fraction, tells us how many parts are in the whole. In order to add or subtract one fraction from another, they must have a common denominator, or the same denominator.