Common Denominator/Examples

Examples of Common Denominators

Multiples of $12$

Multiples of $12$ are all common denominators of:

$\dfrac 1 2$, $\dfrac 1 4$, $\dfrac 1 6$

Hence these fractions can be expressed as:

$\dfrac 6 {12}$, $\dfrac 3 {12}$, $\dfrac 2 {12}$

$2$, $3$ and $7$

The fractions:

$\dfrac 1 2$, $\dfrac 1 3$, $\dfrac 3 7$

have common denominators:

$42$, $84$, $126$, $168$

and so on.

The lowest common denominator of $\dfrac 1 2$, $\dfrac 1 3$, $\dfrac 3 7$ is $42$.

$3$, $8$ and $6$

The fractions:

$\dfrac 1 3$, $\dfrac 7 8$, $\dfrac 5 6$

all have a common denominator of $24$.

Hence:

\(\ds \dfrac 1 3 + \dfrac 7 8 - \dfrac 5 6\)

\(=\)

\(\ds \dfrac 8 {24} + \dfrac {21} {24} - \dfrac {20} {24}\)

\(\ds \)

\(=\)

\(\ds \dfrac {8 + 21 - 20} {24}\)

\(\ds \)

\(=\)

\(\ds \dfrac 9 {24}\)

\(\ds \)

\(=\)

\(\ds \dfrac 3 8\)