College

Common Denominator Practice

Instructions: Create equivalent fractions with common denominators for each pair of fractions. On this page, we will find the common denominator by multiplying the denominators of the two fractions.

Example:
[tex]\[

\begin{align*}

\frac{1}{2} \times \frac{10}{10} &= \frac{10}{20} \\

\frac{3}{10} \times \frac{2}{2} &= \frac{6}{20} \\

\frac{2}{3} \times \frac{6}{6} &= \frac{12}{18} \\

\frac{2}{6} \times \frac{3}{3} &= \frac{6}{18} \\

\frac{1}{4} \times \frac{8}{8} &= \frac{8}{32} \\

\frac{1}{8} \times \frac{4}{4} &= \frac{4}{32} \\

\frac{1}{2} \times \frac{3}{3} &= \frac{3}{6} \\

\frac{2}{3} \times \frac{2}{2} &= \frac{4}{6} \\

\frac{3}{8} \times \frac{3}{3} &= \frac{9}{24} \\

\frac{1}{3} \times \frac{8}{8} &= \frac{8}{24}

\end{align*}

\][/tex]

Problems:

5.
[tex]\[

\begin{align*}

\frac{2}{5} \times \frac{10}{10} &= \frac{20}{50} \\

\frac{3}{10} \times \frac{5}{5} &= \frac{15}{50}

\end{align*}

\][/tex]

6.
[tex]\[

\begin{align*}

\frac{3}{7} \times \frac{3}{3} &= \frac{9}{21} \\

\frac{2}{3} \times \frac{7}{7} &= \frac{14}{21}

\end{align*}

\][/tex]

7.
[tex]\[

\begin{align*}

\frac{3}{4} \times \frac{}{ } &= \\

\frac{2}{5} \times \frac{}{ } &=

\end{align*}

\][/tex]

8.
[tex]\[

\begin{align*}

\frac{1}{2} \times \frac{}{ } &= \\

\frac{3}{12} \times \frac{}{ } &=

\end{align*}

\][/tex]

Answer :

Sure, let's go through how to create equivalent fractions with common denominators for each pair of fractions:

1. Fractions: [tex]\(\frac{2}{5}\)[/tex] and [tex]\(\frac{3}{10}\)[/tex]

- To find a common denominator, multiply the denominators: [tex]\(5 \times 10 = 50\)[/tex].

- Convert [tex]\(\frac{2}{5}\)[/tex] to a new fraction with the common denominator:
[tex]\[
\frac{2}{5} \times \frac{10}{10} = \frac{20}{50}
\][/tex]

- Convert [tex]\(\frac{3}{10}\)[/tex] to a new fraction with the common denominator:
[tex]\[
\frac{3}{10} \times \frac{5}{5} = \frac{15}{50}
\][/tex]

2. Fractions: [tex]\(\frac{3}{7}\)[/tex] and [tex]\(\frac{2}{3}\)[/tex]

- To find a common denominator, multiply the denominators: [tex]\(7 \times 3 = 21\)[/tex].

- Convert [tex]\(\frac{3}{7}\)[/tex] to a new fraction with the common denominator:
[tex]\[
\frac{3}{7} \times \frac{3}{3} = \frac{9}{21}
\][/tex]

- Convert [tex]\(\frac{2}{3}\)[/tex] to a new fraction with the common denominator:
[tex]\[
\frac{2}{3} \times \frac{7}{7} = \frac{14}{21}
\][/tex]

By following these steps, we created equivalent fractions for each pair with a common denominator. The results are:

- [tex]\(\frac{20}{50}\)[/tex] and [tex]\(\frac{15}{50}\)[/tex]
- [tex]\(\frac{9}{21}\)[/tex] and [tex]\(\frac{14}{21}\)[/tex]

These equivalent fractions have the same denominators, which makes them easier to compare or combine if needed.