College

Student Name: _______________________

**Common Denominator Practice**

**Directions:** Create equivalent fractions with common denominators for each pair of fractions. On this page, we'll find the common denominator by multiplying the denominators of the two fractions.

**Example:**
\[
\frac{1}{2} \times \frac{10}{10} = \frac{10}{20} \\
\frac{3}{10} \times \frac{2}{2} = \frac{6}{20}
\]

1.
\[
\frac{2}{3} \times \frac{6}{6} = \frac{12}{18} \\
\frac{2}{6} \times \frac{3}{3} = \frac{6}{18}
\]

2.
\[
\frac{1}{4} \times \frac{8}{8} = \frac{8}{32} \\
\frac{1}{8} \times \frac{4}{4} = \frac{4}{32}
\]

3.
\[
\frac{1}{2} \times \frac{3}{3} = \frac{3}{6} \\
\frac{2}{3} \times \frac{2}{2} = \frac{4}{6}
\]

4.
\[
\frac{3}{8} \times \frac{3}{3} = \frac{9}{24} \\
\frac{1}{3} \times \frac{8}{8} = \frac{8}{24}
\]

5.
\[
\frac{2}{5} \times \frac{10}{10} = \frac{20}{50} \\
\frac{3}{10} \times \frac{5}{5} = \frac{15}{50}
\]

6.
\[
\frac{3}{7} \times \frac{3}{3} = \frac{9}{21} \\
\frac{2}{3} \times \frac{7}{7} = \frac{14}{21}
\]

Answer :

Sure! Let's work through each pair of fractions to find equivalent fractions with a common denominator by multiplying their denominators.

1. Fractions: [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{2}{6}\)[/tex]:

- Common Denominator: Multiply the denominators, [tex]\(3 \times 6 = 18\)[/tex].
- Equivalent Fractions:
- [tex]\(\frac{2}{3} \times \frac{6}{6} = \frac{12}{18}\)[/tex]
- [tex]\(\frac{2}{6} \times \frac{3}{3} = \frac{6}{18}\)[/tex]

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

- Common Denominator: Multiply the denominators, [tex]\(5 \times 10 = 50\)[/tex].
- Equivalent Fractions:
- [tex]\(\frac{2}{5} \times \frac{10}{10} = \frac{20}{50}\)[/tex]
- [tex]\(\frac{3}{10} \times \frac{5}{5} = \frac{15}{50}\)[/tex]

3. Fractions: [tex]\(\frac{1}{4}\)[/tex] and [tex]\(\frac{1}{8}\)[/tex]:

- Common Denominator: Multiply the denominators, [tex]\(4 \times 8 = 32\)[/tex].
- Equivalent Fractions:
- [tex]\(\frac{1}{4} \times \frac{8}{8} = \frac{8}{32}\)[/tex]
- [tex]\(\frac{1}{8} \times \frac{4}{4} = \frac{4}{32}\)[/tex]

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

- Common Denominator: Multiply the denominators, [tex]\(2 \times 3 = 6\)[/tex].
- Equivalent Fractions:
- [tex]\(\frac{1}{2} \times \frac{3}{3} = \frac{3}{6}\)[/tex]
- [tex]\(\frac{2}{3} \times \frac{2}{2} = \frac{4}{6}\)[/tex]

5. Fractions: [tex]\(\frac{3}{8}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex]:

- Common Denominator: Multiply the denominators, [tex]\(8 \times 3 = 24\)[/tex].
- Equivalent Fractions:
- [tex]\(\frac{3}{8} \times \frac{3}{3} = \frac{9}{24}\)[/tex]
- [tex]\(\frac{1}{3} \times \frac{8}{8} = \frac{8}{24}\)[/tex]

These steps provide the equivalent fractions for each pair with a common denominator.