Student Name:

Common Denominator Practice

Directions: Create equivalent fractions with common denominators for each pair of fractions. Find the common denominator by multiplying the denominators of the two fractions.

Example:

[tex]\[ \frac{1}{2} \times \frac{10}{10} = \frac{10}{20} \][/tex]

[tex]\[ \frac{3}{10} \times \frac{2}{2} = \frac{6}{20} \][/tex]

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

[tex]\[ \frac{1}{8} \times \frac{4}{4} = \frac{4}{32} \][/tex]

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

[tex]\[ \frac{2}{3} \times \frac{2}{2} = \frac{4}{6} \][/tex]

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

[tex]\[ \frac{1}{3} \times \frac{8}{8} = \frac{8}{24} \][/tex]

5.
[tex]\[ \frac{2}{5} \times \frac{10}{10} = \frac{20}{50} \][/tex]

[tex]\[ \frac{3}{10} \times \frac{5}{5} = \frac{15}{50} \][/tex]

6.
[tex]\[ \frac{3}{7} \times \ldots \][/tex]

[tex]\[ \frac{2}{3} \times \ldots \][/tex]

7.
[tex]\[ \frac{3}{4} \times \ldots \][/tex]

[tex]\[ \frac{2}{5} \times \ldots \][/tex]

8.
[tex]\[ \frac{1}{2} \times \ldots \][/tex]

[tex]\[ \frac{3}{12} \times \ldots \][/tex]

Sure! Let's work through creating equivalent fractions with common denominators step by step.

### Problem 6:
Fractions: [tex]$ \frac{3}{7} $[/tex] and [tex]$ \frac{2}{3} $[/tex]

1. Find the Common Denominator: Multiply the denominators of both fractions:
- [tex]$ 7 \times 3 = 21 $[/tex]

2. Adjust each fraction to have this common denominator:
- For [tex]$ \frac{3}{7} $[/tex]: Multiply both the numerator and denominator by 3:
- [tex]$ \frac{3 \times 3}{7 \times 3} = \frac{9}{21} $[/tex]
- For [tex]$ \frac{2}{3} $[/tex]: Multiply both the numerator and denominator by 7:
- [tex]$ \frac{2 \times 7}{3 \times 7} = \frac{14}{21} $[/tex]

So, the equivalent fractions are [tex]$ \frac{9}{21} $[/tex] and [tex]$ \frac{14}{21} $[/tex].

### Problem 7:
Fractions: [tex]$ \frac{3}{4} $[/tex] and [tex]$ \frac{2}{5} $[/tex]

1. Find the Common Denominator: Multiply the denominators of both fractions:
- [tex]$ 4 \times 5 = 20 $[/tex]

2. Adjust each fraction to have this common denominator:
- For [tex]$ \frac{3}{4} $[/tex]: Multiply both the numerator and denominator by 5:
- [tex]$ \frac{3 \times 5}{4 \times 5} = \frac{15}{20} $[/tex]
- For [tex]$ \frac{2}{5} $[/tex]: Multiply both the numerator and denominator by 4:
- [tex]$ \frac{2 \times 4}{5 \times 4} = \frac{8}{20} $[/tex]

So, the equivalent fractions are [tex]$ \frac{15}{20} $[/tex] and [tex]$ \frac{8}{20} $[/tex].

### Problem 8:
Fractions: [tex]$ \frac{1}{2} $[/tex] and [tex]$ \frac{3}{12} $[/tex]

1. Find the Common Denominator: Multiply the denominators of both fractions:
- [tex]$ 2 \times 12 = 24 $[/tex]

2. Adjust each fraction to have this common denominator:
- For [tex]$ \frac{1}{2} $[/tex]: Multiply both the numerator and denominator by 12:
- [tex]$ \frac{1 \times 12}{2 \times 12} = \frac{12}{24} $[/tex]
- For [tex]$ \frac{3}{12} $[/tex]: Multiply both the numerator and denominator by 2:
- [tex]$ \frac{3 \times 2}{12 \times 2} = \frac{6}{24} $[/tex]

So, the equivalent fractions are [tex]$ \frac{12}{24} $[/tex] and [tex]$ \frac{6}{24} $[/tex].

These steps show how each pair of fractions is converted into equivalent fractions with a common denominator.