Write an equivalent fraction for each of the following.

Here are the solutions for the fractions questions:

1. Write an equivalent fraction for each of the following:

• a) To find an equivalent fraction for $\frac{1}{2}$, we can multiply the numerator and denominator by 2. $$\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \boxed{\frac{2}{4}}$$
• b) To find an equivalent fraction for $\frac{2}{6}$, we can simplify it by dividing the numerator and denominator by their greatest common divisor, which is 2. $$\frac{2}{6} = \frac{2 \div 2}{6 \div 2} = \boxed{\frac{1}{3}}$$
• c) To find an equivalent fraction for $\frac{4}{6}$, we can simplify it by dividing the numerator and denominator by their greatest common divisor, which is 2. $$\frac{4}{6} = \frac{4 \div 2}{6 \div 2} = \boxed{\frac{2}{3}}$$
• d) To find an equivalent fraction for $\frac{1}{3}$, we can multiply the numerator and denominator by 2. $$\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \boxed{\frac{2}{6}}$$
• e) The fraction $\frac{2}{2}$ represents a whole. $$\frac{2}{2} = \boxed{1}$$
• f) To find an equivalent fraction for $\frac{3}{6}$, we can simplify it by dividing the numerator and denominator by their greatest common divisor, which is 3. $$\frac{3}{6} = \frac{3 \div 3}{6 \div 3} = \boxed{\frac{1}{2}}$$
• g) To find an equivalent fraction for $\frac{2}{3}$, we can multiply the numerator and denominator by 2. $$\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \boxed{\frac{4}{6}}$$
• h) The fraction $\frac{6}{6}$ represents a whole. $$\frac{6}{6} = \boxed{1}$$
• i) To find an equivalent fraction for $\frac{1}{3}$, we can multiply the numerator and denominator by 2. $$\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \boxed{\frac{2}{6}}$$
• j) To find an equivalent fraction for $\frac{2}{3}$, we can multiply the numerator and denominator by 2. $$\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \boxed{\frac{4}{6}}$$
• k) To find an equivalent fraction for $\frac{1}{2}$, we can multiply the numerator and denominator by 2. $$\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \boxed{\frac{2}{4}}$$
• l) To find an equivalent fraction for $\frac{5}{6}$, we can multiply the numerator and denominator by 2. $$\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \boxed{\frac{10}{12}}$$

2. Fill in <, > or =:

• a) Compare $\frac{1}{2}$ and $\frac{1}{3}$. To compare, convert to a common denominator of 6: $\frac{1}{2} = \frac{3}{6}$ and $\frac{1}{3} = \frac{2}{6}$. $$\frac{3}{6} > \frac{2}{6} \implies \frac{1}{2} \boxed{>} \frac{1}{3}$$
• b) Compare $\frac{1}{2}$ and $\frac{1}{6}$. To compare, convert to a common denominator of 6: $\frac{1}{2} = \frac{3}{6}$. $$\frac{3}{6} > \frac{1}{6} \implies \frac{1}{2} \boxed{>} \frac{1}{6}$$
• c) Compare $\frac{1}{3}$ and $\frac{3}{6}$. To compare, convert to a common denominator of 6: $\frac{1}{3} = \frac{2}{6}$. $$\frac{2}{6} < \frac{3}{6} \implies \frac{1}{3} \boxed{<} \frac{3}{6}$$
• d) Compare $\frac{1}{2}$ and $\frac{2}{3}$. To compare, convert to a common denominator of 6: $\frac{1}{2} = \frac{3}{6}$ and $\frac{2}{3} = \frac{4}{6}$. $$\frac{3}{6} < \frac{4}{6} \implies \frac{1}{2} \boxed{<} \frac{2}{3}$$
• e) Compare $\frac{2}{3}$ and $\frac{1}{6}$. To compare, convert to a common denominator of 6: $\frac{2}{3} = \frac{4}{6}$. $$\frac{4}{6} > \frac{1}{6} \implies \frac{2}{3} \boxed{>} \frac{1}{6}$$
• f) Compare $\frac{5}{6}$ and $\frac{2}{3}$. To compare, convert to a common denominator of 6: $\frac{2}{3} = \frac{4}{6}$. $$\frac{5}{6} > \frac{4}{6} \implies \frac{5}{6} \boxed{>} \frac{2}{3}$$
• g) Compare $\frac{2}{3}$ and $\frac{6}{6}$. Simplify $\frac{6}{6} = 1$. $$\frac{2}{3} < 1 \implies \frac{2}{3} \boxed{<} \frac{6}{6}$$
• h) Compare $\frac{1}{3}$ and $\frac{4}{6}$. To compare, convert to a common denominator of 6: $\frac{1}{3} = \frac{2}{6}$. $$\frac{2}{6} < \frac{4}{6} \implies \frac{1}{3} \boxed{<} \frac{4}{6}$$
• i) Compare $\frac{1}{6}$ and $\frac{2}{6}$. The denominators are already the same. $$\frac{1}{6} < \frac{2}{6} \implies \frac{1}{6} \boxed{<} \frac{2}{6}$$
• j) Compare $\frac{1}{2}$ and $\frac{3}{3}$. Simplify $\frac{3}{3} = 1$. $$\frac{1}{2} < 1 \implies \frac{1}{2} \boxed{<} \frac{3}{3}$$
• k) Compare $\frac{1}{2}$ and $\frac{1}{6}$. To compare, convert to a common denominator of 6: $\frac{1}{2} = \frac{3}{6}$. $$\frac{3}{6} > \frac{1}{6} \implies \frac{1}{2} \boxed{>} \frac{1}{6}$$