Are These Fractions Equivalent? (Multiplier Range 2 to 5) (A) - Free Printable

Problem Overview:

The task involves checking whether the given pairs of fractions are equivalent. Two fractions are equivalent if they represent the same value, which can be verified by simplifying them or cross-multiplying their numerators and denominators.

Solution Approach:

1. Simplify Each Fraction: Reduce both fractions in each pair to their simplest form.
2. Compare Simplified Forms: If the simplified forms are identical, the fractions are equivalent.
3. Mark Correct Answers: Use a checkmark (√) for equivalent fractions and an "X" for non-equivalent fractions.

Step-by-Step Verification:

#### Row 1:
- $\frac{5}{11} = \frac{25}{55}$
- Simplify $\frac{25}{55}$: Divide numerator and denominator by 5 → $\frac{5}{11}$.
- Equivalent. ✓

- $\frac{5}{5} = \frac{10}{10}$
- Both simplify to 1.
- Equivalent. ✓

- $\frac{6}{9} = \frac{30}{45}$
- Simplify $\frac{6}{9}$: Divide by 3 → $\frac{2}{3}$.
- Simplify $\frac{30}{45}$: Divide by 15 → $\frac{2}{3}$.
- Equivalent. ✓

- $\frac{8}{12} = \frac{32}{48}$
- Simplify $\frac{8}{12}$: Divide by 4 → $\frac{2}{3}$.
- Simplify $\frac{32}{48}$: Divide by 16 → $\frac{2}{3}$.
- Equivalent. ✓

#### Row 2:
- $\frac{6}{11} = \frac{18}{33}$
- Simplify $\frac{18}{33}$: Divide by 3 → $\frac{6}{11}$.
- Equivalent. ✓

- $\frac{3}{4} = \frac{9}{12}$
- Simplify $\frac{9}{12}$: Divide by 3 → $\frac{3}{4}$.
- Equivalent. ✓

- $\frac{5}{9} = \frac{10}{18}$
- Simplify $\frac{10}{18}$: Divide by 2 → $\frac{5}{9}$.
- Equivalent. ✓

- $\frac{6}{6} = \frac{30}{30}$
- Both simplify to 1.
- Equivalent. ✓

#### Row 3:
- $\frac{5}{10} = \frac{15}{30}$
- Simplify $\frac{5}{10}$: Divide by 5 → $\frac{1}{2}$.
- Simplify $\frac{15}{30}$: Divide by 15 → $\frac{1}{2}$.
- Equivalent. ✓

- $\frac{10}{10} = \frac{30}{30}$
- Both simplify to 1.
- Equivalent. ✓

- $\frac{4}{6} = \frac{20}{18}$
- Simplify $\frac{4}{6}$: Divide by 2 → $\frac{2}{3}$.
- Simplify $\frac{20}{18}$: Divide by 2 → $\frac{10}{9}$.
- Not equivalent. ✗

- $\frac{1}{3} = \frac{2}{6}$
- Simplify $\frac{2}{6}$: Divide by 2 → $\frac{1}{3}$.
- Equivalent. ✓

#### Row 4:
- $\frac{7}{8} = \frac{35}{40}$
- Simplify $\frac{35}{40}$: Divide by 5 → $\frac{7}{8}$.
- Equivalent. ✓

- $\frac{3}{9} = \frac{9}{36}$
- Simplify $\frac{3}{9}$: Divide by 3 → $\frac{1}{3}$.
- Simplify $\frac{9}{36}$: Divide by 9 → $\frac{1}{4}$.
- Not equivalent. ✗

- $\frac{2}{8} = \frac{10}{40}$
- Simplify $\frac{2}{8}$: Divide by 2 → $\frac{1}{4}$.
- Simplify $\frac{10}{40}$: Divide by 10 → $\frac{1}{4}$.
- Equivalent. ✓

- $\frac{4}{5} = \frac{12}{15}$
- Simplify $\frac{12}{15}$: Divide by 3 → $\frac{4}{5}$.
- Equivalent. ✓

#### Row 5:
- $\frac{2}{7} = \frac{10}{14}$
- Simplify $\frac{10}{14}$: Divide by 2 → $\frac{5}{7}$.
- Not equivalent. ✗

- $\frac{4}{8} = \frac{12}{32}$
- Simplify $\frac{4}{8}$: Divide by 4 → $\frac{1}{2}$.
- Simplify $\frac{12}{32}$: Divide by 4 → $\frac{3}{8}$.
- Not equivalent. ✗

- $\frac{1}{2} = \frac{2}{10}$
- Simplify $\frac{2}{10}$: Divide by 2 → $\frac{1}{5}$.
- Not equivalent. ✗

- $\frac{5}{11} = \frac{15}{33}$
- Simplify $\frac{15}{33}$: Divide by 3 → $\frac{5}{11}$.
- Equivalent. ✓

#### Row 6:
- $\frac{3}{10} = \frac{12}{40}$
- Simplify $\frac{12}{40}$: Divide by 4 → $\frac{3}{10}$.
- Equivalent. ✓

- $\frac{3}{7} = \frac{6}{14}$
- Simplify $\frac{6}{14}$: Divide by 2 → $\frac{3}{7}$.
- Equivalent. ✓

- $\frac{7}{9} = \frac{21}{27}$
- Simplify $\frac{21}{27}$: Divide by 3 → $\frac{7}{9}$.
- Equivalent. ✓

- $\frac{1}{6} = \frac{5}{30}$
- Simplify $\frac{5}{30}$: Divide by 5 → $\frac{1}{6}$.
- Equivalent. ✓

#### Row 7:
- $\frac{9}{9} = \frac{18}{18}$
- Both simplify to 1.
- Equivalent. ✓

- $\frac{5}{9} = \frac{10}{18}$
- Simplify $\frac{10}{18}$: Divide by 2 → $\frac{5}{9}$.
- Equivalent. ✓

- $\frac{1}{2} = \frac{2}{4}$
- Simplify $\frac{2}{4}$: Divide by 2 → $\frac{1}{2}$.
- Equivalent. ✓

- $\frac{4}{7} = \frac{8}{14}$
- Simplify $\frac{8}{14}$: Divide by 2 → $\frac{4}{7}$.
- Equivalent. ✓

#### Row 8:
- $\frac{6}{8} = \frac{18}{32}$
- Simplify $\frac{6}{8}$: Divide by 2 → $\frac{3}{4}$.
- Simplify $\frac{18}{32}$: Divide by 2 → $\frac{9}{16}$.
- Not equivalent. ✗

- $\frac{5}{11} = \frac{15}{33}$
- Simplify $\frac{15}{33}$: Divide by 3 → $\frac{5}{11}$.
- Equivalent. ✓

- $\frac{6}{6} = \frac{24}{30}$
- Simplify $\frac{6}{6}$: 1.
- Simplify $\frac{24}{30}$: Divide by 6 → $\frac{4}{5}$.
- Not equivalent. ✗

- $\frac{1}{4} = \frac{4}{4}$
- Simplify $\frac{4}{4}$: 1.
- Not equivalent. ✗

#### Row 9:
- $\frac{1}{7} = \frac{5}{35}$
- Simplify $\frac{5}{35}$: Divide by 5 → $\frac{1}{7}$.
- Equivalent. ✓

- $\frac{3}{5} = \frac{9}{15}$
- Simplify $\frac{9}{15}$: Divide by 3 → $\frac{3}{5}$.
- Equivalent. ✓

- $\frac{2}{2} = \frac{8}{10}$
- Simplify $\frac{2}{2}$: 1.
- Simplify $\frac{8}{10}$: Divide by 2 → $\frac{4}{5}$.
- Not equivalent. ✗

- $\frac{3}{3} = \frac{15}{9}$
- Simplify $\frac{3}{3}$: 1.
- Simplify $\frac{15}{9}$: Divide by 3 → $\frac{5}{3}$.
- Not equivalent. ✗

Final Answer:

The marked answers in the image are correct based on the verification above. The final boxed answer is:

\[
\boxed{\text{See the marked answers in the image.}}
\]