Equivalent Fractions worksheet for Grade 3 students to practice finding equivalent fractions.

To find equivalent fractions, we multiply or divide the numerator (top number) and the denominator (bottom number) by the same number. This keeps the value of the fraction the same.

Here is the step-by-step solution for each row:

Row 1: $\frac{1}{2}$
* Already solved in the image: $\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{5}{10} = \frac{6}{12}$

Row 2: Start with $\frac{1}{3}$
* To get denominator 6: Multiply top and bottom by 2 $\rightarrow$ $\frac{2}{6}$
* To get numerator 3: Multiply top and bottom by 3 $\rightarrow$ $\frac{3}{9}$
* To get denominator 12: Multiply top and bottom by 4 $\rightarrow$ $\frac{4}{12}$
* To get numerator 5: Multiply top and bottom by 5 $\rightarrow$ $\frac{5}{15}$
* To get denominator 18: Multiply top and bottom by 6 $\rightarrow$ $\frac{6}{18}$
* Result: $\frac{1}{3} = \frac{2}{6} = \frac{3}{9} = \frac{4}{12} = \frac{5}{15} = \frac{6}{18}$

Row 3: Start with $\frac{1}{7}$
* Multiply by 2: $\frac{2}{14}$
* Multiply by 3: $\frac{3}{21}$
* Multiply by 4: $\frac{4}{28}$
* Multiply by 5: $\frac{5}{35}$
* Multiply by 6: $\frac{6}{42}$
* Result: $\frac{1}{7} = \frac{2}{14} = \frac{3}{21} = \frac{4}{28} = \frac{5}{35} = \frac{6}{42}$

Row 4: Start with $\frac{2}{3}$
* Multiply by 2: $\frac{4}{6}$
* Given numerator 6 (multiply by 3): $\frac{6}{9}$
* Given denominator 12 (multiply by 4): $\frac{8}{12}$
* Given denominator 15 (multiply by 5): $\frac{10}{15}$
* Given numerator 12 (multiply by 6): $\frac{12}{18}$
* Result: $\frac{2}{3} = \frac{4}{6} = \frac{6}{9} = \frac{8}{12} = \frac{10}{15} = \frac{12}{18}$

Row 5: Start with $\frac{1}{4}$
* Given numerator 3 (multiply by 3): $\frac{3}{12}$
* Given denominator 20 (multiply by 5): $\frac{5}{20}$
* Multiply by 4: $\frac{4}{16}$
* Multiply by 6: $\frac{6}{24}$
* Multiply by 7: $\frac{7}{28}$
* Result: $\frac{1}{4} = \frac{3}{12} = \frac{5}{20} = \frac{4}{16} = \frac{6}{24} = \frac{7}{28}$

Row 6: Start with $\frac{3}{8}$
* Multiply by 2: $\frac{6}{16}$
* Given denominator 24 (multiply by 3): $\frac{9}{24}$
* Given denominator 32 (multiply by 4): $\frac{12}{32}$
* Given numerator 15 (multiply by 5): $\frac{15}{40}$
* Given denominator 48 (multiply by 6): $\frac{18}{48}$
* Result: $\frac{3}{8} = \frac{6}{16} = \frac{9}{24} = \frac{12}{32} = \frac{15}{40} = \frac{18}{48}$

Row 7: Start with $\frac{1}{5}$
* Given denominator 10 (multiply by 2): $\frac{2}{10}$
* Given denominator 15 (multiply by 3): $\frac{3}{15}$
* Multiply by 4: $\frac{4}{20}$
* Multiply by 5: $\frac{5}{25}$
* Given denominator 30 (multiply by 6): $\frac{6}{30}$
* Result: $\frac{1}{5} = \frac{2}{10} = \frac{3}{15} = \frac{4}{20} = \frac{5}{25} = \frac{6}{30}$

Row 8: Start with $\frac{5}{10}$
* First, simplify $\frac{5}{10}$ to $\frac{1}{2}$. Now we can just follow the pattern from Row 1, but keeping the numbers larger if we want, or simplifying first makes it easier. Let's create equivalents for $\frac{1}{2}$ starting from scratch or using the simplified form.
* Simplify to $\frac{1}{2}$.
* Multiply by 2: $\frac{2}{4}$
* Multiply by 3: $\frac{3}{6}$
* Multiply by 4: $\frac{4}{8}$
* Multiply by 5: $\frac{5}{10}$ (This is the start)
* Multiply by 6: $\frac{6}{12}$
* *Note: Since the problem starts with $\frac{5}{10}$, you can also just multiply 5 and 10 by other numbers.*
* Multiply by 2: $\frac{10}{20}$
* Multiply by 3: $\frac{15}{30}$
* Multiply by 4: $\frac{20}{40}$
* Multiply by 5: $\frac{25}{50}$
* Multiply by 6: $\frac{30}{60}$
* Let's provide the simplest equivalents based on reducing to $\frac{1}{2}$ as that is standard, but technically any equivalent works. Let's stick to the simplest multiples of the reduced form $\frac{1}{2}$ or multiples of the original $\frac{5}{10}$. Usually, these worksheets expect you to fill in the blanks sequentially. Let's assume sequential multiplication of the base fraction $\frac{1}{2}$ derived from $\frac{5}{10}$.
* Actually, looking at Row 1, it goes $\frac{1}{2}, \frac{2}{4}...$ Row 8 starts with $\frac{5}{10}$. If we treat $\frac{5}{10}$ as the base "1x", then:
* Next could be $\frac{10}{20}$ (2x), $\frac{15}{30}$ (3x), $\frac{20}{40}$ (4x), $\frac{25}{50}$ (5x), $\frac{30}{60}$ (6x).
* Alternatively, simplify to $\frac{1}{2}$ and use $\frac{1}{2}, \frac{2}{4}, \frac{3}{6}...$ but the first box is already filled as $\frac{5}{10}$. So the subsequent boxes should likely be larger equivalents.
* Let's provide: $\frac{10}{20}, \frac{15}{30}, \frac{20}{40}, \frac{25}{50}, \frac{30}{60}$.

Final Answer:
1. $\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{5}{10} = \frac{6}{12}$
2. $\frac{1}{3} = \frac{2}{6} = \frac{3}{9} = \frac{4}{12} = \frac{5}{15} = \frac{6}{18}$
3. $\frac{1}{7} = \frac{2}{14} = \frac{3}{21} = \frac{4}{28} = \frac{5}{35} = \frac{6}{42}$
4. $\frac{2}{3} = \frac{4}{6} = \frac{6}{9} = \frac{8}{12} = \frac{10}{15} = \frac{12}{18}$
5. $\frac{1}{4} = \frac{3}{12} = \frac{5}{20} = \frac{4}{16} = \frac{6}{24} = \frac{7}{28}$
6. $\frac{3}{8} = \frac{6}{16} = \frac{9}{24} = \frac{12}{32} = \frac{15}{40} = \frac{18}{48}$
7. $\frac{1}{5} = \frac{2}{10} = \frac{3}{15} = \frac{4}{20} = \frac{5}{25} = \frac{6}{30}$
8. $\frac{5}{10} = \frac{10}{20} = \frac{15}{30} = \frac{20}{40} = \frac{25}{50} = \frac{30}{60}$