Generate and Explain Equivalent Fractions - 3rd Grade Math

1. What number completes the equivalent fraction: $\frac{3}{4} = \frac{\square}{12}$?

   $9$. Since $4 \times 3 = 12$, multiply numerator by 3: $3 \times 3 = 9$.

2. Identify the missing factor: $\frac{2}{3} = \frac{8}{12}$ uses multiplying by $\square$.

   $4$. Both $2 \times 4 = 8$ and $3 \times 4 = 12$, so the factor is 4.

3. Which statement is true: $\frac{2}{3} = \frac{4}{6}$ or $\frac{2}{3} = \frac{4}{8}$?

   $\frac{2}{3} = \frac{4}{6}$. $\frac{2 \times 2}{3 \times 2} = \frac{4}{6}$ is correct; $\frac{4}{8} \neq \frac{2}{3}$.

4. Which option is equivalent to $\frac{1}{4}$: $\frac{2}{8}$ or $\frac{3}{8}$?

   $\frac{2}{8}$. $\frac{1 \times 2}{4 \times 2} = \frac{2}{8}$, while $\frac{3}{8} \neq \frac{1}{4}$.

5. What is an equivalent fraction to $\frac{4}{5}$ with denominator $10$?

   $\frac{8}{10}$. Multiply both numerator and denominator by 2: $\frac{4 \times 2}{5 \times 2}$.

6. What is an equivalent fraction to $\frac{1}{3}$ with denominator $9$?

   $\frac{3}{9}$. Multiply both numerator and denominator by 3: $\frac{1 \times 3}{3 \times 3}$.

7. Which option is equivalent to $\frac{1}{3}$: $\frac{2}{6}$ or $\frac{2}{5}$?

   $\frac{2}{6}$. $\frac{1 \times 2}{3 \times 2} = \frac{2}{6}$, while $\frac{2}{5}$ has wrong ratio.

8. What is an equivalent fraction to $\frac{2}{3}$ with denominator $6$?

   $\frac{4}{6}$. Multiply both numerator and denominator by $2$.

9. What number completes the equivalent fraction: $\frac{4}{7} = \frac{12}{\square}$?

   $21$. Since $4 \times 3 = 12$, multiply denominator by 3: $7 \times 3 = 21$.

10. What is the simplified equivalent fraction for $\frac{3}{6}$?

    $\frac{1}{2}$. Divide both numerator and denominator by their GCF of $3$.

11. What operation on numerator and denominator always makes an equivalent fraction?

    Multiply both by the same nonzero number. This preserves the ratio between numerator and denominator.

12. What is the simplified equivalent fraction for $\frac{4}{6}$?

    $\frac{2}{3}$. Divide both numerator and denominator by their GCF of $2$.

13. Which option is equivalent to $\frac{3}{4}$: $\frac{6}{8}$ or $\frac{6}{10}$?

    $\frac{6}{8}$. $\frac{3 \times 2}{4 \times 2} = \frac{6}{8}$, while $\frac{6}{10}$ has wrong ratio.

14. What is an equivalent fraction to $\frac{6}{8}$ in simplest form?

    $\frac{3}{4}$. Divide both numerator and denominator by 2: $\frac{6 \div 2}{8 \div 2}$.

15. Which fraction is equivalent to $\frac{3}{4}$: $\frac{6}{8}$ or $\frac{6}{10}$?

    $\frac{6}{8}$. $\frac{3}{4} = \frac{6}{8}$ when multiplied by $2$.

16. What number completes the equivalent fraction: $\frac{1}{2} = \frac{\square}{8}$?

    $4$. Since $2 \times 4 = 8$, multiply numerator by 4: $1 \times 4 = 4$.

17. What is an equivalent fraction to $\frac{1}{2}$ with denominator $6$?

    $\frac{3}{6}$. Multiply both numerator and denominator by $3$.

18. Which fraction is equivalent to $\frac{2}{3}$: $\frac{4}{6}$ or $\frac{4}{5}$?

    $\frac{4}{6}$. $\frac{2}{3} = \frac{4}{6}$ when multiplied by $2$.

19. What is the simplified equivalent fraction for $\frac{2}{4}$?

    $\frac{1}{2}$. Divide both numerator and denominator by their GCF of $2$.

20. What number makes $\frac{2}{3}=\frac{?}{12}$ true?

    $8$. Since $12 = 3 \times 4$, multiply numerator $2$ by $4$ to get $8$.

21. What operation on numerator and denominator can make a simpler equivalent fraction?

    Divide both by the same number greater than $1$. This reduces the fraction while keeping the same value.

22. What is an equivalent fraction to $\frac{1}{2}$ with denominator $4$?

    $\frac{2}{4}$. Multiply both numerator and denominator by $2$.

23. What is an equivalent fraction to $\frac{4}{5}$ with denominator $10$?

    $\frac{8}{10}$. Multiply both numerator and denominator by $2$: $\frac{4 \times 2}{5 \times 2}$.

24. Identify the missing denominator: $\frac{3}{5}=\frac{9}{?}$.

    $15$. Since $3 \times 3 = 9$, multiply $5$ by $3$.

25. What is the missing denominator in $\frac{5}{6}=\frac{10}{?}$?

    $12$. Since numerator doubles from $5$ to $10$, denominator doubles to $12$.

26. Identify the missing numerator: $\frac{5}{6}=\frac{?}{12}$.

    $10$. Since $6 \times 2 = 12$, multiply $5$ by $2$.

27. What is an equivalent fraction to $\frac{1}{2}$ with denominator $4$?

    $\frac{2}{4}$. Multiply both numerator and denominator by 2: $\frac{1 \times 2}{2 \times 2}$

28. What is the missing denominator: $\frac{2}{3}=\frac{8}{?}$?

    $12$. Since $2 \times 4 = 8$, multiply $3$ by $4$.

29. What is the missing numerator: $\frac{4}{7}=\frac{?}{21}$?

    $12$. Since $7 \times 3 = 21$, multiply $4$ by $3$.

30. What is an equivalent fraction to $\frac{3}{5}$ with denominator $15$?

    $\frac{9}{15}$. Multiply both numerator and denominator by $3$: $\frac{3 \times 3}{5 \times 3}$.

31. What is an equivalent fraction to $\frac{9}{12}$ in simplest form?

    $\frac{3}{4}$. Divide both numerator and denominator by $3$.

32. Which option is equivalent to $\frac{2}{3}$: $\frac{4}{6}$ or $\frac{4}{9}$?

    $\frac{4}{6}$. $\frac{2 \times 2}{3 \times 2} = \frac{4}{6}$, while $\frac{4}{9} \neq \frac{2}{3}$.

33. Which option is equivalent to $\frac{3}{5}$: $\frac{6}{10}$ or $\frac{6}{12}$?

    $\frac{6}{10}$. $\frac{3 \times 2}{5 \times 2} = \frac{6}{10}$, while $\frac{6}{12} \neq \frac{3}{5}$.

34. What is an equivalent fraction to $\frac{3}{4}$ with denominator $8$?

    $\frac{6}{8}$. Multiply both numerator and denominator by 2: $\frac{3 \times 2}{4 \times 2}$.

35. What operation makes an equivalent fraction when applied to numerator and denominator?

    Multiply or divide both by the same nonzero number. This creates a fraction with the same value but different numbers.

36. What number makes $\frac{4}{6}=\frac{2}{?}$ true?

    $3$. Since numerator goes from $4$ to $2$ (divide by $2$), denominator becomes $3$.

37. What is an equivalent fraction to $\frac{2}{3}$ with denominator $6$?

    $\frac{4}{6}$. Multiply both numerator and denominator by 2: $\frac{2 \times 2}{3 \times 2}$.

38. What number completes the equivalent fraction: $\frac{2}{5} = \frac{\square}{15}$?

    $6$. Since $5 \times 3 = 15$, multiply numerator by 3: $2 \times 3 = 6$.

39. What is an equivalent fraction to $\frac{4}{6}$ in simplest form?

    $\frac{2}{3}$. Divide both numerator and denominator by 2: $\frac{4 \div 2}{6 \div 2}$.

40. What is the missing numerator: $\frac{7}{8}=\frac{?}{16}$?

    $14$. Since $8 \times 2 = 16$, multiply $7$ by $2$.

41. What is an equivalent fraction to $\frac{3}{4}$ with denominator $8$?

    $\frac{6}{8}$. Multiply both numerator and denominator by $2$.

42. What is the simplified equivalent fraction for $\frac{6}{8}$?

    $\frac{3}{4}$. Divide both numerator and denominator by their GCF of $2$.

43. What does it mean for two fractions to be equivalent?

    They name the same amount, even if the numbers are different. Equivalent fractions represent the same portion of a whole.

44. What is an equivalent fraction to $\frac{1}{2}$ with denominator $6$?

    $\frac{3}{6}$. Multiply both numerator and denominator by 3: $\frac{1 \times 3}{2 \times 3}$

45. Which option is equivalent to $\frac{2}{3}$: $\frac{4}{6}$ or $\frac{4}{9}$?

    $\frac{4}{6}$. $\frac{2 \times 2}{3 \times 2} = \frac{4}{6}$, while $\frac{4}{9}$ has wrong ratio.

46. What number makes $\frac{3}{5}=\frac{?}{10}$ true?

    $6$. Since $10 = 5 \times 2$, multiply numerator $3$ by $2$ to get $6$.

47. What is an equivalent fraction to $\frac{2}{4}$ in simplest form?

    $\frac{1}{2}$. Divide both numerator and denominator by 2: $\frac{2 \div 2}{4 \div 2}$

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