Understand Equivalent Fractions Concept - 3rd Grade Math

1. Which fraction names the same location as $\frac{2}{4}$ on a number line: $\frac{1}{2}$ or $\frac{1}{4}$?

   $\frac{1}{2}$. $\frac{2}{4}$ simplifies to $\frac{1}{2}$ by dividing by 2.

2. Which statement is true: $\frac{2}{8}=\frac{1}{4}$ or $\frac{2}{8}=\frac{1}{3}$?

   $\frac{2}{8}=\frac{1}{4}$. Divide $\frac{2}{8}$ by 2 to get $\frac{1}{4}$, not $\frac{1}{3}$.

3. What is the missing numerator so that $\frac{3}{7}= \frac{?}{14}$?

   $\frac{6}{14}$. Multiply numerator by 2 since denominator was multiplied by 2: $3 \times 2 = 6$.

4. Which fraction is equivalent to $\frac{2}{3}$: $\frac{4}{6}$ or $\frac{4}{7}$?

   $\frac{4}{6}$. Both equal $\frac{2}{3}$ when simplified ($\frac{4}{6} = \frac{4÷2}{6÷2} = \frac{2}{3}$).

5. What must be true about the size of two equivalent fractions?

   They represent the same size (the same amount of the whole). Equivalent fractions represent equal parts of a whole.

6. Identify the missing number: $\frac{2}{5}=\frac{?}{10}$.

   $4$. Since $5×2=10$, multiply $2×2=4$.

7. Which fraction is equivalent to $\frac{1}{4}$: $\frac{2}{8}$ or $\frac{2}{6}$?

   $\frac{2}{8}$. Both equal $\frac{1}{4}$ when simplified ($\frac{2}{8} = \frac{2÷2}{8÷2} = \frac{1}{4}$).

8. Identify the equivalent fraction to $\frac{6}{8}$ in simplest form.

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

9. What is the missing fraction so that $\frac{3}{4} = \frac{?}{8}$?

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

10. Which fraction is equivalent to $\frac{7}{8}$: $\frac{14}{16}$ or $\frac{14}{18}$?

    $\frac{14}{16}$. Both equal $\frac{7}{8}$ when simplified ($\frac{14}{16} = \frac{14÷2}{16÷2} = \frac{7}{8}$).

11. Which fraction is equivalent to $\frac{3}{5}$: $\frac{6}{10}$ or $\frac{6}{15}$?

    $\frac{6}{10}$. Both equal $\frac{3}{5}$ when simplified ($\frac{6}{10} = \frac{6÷2}{10÷2} = \frac{3}{5}$).

12. Which fraction is equivalent to $\frac{6}{9}$: $\frac{2}{3}$ or $\frac{3}{5}$?

    $\frac{2}{3}$. Simplify $\frac{6}{9}$ by dividing both parts by 3 to get $\frac{2}{3}$.

13. What does it mean for two fractions to be equivalent on a number line?

    They are at the same point (same distance from $0$). Equivalent fractions land on the exact same spot when measured from zero.

14. Which point matches both $\frac{1}{2}$ and $\frac{2}{4}$ on a number line from $0$ to $1$?

    The point halfway between $0$ and $1$. Both fractions equal 0.5, placing them at the midpoint.

15. Which fraction is equivalent to $\frac{3}{5}$: $\frac{6}{10}$, $\frac{3}{10}$, or $\frac{5}{3}$?

    $\frac{6}{10}$. Multiply both parts by 2: $3 \times 2 = 6$ and $5 \times 2 = 10$.

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

    $\frac{2}{3}$. Simplify $\frac{4}{6}$ by dividing both parts by 2 to get $\frac{2}{3}$.

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

    $\frac{4}{6}$. Multiply top and bottom by 2: $2×2=4$ and $3×2=6$.

18. Which fraction is equivalent to $\frac{2}{8}$ in simplest form?

    $\frac{1}{4}$. Divide both numerator and denominator by 2: $\frac{2 \div 2}{8 \div 2} = \frac{1}{4}$

19. Which fraction is equivalent to $\frac{4}{5}$: $\frac{8}{10}$, $\frac{4}{10}$, or $\frac{5}{4}$?

    $\frac{8}{10}$. Multiply by 2: $4×2=8$ and $5×2=10$.

20. What does it mean for two fractions to be equivalent on a number line?

    They name the same point (the same size) on the number line. Equivalent fractions represent the same location on the number line.

21. What is the missing fraction so that $\frac{2}{5} = \frac{?}{10}$?

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

22. Which fraction is equivalent to $\frac{2}{5}$: $\frac{4}{10}$ or $\frac{4}{12}$?

    $\frac{4}{10}$. Both equal $\frac{2}{5}$ when simplified ($\frac{4}{10} = \frac{4÷2}{10÷2} = \frac{2}{5}$).

23. Choose the fraction that names the same point as $\frac{0}{5}$ on a number line.

    $0$. $\frac{0}{5} = 0$ because zero divided by any number equals zero.

24. Which option shows a fraction equivalent to $\frac{1}{2}$: $\frac{2}{3}$, $\frac{3}{6}$, or $\frac{2}{5}$?

    $\frac{3}{6}$. $\frac{3}{6} = \frac{1}{2}$ when simplified by dividing by 3.

25. What operation can you do to both numerator and denominator to make an equivalent fraction?

    Multiply or divide both by the same nonzero number. This preserves the fraction's value by scaling equally.

26. Which option shows a fraction equivalent to $\frac{2}{3}$: $\frac{3}{4}$, $\frac{4}{6}$, or $\frac{3}{6}$?

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

27. What does it mean for two fractions to be equivalent in size?

    They represent the same amount of a whole. Equal fractions show the same portion, just divided differently.

28. What is the missing fraction so that $\frac{2}{3} = \frac{?}{6}$?

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

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

    $\frac{6}{8}$. Both equal $\frac{3}{4}$ when simplified ($\frac{6}{8} = \frac{6÷2}{8÷2} = \frac{3}{4}$).

30. Identify the equivalent fraction to $\frac{2}{4}$ in simplest form.

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

31. Identify the missing number: $\frac{3}{4}=\frac{?}{8}$.

    $6$. Since $4×2=8$, multiply $3×2=6$.

32. Which statement is true if $\frac{a}{b}$ and $\frac{c}{d}$ are equivalent fractions?

    They name the same point on the number line. Equivalent fractions represent the same value on a number line.

33. What is the missing numerator so that $\frac{5}{8}= \frac{?}{16}$?

    $\frac{10}{16}$. Multiply numerator by 2 since denominator was multiplied by 2: $5 \times 2 = 10$.

34. Find and correct the false statement: $\frac{2}{4}=\frac{2}{8}$.

    Correct: $\frac{2}{4}=\frac{4}{8}$. $\frac{2}{4}$ doubled equals $\frac{4}{8}$, not $\frac{2}{8}$.

35. Which fraction is equivalent to $\frac{5}{10}$: $\frac{1}{2}$ or $\frac{2}{5}$?

    $\frac{1}{2}$. Simplify $\frac{5}{10}$ by dividing both parts by 5 to get $\frac{1}{2}$.

36. Which fraction is equivalent to $\frac{1}{3}$: $\frac{2}{6}$, $\frac{3}{6}$, or $\frac{1}{6}$?

    $\frac{2}{6}$. Multiply both by 2: $1×2=2$ and $3×2=6$.

37. Which fraction is equivalent to $\frac{3}{6}$ in simplest form?

    $\frac{1}{2}$. Divide both numerator and denominator by 3: $\frac{3 \div 3}{6 \div 3} = \frac{1}{2}$.

38. Which fraction is equivalent to $\frac{5}{6}$: $\frac{10}{12}$, $\frac{5}{12}$, or $\frac{6}{5}$?

    $\frac{10}{12}$. Multiply numerator and denominator by 2: $5×2=10$, $6×2=12$.

39. Which fraction is equivalent to $\frac{9}{12}$: $\frac{3}{4}$ or $\frac{2}{3}$?

    $\frac{3}{4}$. Simplify $\frac{9}{12}$ by dividing both parts by 3 to get $\frac{3}{4}$.

40. Identify the equivalent fraction to $\frac{4}{6}$ in simplest form.

    $\frac{2}{3}$. Divide both by their GCF of 2: $4÷2=2$ and $6÷2=3$.

41. Which fraction is equivalent to $\frac{6}{9}$: $\frac{2}{3}$, $\frac{3}{2}$, or $\frac{6}{3}$?

    $\frac{2}{3}$. Divide both by 3: $6 \div 3 = 2$ and $9 \div 3 = 3$.

42. Which option shows a fraction equivalent to $\frac{3}{5}$: $\frac{6}{10}$, $\frac{5}{6}$, or $\frac{3}{10}$?

    $\frac{6}{10}$. $\frac{6}{10} = \frac{3}{5}$ when simplified by dividing by 2.

43. Which fraction is equivalent to $\frac{1}{2}$: $\frac{2}{4}$, $\frac{2}{3}$, or $\frac{1}{3}$?

    $\frac{2}{4}$. Both equal $\frac{1}{2}$ since $2÷2=1$ and $4÷2=2$.

44. What is the missing fraction so that $\frac{1}{3} = \frac{?}{6}$?

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

45. Which statement best describes why $\frac{2}{2}$ and $\frac{4}{4}$ are equivalent?

    Both equal $1$ and mark the same point on the number line. When numerator equals denominator, the fraction equals $1$.

46. Which point is the same on a number line: $\frac{1}{2}$ or $\frac{3}{6}$?

    They are the same point: $\frac{1}{2}=\frac{3}{6}$. Both simplify to $\frac{1}{2}$ when reduced.

47. Which fraction is equivalent to $\frac{6}{9}$ in simplest form?

    $\frac{2}{3}$. Divide both numerator and denominator by 3: $\frac{6 \div 3}{9 \div 3} = \frac{2}{3}$.

48. Which pair of fractions names the same point on a number line: $\frac{2}{6}$ and $\frac{1}{3}$, or $\frac{2}{6}$ and $\frac{1}{4}$?

    $\frac{2}{6}$ and $\frac{1}{3}$. Both simplify to $\frac{1}{3}$, representing the same value.

49. What is the missing fraction so that $\frac{4}{6}= \frac{?}{3}$?

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

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

    $\frac{2}{6}$. Both equal $\frac{1}{3}$ when simplified ($\frac{2}{6} = \frac{2÷2}{6÷2} = \frac{1}{3}$).

51. Choose the fraction that names the same point as $\frac{4}{4}$ on a number line.

    $1$. $\frac{4}{4} = 1$ because numerator equals denominator.

52. Which fraction is equivalent to $\frac{7}{8}$: $\frac{14}{16}$, $\frac{7}{16}$, or $\frac{8}{7}$?

    $\frac{14}{16}$. Double both parts: $7×2=14$ and $8×2=16$.

53. Identify the equivalent pair: $\frac{2}{4}$ and $\frac{3}{6}$, or $\frac{2}{4}$ and $\frac{3}{5}$?

    $\frac{2}{4}$ and $\frac{3}{6}$. Both simplify to $\frac{1}{2}$ when divided by their GCF.

54. Which fraction is equivalent to $\frac{8}{12}$: $\frac{2}{3}$ or $\frac{3}{8}$?

    $\frac{2}{3}$. Simplify $\frac{8}{12}$ by dividing both parts by 4 to get $\frac{2}{3}$.

55. Which fraction is equivalent to $\frac{1}{2}$: $\frac{2}{4}$ or $\frac{2}{5}$?

    $\frac{2}{4}$. Both equal $\frac{1}{2}$ when simplified ($\frac{2}{4} = \frac{2÷2}{4÷2} = \frac{1}{2}$).

56. Identify the equivalent fraction to $\frac{3}{4}$ when both numerator and denominator are doubled.

    $\frac{6}{8}$. Doubling means multiply by 2: $3×2=6$ and $4×2=8$.

57. What number line fact shows $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent?

    They mark the same point on the number line. Equal fractions represent the same distance from zero.

58. What is the missing fraction so that $ \frac{1}{2}= \frac{?}{4}$?

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

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