Understand Fractions as Unit Fraction Multiples - 4th Grade Math

1. What is $\frac{7}{8}$ written as a multiple of a unit fraction?

   $7\times\frac{1}{8}$. The numerator 7 tells us to multiply $\frac{1}{8}$ by 7.

2. What is $\frac{3}{6}$ written as a multiple of a unit fraction?

   $3\times\frac{1}{6}$. The numerator 3 tells us to multiply $\frac{1}{6}$ by 3.

3. Find the product: $6\times\frac{1}{5}$.

   $\frac{6}{5}$. Multiplying gives numerator 6 over denominator 5.

4. What is the missing number in $\frac{8}{9}=\square\times\frac{1}{9}$?

   $8$. The numerator equals the multiplier.

5. What does the denominator $b$ tell you in the unit fraction $\frac{1}{b}$?

   The whole is split into $b$ equal parts. The denominator shows how many equal pieces make one whole.

6. What fraction equals $12 \times \left(\frac{1}{9}\right)$?

   $\frac{12}{9}$. Multiplying 12 copies of $\frac{1}{9}$ gives numerator 12 and denominator 9.

7. What is the missing denominator in $\frac{5}{\square}=5\times\frac{1}{8}$?

   $8$. The denominator matches the unit fraction's denominator.

8. What is $\frac{5}{4}$ written as a product of a whole number and a unit fraction?

   $\frac{5}{4}=5\times\frac{1}{4}$. The numerator 5 multiplied by the unit fraction $\frac{1}{4}$

9. What fraction equals $3 \times \left(\frac{1}{4}\right)$?

   $\frac{3}{4}$. Multiplying 3 copies of $\frac{1}{4}$ gives numerator 3 and denominator 4.

10. What is $\frac{9}{2}$ written as a multiple of $\frac{1}{2}$?

    $\frac{9}{2}=9\times\frac{1}{2}$. Nine halves means 9 groups of $\frac{1}{2}$.

11. Identify the missing number: $\frac{8}{5} = \square \times \left(\frac{1}{5}\right)$.

    $8$. The numerator of the fraction tells how many unit fractions to multiply.

12. What fraction equals $8 \times \left(\frac{1}{2}\right)$?

    $\frac{8}{2}$. Multiplying 8 copies of $\frac{1}{2}$ gives numerator 8 and denominator 2.

13. What does the numerator $a$ mean in $\frac{a}{b} = a \times \left(\frac{1}{b}\right)$?

    $a$ copies of $\frac{1}{b}$. The numerator tells how many unit fractions to multiply together.

14. What is the denominator in $\frac{a}{b}$ if $\frac{a}{b}=a \times \frac{1}{b}$?

    $b$. The denominator stays the same in both forms.

15. What equation rewrites $\frac{4}{7}$ as a multiple of a unit fraction?

    $\frac{4}{7} = 4 \times \left(\frac{1}{7}\right)$. Shows that $\frac{4}{7}$ equals 4 copies of the unit fraction $\frac{1}{7}$.

16. What is $\frac{9}{10}$ written as a multiple of a unit fraction?

    $9\times\frac{1}{10}$. The numerator 9 tells us to multiply $\frac{1}{10}$ by 9.

17. What multiplication expression writes $\frac{2}{9}$ as a multiple of a unit fraction?

    $2 \times \left(\frac{1}{9}\right)$. The numerator 2 shows how many copies of $\frac{1}{9}$ are needed.

18. What is the unit fraction in the expression $\frac{a}{b} = a \times \left(\frac{1}{b}\right)$?

    $\frac{1}{b}$. The unit fraction has numerator 1 and the same denominator as the original fraction.

19. Identify the missing number: $\frac{7}{12} = 7 \times \left(\frac{1}{\square}\right)$.

    $12$. The denominator of the unit fraction matches the original denominator.

20. What is the unit fraction in the fraction $\frac{a}{b}$?

    $\frac{1}{b}$. The unit fraction has numerator 1 and the same denominator.

21. What is $\frac{7}{8}$ written as a multiple of $\frac{1}{8}$?

    $\frac{7}{8}=7\times\frac{1}{8}$. The numerator 7 tells us how many eighths we have.

22. What is the missing denominator in $5\times\frac{1}{\_\_\_}=\frac{5}{13}$?

    $13$. The denominator matches the fraction's denominator.

23. What equation records the conclusion when a model shows $5$ groups of $\frac{1}{4}$?

    $\frac{5}{4}=5\times\frac{1}{4}$. This equation shows 5 groups of $\frac{1}{4}$.

24. What equation rewrites $\frac{9}{10}$ as a multiple of a unit fraction?

    $\frac{9}{10} = 9 \times \left(\frac{1}{10}\right)$. Shows that $\frac{9}{10}$ equals 9 copies of the unit fraction $\frac{1}{10}$.

25. What does it mean to write $\frac{a}{b}$ as a multiple of a unit fraction?

    $\frac{a}{b}=a\times\frac{1}{b}$. Express the fraction as the numerator times the unit fraction.

26. Find and correct the error: $\frac{5}{9} = 5 \times \left(\frac{1}{5}\right)$.

    $\frac{5}{9} = 5 \times \left(\frac{1}{9}\right)$. The unit fraction must have denominator 9 to match the original fraction.

27. What is $\frac{2}{3}$ written as a sum of unit fractions with the same denominator?

    $\frac{1}{3}+\frac{1}{3}$. Two copies of $\frac{1}{3}$ equal $\frac{2}{3}$.

28. Which unit fraction is being multiplied in $\frac{13}{6} = 13 \times \left(\frac{1}{6}\right)$?

    $\frac{1}{6}$. The unit fraction has the same denominator as the original fraction.

29. What is $\frac{4}{7}$ written as repeated addition of $\frac{1}{7}$?

    $\frac{1}{7}+\frac{1}{7}+\frac{1}{7}+\frac{1}{7}$. Four sevenths equals adding one seventh four times.

30. What is the missing unit fraction in $11\times\_\_\_ =\frac{11}{15}$?

    $\frac{1}{15}$. Eleven fifteenths needs the unit fraction $\frac{1}{15}$.

31. Which equation correctly rewrites $\frac{4}{9}$ using a unit fraction?

    $\frac{4}{9}=4\times\frac{1}{9}$. Four ninths equals 4 groups of one ninth.

32. Which equation correctly rewrites $frac{6}{7}$ using a unit fraction?

    $\frac{6}{7}=6\times\frac{1}{7}$. Six sevenths equals 6 groups of one seventh.

33. Find the product: $12\times\frac{1}{8}$.

    $\frac{12}{8}$. Multiplying gives numerator 12 over denominator 8.

34. Find and correct the error: $frac{5}{4}=5\times\frac{1}{5}$.

    Correct: $\frac{5}{4}=5\times\frac{1}{4}$. The unit fraction must match the original denominator 4.

35. What is $\frac{5}{6}$ written as a sum of unit fractions with the same denominator?

    $\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}$. Five copies of $\frac{1}{6}$ equal $\frac{5}{6}$.

36. What is the value of $5\times\frac{1}{4}$ written as a single fraction?

    $\frac{5}{4}$. Multiply: $5 \times \frac{1}{4} = \frac{5}{4}$.

37. What equation rewrites $\frac{11}{8}$ as a multiple of a unit fraction?

    $\frac{11}{8} = 11 \times \left(\frac{1}{8}\right)$. Shows that $\frac{11}{8}$ equals 11 copies of the unit fraction $\frac{1}{8}$.

38. Find and correct the error: $\frac{6}{7} = 7 \times \left(\frac{1}{6}\right)$.

    $\frac{6}{7} = 6 \times \left(\frac{1}{7}\right)$. The numerator and denominator were swapped in the incorrect equation.

39. Which expression equals $\frac{12}{5}$: $12\times\frac{1}{5}$ or $5\times\frac{1}{12}$?

    $12\times\frac{1}{5}$. Check: $12 \times \frac{1}{5} = \frac{12}{5}$ ✓.

40. What is $\frac{1}{6}$ written as a multiple of $\frac{1}{6}$?

    $\frac{1}{6}=1\times\frac{1}{6}$. One sixth is already a unit fraction, so multiply by 1.

41. What is $\frac{2}{3}$ written as repeated addition of $\frac{1}{3}$?

    $\frac{1}{3}+\frac{1}{3}$. Two thirds equals adding one third twice.

42. What does $4 \times \left(\frac{1}{6}\right)$ mean in words?

    Four copies of $\frac{1}{6}$. Multiplication means taking 4 equal parts, each worth $\frac{1}{6}$.

43. What is $\frac{3}{10}$ written as a multiple of $\frac{1}{10}$?

    $\frac{3}{10}=3\times\frac{1}{10}$. Three tenths equals 3 groups of one tenth.

44. Identify the unit fraction being multiplied in $\frac{13}{4}=13\times\frac{1}{4}$.

    $\frac{1}{4}$. The unit fraction has the same denominator as the original.

45. What equation rewrites $\frac{7}{3}$ as a multiple of a unit fraction?

    $\frac{7}{3} = 7 \times \left(\frac{1}{3}\right)$. Shows that $\frac{7}{3}$ equals 7 copies of the unit fraction $\frac{1}{3}$.

46. What fraction equals $11\times\frac{1}{12}$?

    $\frac{11}{12}$. Multiplying gives $\frac{11}{12}$.

47. What fraction equals $4\times\frac{1}{7}$?

    $\frac{4}{7}$. Multiplying gives $\frac{4}{7}$.

48. What does the numerator $a$ represent in $\frac{a}{b}=a\times\frac{1}{b}$?

    The number of groups of $\frac{1}{b}$. It counts how many unit fractions we need.

49. What is the unit fraction in the fraction $\frac{a}{b}$?

    $\frac{1}{b}$. The unit fraction has numerator 1 and the same denominator.

50. What is the missing numerator in $\frac{\square}{6}=9\times\frac{1}{6}$?

    $9$. The numerator equals the multiplier.

51. Find and correct the error: $\frac{6}{8}=8\times\frac{1}{6}$.

    Correct: $\frac{6}{8}=6\times\frac{1}{8}$. The numerator tells how many unit fractions.

52. What fraction equals $6\times\frac{1}{5}$?

    $\frac{6}{5}$. Multiplying gives $\frac{6}{5}$.

53. What multiplication expression writes $\frac{10}{3}$ as a multiple of a unit fraction?

    $10 \times \left(\frac{1}{3}\right)$. The numerator 10 shows how many copies of $\frac{1}{3}$ are needed.

54. What is the numerator in $\frac{a}{b}$ if $\frac{a}{b}=a \times \frac{1}{b}$?

    $a$. The numerator tells how many unit fractions we need.

55. What fraction equals $6 \times \left(\frac{1}{5}\right)$?

    $\frac{6}{5}$. Multiplying 6 copies of $\frac{1}{5}$ gives numerator 6 and denominator 5.

56. Identify the correct rewrite of $\frac{10}{10}$ as a multiple of a unit fraction.

    $\frac{10}{10}=10\times\frac{1}{10}$. Ten tenths equals 10 groups of one tenth.

57. What does it mean to write $\frac{a}{b}$ as a multiple of a unit fraction?

    $\frac{a}{b}=a\times\frac{1}{b}$. The numerator tells how many unit fractions to multiply.

58. What equation rewrites $\frac{5}{4}$ as a multiple of a unit fraction?

    $\frac{5}{4} = 5 \times \left(\frac{1}{4}\right)$. Shows that $\frac{5}{4}$ equals 5 copies of the unit fraction $\frac{1}{4}$.

59. What is the missing number in _ _ _ \times \frac{1}{12} = \frac{8}{12}?

    $8$. The numerator 8 tells how many twelfths we need.

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