Multiply Fractions by Whole Numbers - 4th Grade Math

1. What is $8 \times \frac{1}{4}$?

   $\frac{8}{4}$. Place $8 \times 1 = 8$ in the numerator, keep denominator $4$.

2. What is $2 \times \frac{7}{10}$?

   $\frac{14}{10}$. Multiply: $2 \times 7 = 14$ in the numerator, keep denominator $10$.

3. Find and correct the error: $4 \times \frac{2}{7} = \frac{8}{28}$.

   Correct: $4 \times \frac{2}{7} = \frac{8}{7}$. Error: multiplied both parts; only multiply the numerator.

4. Which part changes in $n \times \frac{a}{b}$: numerator, denominator, or both?

   The numerator only. When multiplying by a whole number, only multiply the numerator.

5. What is $10 \times \frac{3}{10}$ as a fraction?

   $\frac{30}{10}$. Apply the formula: $10 \times \frac{3}{10} = \frac{10 \times 3}{10} = \frac{30}{10}$.

6. What is $2 \times \frac{7}{4}$ as an improper fraction?

   $\frac{14}{4}$. Apply the formula: $2 \times \frac{7}{4} = \frac{2 \times 7}{4} = \frac{14}{4}$.

7. Identify the missing number: $3 \times \frac{\square}{10} = \frac{21}{10}$.

   $7$. Since $\frac{21}{10} = \frac{3 \times 7}{10}$, the missing numerator is $7$.

8. What is $3 \times \frac{2}{5}$?

   $\frac{6}{5}$. Apply the rule: $3 \times 2 = 6$ in the numerator, keep denominator $5$.

9. Find and correct the error: $6 \times \frac{1}{9} = \frac{1}{54}$.

   Correct: $6 \times \frac{1}{9} = \frac{6}{9}$. Error: inverted the multiplication; multiply numerator by whole number.

10. What is $6 \times \frac{4}{9}$ as an improper fraction?

    $\frac{24}{9}$. Apply the formula: $6 \times \frac{4}{9} = \frac{6 \times 4}{9} = \frac{24}{9}$.

11. Identify the missing number: $\Box \times \frac{2}{7} = \frac{10}{7}$.

    $5$. Since $5 \times 2 = 10$, the missing whole number is $5$.

12. Rewrite $3 \times \frac{2}{5}$ as a multiple of $\frac{1}{5}$.

    $6 \times \frac{1}{5}$. Since $3 \times 2 = 6$, this equals $6$ copies of $\frac{1}{5}$.

13. What is $0 \times \frac{5}{8}$ as a fraction?

    $0$. Zero times any fraction equals zero.

14. What is $3 \times \frac{2}{5}$ as an improper fraction?

    $\frac{6}{5}$. Apply the formula: $3 \times \frac{2}{5} = \frac{3 \times 2}{5} = \frac{6}{5}$.

15. Rewrite $7 \times \frac{4}{9}$ as a multiple of $\frac{1}{9}$.

    $28 \times \frac{1}{9}$. Since $7 \times 4 = 28$, this equals $28$ copies of $\frac{1}{9}$.

16. What is $9 \times \frac{5}{12}$?

    $\frac{45}{12}$. Multiply: $9 \times 5 = 45$ in the numerator, keep denominator $12$.

17. Identify the missing number: $4 \times \frac{3}{\Box} = \frac{12}{11}$.

    $11$. Since $\frac{12}{11} = \frac{4 \times 3}{11}$, the missing denominator is $11$.

18. Rewrite $6 \times \frac{2}{3}$ as a multiple of $\frac{1}{3}$.

    $12 \times \frac{1}{3}$. Since $6 \times 2 = 12$, this equals $12$ copies of $\frac{1}{3}$.

19. State the formula for multiplying a whole number $n$ by a fraction $\frac{a}{b}$.

    $n \times \frac{a}{b} = \frac{n \times a}{b}$. Multiply the whole number by the numerator, keep the denominator.

20. What is $6 \times \frac{4}{9}$ written as a multiple of $\frac{1}{9}$?

    $24 \times \frac{1}{9}$. Since $\frac{4}{9} = 4 \times \frac{1}{9}$, we get $6 \times 4 \times \frac{1}{9} = 24 \times \frac{1}{9}$.

21. What is $4 \times \frac{3}{8}$?

    $\frac{12}{8}$. Multiply: $4 \times 3 = 12$ in the numerator, keep denominator $8$.

22. Find and correct the error: $5 \times \frac{2}{9} = \frac{10}{45}$.

    Correct: $5 \times \frac{2}{9} = \frac{10}{9}$. The error multiplied both numerator and denominator; only multiply the numerator.

23. What is $4 \times \frac{3}{8}$ written as a multiple of $\frac{1}{8}$?

    $12 \times \frac{1}{8}$. Since $\frac{3}{8} = 3 \times \frac{1}{8}$, we get $4 \times 3 \times \frac{1}{8} = 12 \times \frac{1}{8}$.

24. What is $6 \times \frac{2}{3}$?

    $\frac{12}{3}$. Multiply: $6 \times 2 = 12$ in the numerator, keep denominator $3$.

25. What is the fraction that represents one part when a whole is split into $b$ equal parts?

    $\frac{1}{b}$. Unit fraction represents one part of $b$ equal parts.

26. What is $5 \times \frac{1}{6}$ as a fraction?

    $\frac{5}{6}$. Apply the formula: $5 \times \frac{1}{6} = \frac{5 \times 1}{6} = \frac{5}{6}$.

27. Rewrite $4 \times \frac{3}{8}$ as a multiple of $\frac{1}{8}$.

    $12 \times \frac{1}{8}$. Since $4 \times 3 = 12$, this equals $12$ copies of $\frac{1}{8}$.

28. Rewrite $2 \times \frac{7}{10}$ as a multiple of $\frac{1}{10}$.

    $14 \times \frac{1}{10}$. Since $2 \times 7 = 14$, this equals $14$ copies of $\frac{1}{10}$.

29. Identify the missing number: $3 \times \frac{\Box}{5} = \frac{12}{5}$.

    $4$. Since $3 \times 4 = 12$, the missing numerator is $4$.

30. What does it mean to view $n \times \frac{a}{b}$ as a multiple of $\frac{1}{b}$?

    $n \times \frac{a}{b} = (n \times a) \times \frac{1}{b}$. Shows that multiplying by $\frac{a}{b}$ equals $a$ copies of $\frac{1}{b}$.

31. What is $3 \times \frac{2}{5}$ written as a multiple of $\frac{1}{5}$?

    $6 \times \frac{1}{5}$. Since $\frac{2}{5} = 2 \times \frac{1}{5}$, we get $3 \times 2 \times \frac{1}{5} = 6 \times \frac{1}{5}$.

32. What is $7 \times \frac{4}{9}$?

    $\frac{28}{9}$. Multiply: $7 \times 4 = 28$ in the numerator, keep denominator $9$.

33. Identify the missing number: $9 \times \frac{2}{7} = \frac{\square}{7}$.

    $18$. Multiply: $9 \times 2 = 18$, so the numerator is $18$.

34. Find and correct the error: $3 \times \frac{4}{7} = \frac{4}{21}$.

    Correct: $3 \times \frac{4}{7} = \frac{12}{7}$. The error divided instead of multiplying; multiply $3 \times 4 = 12$.

35. Identify the missing number: $\square \times \frac{5}{6} = \frac{20}{6}$.

    $4$. Since $\frac{20}{6} = \frac{4 \times 5}{6}$, the whole number is $4$.

36. State the formula for multiplying a whole number $n$ by a fraction $\frac{a}{b}$.

    $n \times \frac{a}{b} = \frac{n \times a}{b}$. Multiply the whole number by the numerator, keeping the same denominator.

37. What is $5 \times \frac{1}{6}$?

    $\frac{5}{6}$. Place $5 \times 1 = 5$ in the numerator, keep denominator $6$.

38. Identify the missing number: $8 \times \frac{3}{5} = \frac{\square}{5}$.

    $24$. Multiply: $8 \times 3 = 24$, so the numerator is $24$.

39. What is $7 \times \frac{2}{3}$ as an improper fraction?

    $\frac{14}{3}$. Apply the formula: $7 \times \frac{2}{3} = \frac{7 \times 2}{3} = \frac{14}{3}$.

40. What is $4 \times \frac{3}{8}$ as an improper fraction?

    $\frac{12}{8}$. Apply the formula: $4 \times \frac{3}{8} = \frac{4 \times 3}{8} = \frac{12}{8}$.

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