Find Area With Fractional Sides - 5th Grade Math

1. Identify the unit square side length used to tile a $\frac{3}{4}$ by $\frac{2}{3}$ rectangle.

   $\frac{1}{12}$. LCM of denominators 4 and 3 is 12, so unit square has side $\frac{1}{12}$.

2. What is $72 \times \frac{1}{144}$ (the tiled area for the $\frac{3}{4}$ by $\frac{2}{3}$ rectangle)?

   $\frac{1}{2}$. $72 \times \frac{1}{144} = \frac{72}{144} = \frac{1}{2}$, confirming the tiled area.

3. Compute $\frac{3}{5} \times \frac{4}{7}$ to match the tiled area model.

   $\frac{12}{35}$. Multiply numerators and denominators: $\frac{3 \times 4}{5 \times 7}$.

4. What is the area of a rectangle with side lengths $\frac{3}{4}$ and $\frac{2}{5}$?

   $\frac{3}{10}$. Multiply: $\frac{3}{4} \times \frac{2}{5} = \frac{6}{20} = \frac{3}{10}$.

5. What is the area of a rectangle with side lengths $1\frac{1}{2}$ and $\frac{2}{3}$?

   $1$. Convert: $1\frac{1}{2} = \frac{3}{2}$, then $\frac{3}{2} \times \frac{2}{3} = 1$.

6. Identify the unit square side lengths used to tile a $\frac{3}{4}$ by $\frac{2}{3}$ rectangle.

   $\frac{1}{4}$ by $\frac{1}{3}$. Use denominators of each fraction as tile dimensions.

7. What is the area of a rectangle with side lengths $\frac{4}{9}$ and $\frac{3}{5}$?

   $\frac{4}{15}$. Multiply: $\frac{4}{9} \times \frac{3}{5} = \frac{12}{45} = \frac{4}{15}$.

8. What is the area of a rectangle with side lengths $\frac{5}{12}$ and $\frac{6}{7}$?

   $\frac{5}{14}$. Multiply: $\frac{5}{12} \times \frac{6}{7} = \frac{30}{84} = \frac{5}{14}$.

9. What is the area of a $\frac{3}{4}$ by $\frac{2}{3}$ rectangle (in square units)?

   $\frac{1}{2}$ square unit. Multiply: $\frac{3}{4} \times \frac{2}{3} = \frac{6}{12} = \frac{1}{2}$.

10. How many $\frac{1}{3}$-length segments fit along a side of length $\frac{2}{3}$?

    $2$. Divide: $\frac{2}{3} \div \frac{1}{3} = 2$.

11. How many tiles are in an array with $3$ columns and $4$ rows?

    $12$ tiles. Total tiles = rows × columns = $4 \times 3 = 12$.

12. What is the area of a rectangle with side lengths $\frac{3}{10}$ and $\frac{5}{6}$?

    $\frac{1}{4}$ square unit. Multiply: $\frac{3}{10} \times \frac{5}{6} = \frac{15}{60} = \frac{1}{4}$.

13. How many $\frac{1}{12}$ by $\frac{1}{12}$ tiles fit in a $\frac{3}{4}$ by $\frac{2}{3}$ rectangle?

    $72$ tiles. $\frac{\frac{3}{4}}{\frac{1}{12}} = 9$ tiles wide, $\frac{\frac{2}{3}}{\frac{1}{12}} = 8$ tiles tall, so $9 \times 8 = 72$.

14. Identify the missing side length if $A = \frac{3}{10}$ and one side is $\frac{3}{4}$.

    $\frac{2}{5}$. Divide area by known side: $\frac{3}{10} \div \frac{3}{4} = \frac{3}{10} \times \frac{4}{3} = \frac{2}{5}$.

15. What total area is covered by $12$ tiles of area $\frac{1}{35}$ each?

    $\frac{12}{35}$. Total area = tiles × area per tile = $12 \times \frac{1}{35}$.

16. Identify the unit fraction side length of each tile to model $\frac{3}{5} \times \frac{4}{7}$.

    $\frac{1}{5}$ by $\frac{1}{7}$. Use denominators of each fraction as tile dimensions.

17. What is the area of a rectangle with side lengths $\frac{2}{3}$ and $\frac{3}{5}$?

    $\frac{2}{5}$ square units. Multiply: $\frac{2}{3} \times \frac{3}{5} = \frac{6}{15} = \frac{2}{5}$.

18. How many $\frac{1}{5}$-wide columns fit across a length of $\frac{3}{5}$?

    $3$ columns. $\frac{3}{5} \div \frac{1}{5} = 3$ columns fit exactly.

19. What is the area of a rectangle with side lengths $\frac{9}{10}$ and $\frac{2}{9}$?

    $\frac{1}{5}$ square unit. Multiply: $\frac{9}{10} \times \frac{2}{9} = \frac{18}{90} = \frac{1}{5}$.

20. Using tiling, what is the area of a $\frac{3}{4}$ by $\frac{2}{3}$ rectangle?

    $\frac{1}{2}$ square unit. $6$ tiles each with area $\frac{1}{12}$: $6 \times \frac{1}{12} = \frac{1}{2}$.

21. What is the area of one tile with side length $\frac{1}{12}$?

    $\frac{1}{144}$ square unit. Square with side $\frac{1}{12}$ has area $\frac{1}{12} \times \frac{1}{12} = \frac{1}{144}$.

22. What is the area of a rectangle with side lengths $\frac{1}{2}$ and $\frac{1}{3}$?

    $\frac{1}{6}$ square unit. Multiply: $\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$.

23. What is the area of a rectangle with side lengths $\frac{7}{8}$ and $\frac{3}{4}$?

    $\frac{21}{32}$. Multiply: $\frac{7}{8} \times \frac{3}{4} = \frac{21}{32}$.

24. State the area formula for a rectangle with side lengths $a$ and $b$.

    $A = a \times b$. Area equals length times width for any rectangle.

25. What is the area of a rectangle with side lengths $2\frac{1}{4}$ and $\frac{2}{3}$?

    $\frac{3}{2}$ square units. Convert $2\frac{1}{4} = \frac{9}{4}$, then $\frac{9}{4} \times \frac{2}{3} = \frac{18}{12} = \frac{3}{2}$.

26. What is the area of a rectangle with side lengths $\frac{1}{2}$ and $\frac{3}{4}$?

    $\frac{3}{8}$ square units. Multiply: $\frac{1}{2} \times \frac{3}{4} = \frac{3}{8}$.

27. What is the area of a rectangle with side lengths $\frac{2}{3}$ and $\frac{3}{8}$?

    $\frac{1}{4}$. Multiply: $\frac{2}{3} \times \frac{3}{8} = \frac{6}{24} = \frac{1}{4}$.

28. Identify the missing side length if $A = \frac{1}{6}$ and one side is $\frac{1}{2}$.

    $\frac{1}{3}$. Divide area by known side: $\frac{1}{6} \div \frac{1}{2} = \frac{1}{6} \times 2 = \frac{1}{3}$.

29. What is the area of a rectangle with side lengths $2\frac{1}{4}$ and $\frac{4}{9}$?

    $1$. Convert: $2\frac{1}{4} = \frac{9}{4}$, then $\frac{9}{4} \times \frac{4}{9} = 1$.

30. What is the area of a rectangle with side lengths $\frac{5}{6}$ and $\frac{3}{4}$?

    $\frac{5}{8}$ square units. Multiply: $\frac{5}{6} \times \frac{3}{4} = \frac{15}{24} = \frac{5}{8}$.

31. How many $\frac{1}{4}$ by $\frac{1}{3}$ tiles cover a $\frac{3}{4}$ by $\frac{2}{3}$ rectangle?

    $6$ tiles. $3$ tiles along one side times $2$ tiles along the other.

32. Find the missing side length if $A=\frac{3}{10}$ and one side is $\frac{3}{4}$.

    $\frac{2}{5}$. Solve: $\frac{3}{4} \times ? = \frac{3}{10}$, so $? = \frac{3}{10} \div \frac{3}{4} = \frac{2}{5}$.

33. What is the area of a rectangle with side lengths $\frac{2}{5}$ and $\frac{2}{5}$?

    $\frac{4}{25}$ square unit. Multiply: $\frac{2}{5} \times \frac{2}{5} = \frac{4}{25}$.

34. What is the area of a rectangle with side lengths $\frac{5}{6}$ and $\frac{3}{10}$?

    $\frac{1}{4}$. Multiply: $\frac{5}{6} \times \frac{3}{10} = \frac{15}{60} = \frac{1}{4}$.

35. What is the area of a rectangle with side lengths $\frac{9}{10}$ and $\frac{5}{6}$?

    $\frac{3}{4}$. Multiply: $\frac{9}{10} \times \frac{5}{6} = \frac{45}{60} = \frac{3}{4}$.

36. Choose the correct statement: Tiling a fractional rectangle gives the same area as doing what operation?

    Multiplying the side lengths: $A = l \times w$. Tiling and multiplication both yield the same area result.

37. What is the area of one tile with side lengths $\frac{1}{4}$ and $\frac{1}{3}$?

    $\frac{1}{12}$ square unit. Multiply: $\frac{1}{4} \times \frac{1}{3} = \frac{1}{12}$.

38. What is the area of one tile that is $\frac{1}{5}$ by $\frac{1}{7}$?

    $\frac{1}{35}$. Multiply tile dimensions: $\frac{1}{5} \times \frac{1}{7} = \frac{1}{35}$.

39. What is the area of a rectangle with side lengths $\frac{4}{9}$ and $\frac{3}{8}$?

    $\frac{1}{6}$ square unit. Multiply: $\frac{4}{9} \times \frac{3}{8} = \frac{12}{72} = \frac{1}{6}$.

40. What is the area of a rectangle with side lengths $1\frac{1}{2}$ and $\frac{2}{3}$?

    $1$ square unit. Convert: $1\frac{1}{2} = \frac{3}{2}$, then $\frac{3}{2} \times \frac{2}{3} = 1$.

41. What is the area of a rectangle with side lengths $\frac{11}{12}$ and $\frac{6}{11}$?

    $\frac{1}{2}$ square unit. Multiply: $\frac{11}{12} \times \frac{6}{11} = \frac{66}{132} = \frac{1}{2}$.

42. State the multiplication rule for fractions used to find rectangle area with fractional sides.

    $\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$. Multiply numerators together and denominators together.

43. What is the area of a rectangle with side lengths $\frac{4}{9}$ and $\frac{3}{5}$?

    $\frac{4}{15}$ square unit. Multiply: $\frac{4}{9} \times \frac{3}{5} = \frac{12}{45} = \frac{4}{15}$.

44. How many $\frac{1}{7}$-tall rows fit up a height of $\frac{4}{7}$?

    $4$ rows. $\frac{4}{7} \div \frac{1}{7} = 4$ rows fit exactly.

45. Find and correct the error: $\frac{2}{3} \times \frac{3}{5} = \frac{5}{6}$.

    Correct: $\frac{2}{3} \times \frac{3}{5} = \frac{2}{5}$. The error shows $\frac{5}{6}$ instead of correct product $\frac{6}{15} = \frac{2}{5}$.

46. What is the area of a rectangle with side lengths $\frac{9}{10}$ and $\frac{5}{6}$?

    $\frac{3}{4}$ square unit. Multiply: $\frac{9}{10} \times \frac{5}{6} = \frac{45}{60} = \frac{3}{4}$.

47. What is the area of a rectangle with side lengths $\frac{7}{8}$ and $\frac{4}{7}$?

    $\frac{1}{2}$ square unit. Multiply: $\frac{7}{8} \times \frac{4}{7} = \frac{28}{56} = \frac{1}{2}$.

48. What is the area of a rectangle with side lengths $\frac{11}{12}$ and $\frac{3}{11}$?

    $\frac{1}{4}$. Multiply: $\frac{11}{12} \times \frac{3}{11} = \frac{33}{132} = \frac{1}{4}$.

49. How many $\frac{1}{4}$-length segments fit along a side of length $\frac{3}{4}$?

    $3$. Divide: $\frac{3}{4} \div \frac{1}{4} = 3$.

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