We read your photo as:

Shashank and Vikas have the same storybook. Shashank has read 2/5 of the book and Vikas has read 7/2 of the book. Who has read more pages?

Mathematics

ScanSolve AI Answer

Step-by-step solution

93 steps

Here are the solutions to the problems:

1. Compare the fractions without finding the LCM. Put <,><, > or == in the ∘\circ.

  • 1(a): 14∘24\frac{1}{4} \circ \frac{2}{4}

  1. Compare the numerators since the denominators are the same.

    $$
1 < 2
$$

  2. Therefore,

    $$
\frac{1}{4} < \frac{2}{4}
$$
The answer is $\boxed{<}$
    • 1(b): 35∘37\frac{3}{5} \circ \frac{3}{7}

  3. Compare the denominators since the numerators are the same.

    The fraction with the smaller denominator is larger. 5<7 5 < 7

  4. Therefore,

    $$
\frac{3}{5} > \frac{3}{7}
$$
The answer is $\boxed{>}$
    • 1(c): 34∘38\frac{3}{4} \circ \frac{3}{8}

  5. Compare the denominators.

    $$
4 < 8
$$

  6. Therefore,

    $$
\frac{3}{4} > \frac{3}{8}
$$
The answer is $\boxed{>}$
    • 1(d): 515∘512\frac{5}{15} \circ \frac{5}{12}

  7. Compare the denominators.

    $$
15 > 12
$$

  8. Therefore,

    $$
\frac{5}{15} < \frac{5}{12}
$$
The answer is $\boxed{<}$
    • 1(e): 418∘412\frac{4}{18} \circ \frac{4}{12}

  9. Compare the denominators.

    $$
18 > 12
$$

  10. Therefore,

    $$
\frac{4}{18} < \frac{4}{12}
$$
The answer is $\boxed{<}$
    • 1(f): 919∘910\frac{9}{19} \circ \frac{9}{10}

  11. Compare the denominators.

    $$
19 > 10
$$

  12. Therefore,

    $$
\frac{9}{19} < \frac{9}{10}
$$
The answer is $\boxed{<}$
    • 1(g): 25∘210\frac{2}{5} \circ \frac{2}{10}

  13. Compare the denominators.

    $$
5 < 10
$$

  14. Therefore,

    $$
\frac{2}{5} > \frac{2}{10}
$$
The answer is $\boxed{>}$
    • 1(h): 23∘46\frac{2}{3} \circ \frac{4}{6}

  15. Simplify the second fraction.

    $$
\frac{4}{6} = \frac{2}{3}
$$

  16. Compare the fractions.

    $$
\frac{2}{3} = \frac{2}{3}
$$
The answer is $\boxed{=}$

    2. Compare the fractions and put <,><, > or == in the ∘\circ.

    • 2(a): 34∘23\frac{3}{4} \circ \frac{2}{3}

  17. Cross-multiply the fractions.

    $$
3 \times 3 = 9
$$
$$
4 \times 2 = 8
$$

  18. Compare the products.

    $$
9 > 8
$$

  19. Therefore,

    $$
\frac{3}{4} > \frac{2}{3}
$$
The answer is $\boxed{>}$
    • 2(b): 45∘34\frac{4}{5} \circ \frac{3}{4}

  20. Cross-multiply the fractions.

    $$
4 \times 4 = 16
$$
$$
5 \times 3 = 15
$$

  21. Compare the products.

    $$
16 > 15
$$

  22. Therefore,

    $$
\frac{4}{5} > \frac{3}{4}
$$
The answer is $\boxed{>}$
    • 2(c): 210∘34\frac{2}{10} \circ \frac{3}{4}

  23. Simplify the first fraction.

    $$
\frac{2}{10} = \frac{1}{5}
$$

  24. Cross-multiply 15\frac{1}{5} and 34\frac{3}{4}.

    $$
1 \times 4 = 4
$$
$$
5 \times 3 = 15
$$

  25. Compare the products.

    $$
4 < 15
$$

  26. Therefore,

    $$
\frac{2}{10} < \frac{3}{4}
$$
The answer is $\boxed{<}$
    • 2(d): 25∘34\frac{2}{5} \circ \frac{3}{4}

  27. Cross-multiply the fractions.

    $$
2 \times 4 = 8
$$
$$
5 \times 3 = 15
$$

  28. Compare the products.

    $$
8 < 15
$$

  29. Therefore,

    $$
\frac{2}{5} < \frac{3}{4}
$$
The answer is $\boxed{<}$
    • 2(e): 49∘58\frac{4}{9} \circ \frac{5}{8}

  30. Cross-multiply the fractions.

    $$
4 \times 8 = 32
$$
$$
9 \times 5 = 45
$$

  31. Compare the products.

    $$
32 < 45
$$

  32. Therefore,

    $$
\frac{4}{9} < \frac{5}{8}
$$
The answer is $\boxed{<}$
    • 2(f): 48∘510\frac{4}{8} \circ \frac{5}{10}

  33. Simplify both fractions.

    $$
\frac{4}{8} = \frac{1}{2}
$$
$$
\frac{5}{10} = \frac{1}{2}
$$

  34. Compare the simplified fractions.

    $$
\frac{1}{2} = \frac{1}{2}
$$
The answer is $\boxed{=}$
    • 2(g): 35∘810\frac{3}{5} \circ \frac{8}{10}

  35. Simplify the second fraction.

    $$
\frac{8}{10} = \frac{4}{5}
$$

  36. Compare the fractions.

    $$
\frac{3}{5} < \frac{4}{5}
$$

  37. Therefore,

    $$
\frac{3}{5} < \frac{8}{10}
$$
The answer is $\boxed{<}$
    • 2(h): 516∘28\frac{5}{16} \circ \frac{2}{8}

  38. Simplify the second fraction.

    $$
\frac{2}{8} = \frac{1}{4}
$$

  39. Convert 14\frac{1}{4} to an equivalent fraction with denominator 16.

    $$
\frac{1}{4} = \frac{1 \times 4}{4 \times 4} = \frac{4}{16}
$$

  40. Compare 516\frac{5}{16} and 416\frac{4}{16}.

    $$
5 > 4
$$

  41. Therefore,

    $$
\frac{5}{16} > \frac{2}{8}
$$
The answer is $\boxed{>}$

    3. Arrange in ascending order.

    • 3(a): 13,14,15\frac{1}{3}, \frac{1}{4}, \frac{1}{5}

  42. Since the numerators are the same, the fraction with the largest denominator is the smallest.

  43. Arrange in ascending order.

    $$
\frac{1}{5} < \frac{1}{4} < \frac{1}{3}
$$
The ascending order is $\boxed{\frac{1}{5}, \frac{1}{4}, \frac{1}{3}}$
    • 3(b): 34,38,512\frac{3}{4}, \frac{3}{8}, \frac{5}{12}

  44. Find the LCM of the denominators (4, 8, 12), which is 24.

  45. Convert each fraction to an equivalent fraction with denominator 24.

    $$
\frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24}
$$
$$
\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}
$$
$$
\frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24}
$$

  46. Arrange the fractions in ascending order based on their numerators.

    $$
\frac{9}{24} < \frac{10}{24} < \frac{18}{24}
$$

  47. Write the original fractions in ascending order.

    $$
\frac{3}{8} < \frac{5}{12} < \frac{3}{4}
$$
The ascending order is $\boxed{\frac{3}{8}, \frac{5}{12}, \frac{3}{4}}$
    • 3(c): 12,13,23,34\frac{1}{2}, \frac{1}{3}, \frac{2}{3}, \frac{3}{4}

  48. Find the LCM of the denominators (2, 3, 4), which is 12.

  49. Convert each fraction to an equivalent fraction with denominator 12.

    $$
\frac{1}{2} = \frac{1 \times 6}{2 \times 6} = \frac{6}{12}
$$
$$
\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}
$$
$$
\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}
$$
$$
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
$$

  50. Arrange the fractions in ascending order.

    $$
\frac{4}{12} < \frac{6}{12} < \frac{8}{12} < \frac{9}{12}
$$

  51. Write the original fractions in ascending order.

    $$
\frac{1}{3} < \frac{1}{2} < \frac{2}{3} < \frac{3}{4}
$$
The ascending order is $\boxed{\frac{1}{3}, \frac{1}{2}, \frac{2}{3}, \frac{3}{4}}$
    • 3(d): 1118,59,23,12\frac{11}{18}, \frac{5}{9}, \frac{2}{3}, \frac{1}{2}

  52. Find the LCM of the denominators (18, 9, 3, 2), which is 18.

  53. Convert each fraction to an equivalent fraction with denominator 18.

    $$
\frac{11}{18}
$$
$$
\frac{5}{9} = \frac{5 \times 2}{9 \times 2} = \frac{10}{18}
$$
$$
\frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18}
$$
$$
\frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18}
$$

  54. Arrange the fractions in ascending order.

    $$
\frac{9}{18} < \frac{10}{18} < \frac{11}{18} < \frac{12}{18}
$$

  55. Write the original fractions in ascending order.

    $$
\frac{1}{2} < \frac{5}{9} < \frac{11}{18} < \frac{2}{3}
$$
The ascending order is $\boxed{\frac{1}{2}, \frac{5}{9}, \frac{11}{18}, \frac{2}{3}}$
    • 3(e): 45,910,715,23\frac{4}{5}, \frac{9}{10}, \frac{7}{15}, \frac{2}{3}

  56. Find the LCM of the denominators (5, 10, 15, 3), which is 30.

  57. Convert each fraction to an equivalent fraction with denominator 30.

    $$
\frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30}
$$
$$
\frac{9}{10} = \frac{9 \times 3}{10 \times 3} = \frac{27}{30}
$$
$$
\frac{7}{15} = \frac{7 \times 2}{15 \times 2} = \frac{14}{30}
$$
$$
\frac{2}{3} = \frac{2 \times 10}{3 \times 10} = \frac{20}{30}
$$

  58. Arrange the fractions in ascending order.

    $$
\frac{14}{30} < \frac{20}{30} < \frac{24}{30} < \frac{27}{30}
$$

  59. Write the original fractions in ascending order.

    $$
\frac{7}{15} < \frac{2}{3} < \frac{4}{5} < \frac{9}{10}
$$
The ascending order is $\boxed{\frac{7}{15}, \frac{2}{3}, \frac{4}{5}, \frac{9}{10}}$
    • 3(f): 23,15,56,22\frac{2}{3}, \frac{1}{5}, \frac{5}{6}, \frac{2}{2}

  60. Simplify 22\frac{2}{2} to 1.

    Find the LCM of the denominators (3, 5, 6, 1), which is 30.

  61. Convert each fraction to an equivalent fraction with denominator 30.

    $$
\frac{2}{3} = \frac{2 \times 10}{3 \times 10} = \frac{20}{30}
$$
$$
\frac{1}{5} = \frac{1 \times 6}{5 \times 6} = \frac{6}{30}
$$
$$
\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}
$$
$$
\frac{2}{2} = 1 = \frac{30}{30}
$$

  62. Arrange the fractions in ascending order.

    $$
\frac{6}{30} < \frac{20}{30} < \frac{25}{30} < \frac{30}{30}
$$

  63. Write the original fractions in ascending order.

    $$
\frac{1}{5} < \frac{2}{3} < \frac{5}{6} < \frac{2}{2}
$$
The ascending order is $\boxed{\frac{1}{5}, \frac{2}{3}, \frac{5}{6}, \frac{2}{2}}$

    4. Arrange in descending order.

    • 4(a): 914,57,1121\frac{9}{14}, \frac{5}{7}, \frac{11}{21}

  64. Find the LCM of the denominators (14, 7, 21), which is 42.

  65. Convert each fraction to an equivalent fraction with denominator 42.

    $$
\frac{9}{14} = \frac{9 \times 3}{14 \times 3} = \frac{27}{42}
$$
$$
\frac{5}{7} = \frac{5 \times 6}{7 \times 6} = \frac{30}{42}
$$
$$
\frac{11}{21} = \frac{11 \times 2}{21 \times 2} = \frac{22}{42}
$$

  66. Arrange the fractions in descending order based on their numerators.

    $$
\frac{30}{42} > \frac{27}{42} > \frac{22}{42}
$$

  67. Write the original fractions in descending order.

    $$
\frac{5}{7} > \frac{9}{14} > \frac{11}{21}
$$
The descending order is $\boxed{\frac{5}{7}, \frac{9}{14}, \frac{11}{21}}$
    • 4(b): 38,16,512\frac{3}{8}, \frac{1}{6}, \frac{5}{12}

  68. Find the LCM of the denominators (8, 6, 12), which is 24.

  69. Convert each fraction to an equivalent fraction with denominator 24.

    $$
\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}
$$
$$
\frac{1}{6} = \frac{1 \times 4}{6 \times 4} = \frac{4}{24}
$$
$$
\frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24}
$$

  70. Arrange the fractions in descending order.

    $$
\frac{10}{24} > \frac{9}{24} > \frac{4}{24}
$$

  71. Write the original fractions in descending order.

    $$
\frac{5}{12} > \frac{3}{8} > \frac{1}{6}
$$
The descending order is $\boxed{\frac{5}{12}, \frac{3}{8}, \frac{1}{6}}$
    • 4(c): 1930,25,715\frac{19}{30}, \frac{2}{5}, \frac{7}{15}

  72. Find the LCM of the denominators (30, 5, 15), which is 30.

  73. Convert each fraction to an equivalent fraction with denominator 30.

    $$
\frac{19}{30}
$$
$$
\frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30}
$$
$$
\frac{7}{15} = \frac{7 \times 2}{15 \times 2} = \frac{14}{30}
$$

  74. Arrange the fractions in descending order.

    $$
\frac{19}{30} > \frac{14}{30} > \frac{12}{30}
$$

  75. Write the original fractions in descending order.

    $$
\frac{19}{30} > \frac{7}{15} > \frac{2}{5}
$$
The descending order is $\boxed{\frac{19}{30}, \frac{7}{15}, \frac{2}{5}}$
    • 4(d): 23,34,45,56\frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}

  76. Find the LCM of the denominators (3, 4, 5, 6), which is 60.

  77. Convert each fraction to an equivalent fraction with denominator 60.

    $$
\frac{2}{3} = \frac{2 \times 20}{3 \times 20} = \frac{40}{60}
$$
$$
\frac{3}{4} = \frac{3 \times 15}{4 \times 15} = \frac{45}{60}
$$
$$
\frac{4}{5} = \frac{4 \times 12}{5 \times 12} = \frac{48}{60}
$$
$$
\frac{5}{6} = \frac{5 \times 10}{6 \times 10} = \frac{50}{60}
$$

  78. Arrange the fractions in descending order.

    $$
\frac{50}{60} > \frac{48}{60} > \frac{45}{60} > \frac{40}{60}
$$

  79. Write the original fractions in descending order.

    $$
\frac{5}{6} > \frac{4}{5} > \frac{3}{4} > \frac{2}{3}
$$
The descending order is $\boxed{\frac{5}{6}, \frac{4}{5}, \frac{3}{4}, \frac{2}{3}}$
    • 4(e): 78,310,56,1112\frac{7}{8}, \frac{3}{10}, \frac{5}{6}, \frac{11}{12}

  80. Find the LCM of the denominators (8, 10, 6, 12), which is 120.

  81. Convert each fraction to an equivalent fraction with denominator 120.

    $$
\frac{7}{8} = \frac{7 \times 15}{8 \times 15} = \frac{105}{120}
$$
$$
\frac{3}{10} = \frac{3 \times 12}{10 \times 12} = \frac{36}{120}
$$
$$
\frac{5}{6} = \frac{5 \times 20}{6 \times 20} = \frac{100}{120}
$$
$$
\frac{11}{12} = \frac{11 \times 10}{12 \times 10} = \frac{110}{120}
$$

  82. Arrange the fractions in descending order.

    $$
\frac{110}{120} > \frac{105}{120} > \frac{100}{120} > \frac{36}{120}
$$

  83. Write the original fractions in descending order.

    $$
\frac{11}{12} > \frac{7}{8} > \frac{5}{6} > \frac{3}{10}
$$
The descending order is $\boxed{\frac{11}{12}, \frac{7}{8}, \frac{5}{6}, \frac{3}{10}}$
    • 4(f): 57,59,56,512\frac{5}{7}, \frac{5}{9}, \frac{5}{6}, \frac{5}{12}

  84. Since the numerators are the same, the fraction with the smallest denominator is the largest.

  85. Arrange in descending order.

    $$
\frac{5}{6} > \frac{5}{7} > \frac{5}{9} > \frac{5}{12}
$$
The descending order is $\boxed{\frac{5}{6}, \frac{5}{7}, \frac{5}{9}, \frac{5}{12}}$

    5. Shashank and Vikas have the same storybook. Shashank has read 25\frac{2}{5} of the book and Vikas has read 27\frac{2}{7} of the book. Who has read more pages?

  86. Compare the fractions 25\frac{2}{5} and 27\frac{2}{7}.

  87. Since the numerators are the same, the fraction with the smaller denominator is larger.

    5<7  ⟹  25>275 < 7 \implies \frac{2}{5} > \frac{2}{7}

  88. Conclude who read more.

    Shashank has read more pages.

    The answer is Shashank\boxed{\text{Shashank}}

    6. Reena and Vineeta are classmates. Reena completed her homework in 56\frac{5}{6} of an hour and Vineeta in 34\frac{3}{4} of an hour. Who was faster?

  89. To find who was faster, we need to find who took less time.

    Compare 56\frac{5}{6} and 34\frac{3}{4}.

  90. Find the LCM of the denominators (6, 4), which is 12.

  91. Convert each fraction to an equivalent fraction with denominator 12.

    Reena’s time: 56=5×26×2=1012 hours\text{Reena's time: } \frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12} \text{ hours} Vineeta’s time: 34=3×34×3=912 hours\text{Vineeta's time: } \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \text{ hours}

  92. Compare the times.

    912<1012\frac{9}{12} < \frac{10}{12}

  93. Conclude who was faster (took less time).

    Vineeta took less time, so Vineeta was faster.

    The answer is Vineeta\boxed{\text{Vineeta}}

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QRakesh had 12 books and gave 8 to Amit. Monika had 9 stickers and lost 5. How many books and…QChitra and Vidya are reading story books, aren't they?QRakesh bought 12 books. He gave 8 books to Amit. How many books are left with Rakesh?QRead the Pictograph and answer the following questions: 1. Who reads the most books in a week? 2. On…QRohan had Rs 1275. He bought books worth Rs 789. How much money is left with him?
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.