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Fractions and Rational Numbers

MCQ test, Set 1

  • Set 1 of 10
  • 25 questions
  • 25 marks
  • 30 minutes

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Choose one answer for each question, then check your score at the end. Each correct answer carries 1 mark; there is no negative marking.

  1. A circle is divided into 9 equal parts and 7 parts are shaded. The shaded region is
    Answer and solution

    Answer: (A) 79\displaystyle \frac{7}{9}

    Each part is 19\displaystyle \frac{1}{9}; 77 parts are shaded.

    Shaded region =79\displaystyle = \frac{7}{9}

  2. Two rectangles are each divided into 9 equal parts. All parts of the first and 1 part of the second are shaded. The total shaded region is
    Answer and solution

    Answer: (C) 109\displaystyle \frac{10}{9}

    First figure =1= 1, second =19\displaystyle = \frac{1}{9}

    1+19=99+19=109\displaystyle 1 + \frac{1}{9} = \frac{9}{9} + \frac{1}{9} = \frac{10}{9}

  3. Among 138,114,14,1515\displaystyle \frac{13}{8}, \frac{11}{4}, \frac{1}{4}, \frac{15}{15}, the proper fraction is
    Answer and solution

    Answer: (B) 14\displaystyle \frac{1}{4}

    In a proper fraction the numerator is less than the denominator.

    1<41 < 4, so 14\displaystyle \frac{1}{4} is proper.

  4. The mixed fraction form of 985\displaystyle \frac{98}{5} is
    Answer and solution

    Answer: (B) 1935\displaystyle 19\frac{3}{5}

    98÷598 \div 5: quotient 1919, remainder 33

    985=19+35=1935\displaystyle \frac{98}{5} = 19 + \frac{3}{5} = 19\frac{3}{5}

  5. 10514\displaystyle 10\frac{5}{14} as an improper fraction is
    Answer and solution

    Answer: (C) 14514\displaystyle \frac{145}{14}

    10514=(10×14)+514\displaystyle 10\frac{5}{14} = \frac{(10 \times 14) + 5}{14}

    =140+514=14514\displaystyle = \frac{140 + 5}{14} = \frac{145}{14}

  6. From 38,137,17,34,127,310\displaystyle \frac{3}{8}, \frac{13}{7}, \frac{1}{7}, \frac{3}{4}, \frac{12}{7}, \frac{3}{10}, the like fractions are
    Answer and solution

    Answer: (A) 127,137,17\displaystyle \frac{12}{7}, \frac{13}{7}, \frac{1}{7}

    Like fractions have the same denominator.

    127,137,17\displaystyle \frac{12}{7}, \frac{13}{7}, \frac{1}{7} all have denominator 77.

  7. Among 130\displaystyle \frac{13}{0}, −5-5, 00, −110\displaystyle \frac{-1}{10}, the one that is not a rational number is
    Answer and solution

    Answer: (D) 130\displaystyle \frac{13}{0}

    A rational number is of the form pq\displaystyle \frac{p}{q}, p,qp, q integers and q≠0q \ne 0.

    0=01\displaystyle 0 = \frac{0}{1} and −5=−51\displaystyle -5 = \frac{-5}{1} are rational numbers.

    In 130\displaystyle \frac{13}{0} the denominator is 00, so it is not a rational number.

  8. Which fraction is equivalent to 411\displaystyle \frac{4}{11}?
    Answer and solution

    Answer: (C) 2055\displaystyle \frac{20}{55}

    411=4×511×5=2055\displaystyle \frac{4}{11} = \frac{4 \times 5}{11 \times 5} = \frac{20}{55}

    Multiplying the numerator and the denominator by the same number gives an equivalent fraction.

  9. The simplest form of 2418\displaystyle \frac{24}{18} is
    Answer and solution

    Answer: (D) 43\displaystyle \frac{4}{3}

    H.C.F of 24,18=624, 18 = 6

    2418=24÷618÷6=43\displaystyle \frac{24}{18} = \frac{24 \div 6}{18 \div 6} = \frac{4}{3}

  10. The standard form of 9−33\displaystyle \frac{9}{-33} is
    Answer and solution

    Answer: (D) −311\displaystyle -\frac{3}{11}

    9−33=−933\displaystyle \frac{9}{-33} = -\frac{9}{33}, since (+)/(−)=(−)(+)/(-) = (-)

    H.C.F of 9,33=39, 33 = 3, so =−311\displaystyle = -\frac{3}{11} (the denominator must be positive)

  11. The ascending order of −46,−7,43,−18,7-46, -7, 43, -18, 7 is
    Answer and solution

    Answer: (C) −46,−18,−7,7,43-46, -18, -7, 7, 43

    Negative numbers come before 00 and the positive numbers; −46<−18<−7-46 < -18 < -7.

    Ascending order: −46,−18,−7,7,43-46, -18, -7, 7, 43

  12. The greatest among 74,−32,158,16\displaystyle \frac{7}{4}, -\frac{3}{2}, \frac{15}{8}, \frac{1}{6} is
    Answer and solution

    Answer: (D) 158\displaystyle \frac{15}{8}

    L.C.M of 4,2,8,6=2×2×2×3=244, 2, 8, 6 = 2 \times 2 \times 2 \times 3 = 24

    74=4224,−32=−3624,158=4524,16=424\displaystyle \frac{7}{4} = \frac{42}{24}, -\frac{3}{2} = -\frac{36}{24}, \frac{15}{8} = \frac{45}{24}, \frac{1}{6} = \frac{4}{24}

    The largest numerator is 4545, so the greatest is 158\displaystyle \frac{15}{8}.

  13. 117  □  2516\displaystyle \frac{11}{7} \;\square\; \frac{25}{16}. The sign that goes in the box is
    Answer and solution

    Answer: (B) >>

    11×16=17611 \times 16 = 176, 7×25=1757 \times 25 = 175

    176>175⇒117>2516\displaystyle 176 > 175 \Rightarrow \frac{11}{7} > \frac{25}{16}

  14. 2952+1552−6752=\displaystyle \frac{29}{52} + \frac{15}{52} - \frac{67}{52} =
    Answer and solution

    Answer: (B) −2352\displaystyle -\frac{23}{52}

    Like fractions: keep the denominator, add and subtract the numerators.

    =29+15−6752=−2352\displaystyle = \frac{29 + 15 - 67}{52} = -\frac{23}{52}

  15. 29−1112=\displaystyle \frac{2}{9} - \frac{11}{12} =
    Answer and solution

    Answer: (C) −2536\displaystyle -\frac{25}{36}

    L.C.M of 9,12=3×3×4=369, 12 = 3 \times 3 \times 4 = 36

    =8−3336\displaystyle = \frac{8 - 33}{36}

    =−2536\displaystyle = -\frac{25}{36}

  16. 139−56−23=\displaystyle \frac{13}{9} - \frac{5}{6} - \frac{2}{3} =
    Answer and solution

    Answer: (B) −118\displaystyle -\frac{1}{18}

    L.C.M of 9,6,3=3×3×2=189, 6, 3 = 3 \times 3 \times 2 = 18

    =26−15−1218\displaystyle = \frac{26 - 15 - 12}{18}

    =26−2718\displaystyle = \frac{26 - 27}{18}

    =−118\displaystyle = -\frac{1}{18}

  17. 2−239=\displaystyle 2 - \frac{23}{9} =
    Answer and solution

    Answer: (A) −59\displaystyle -\frac{5}{9}

    Write 2=21\displaystyle 2 = \frac{2}{1}.

    2−239=18−239=−59\displaystyle 2 - \frac{23}{9} = \frac{18 - 23}{9} = -\frac{5}{9}

  18. −911×56=\displaystyle -\frac{9}{11} \times \frac{5}{6} =
    Answer and solution

    Answer: (A) −1522\displaystyle -\frac{15}{22}

    Sign: (−)×(+)=(−)(-) \times (+) = (-)

    =−9×511×6\displaystyle = -\frac{9 \times 5}{11 \times 6}

    =−(3×3)×511×(2×3)\displaystyle = -\frac{(3 \times 3) \times 5}{11 \times (2 \times 3)}

    Cancelling the common factor 33: =−3×511×2=−1522\displaystyle = -\frac{3 \times 5}{11 \times 2} = -\frac{15}{22}

  19. 26×1318=\displaystyle 26 \times \frac{13}{18} =
    Answer and solution

    Answer: (C) 1699\displaystyle \frac{169}{9}

    26=261\displaystyle 26 = \frac{26}{1}

    =26×131×18\displaystyle = \frac{26 \times 13}{1 \times 18}

    =(2×13)×131×(2×3×3)\displaystyle = \frac{(2 \times 13) \times 13}{1 \times (2 \times 3 \times 3)}

    Cancelling the common factor 22: =13×133×3=1699\displaystyle = \frac{13 \times 13}{3 \times 3} = \frac{169}{9}

  20. 413×445=\displaystyle 4\frac{1}{3} \times 4\frac{4}{5} =
    Answer and solution

    Answer: (B) 1045\displaystyle \frac{104}{5}

    Convert to improper fractions first: 413=133,  445=245\displaystyle 4\frac{1}{3} = \frac{13}{3}, \; 4\frac{4}{5} = \frac{24}{5}

    133×245=1045\displaystyle \frac{13}{3} \times \frac{24}{5} = \frac{104}{5}

  21. 98÷107=\displaystyle \frac{9}{8} \div \frac{10}{7} =
    Answer and solution

    Answer: (D) 6380\displaystyle \frac{63}{80}

    98÷107=98×710\displaystyle \frac{9}{8} \div \frac{10}{7} = \frac{9}{8} \times \frac{7}{10} (multiply by the reciprocal)

    =6380\displaystyle = \frac{63}{80}

  22. 3217÷6=\displaystyle \frac{32}{17} \div 6 =
    Answer and solution

    Answer: (A) 1651\displaystyle \frac{16}{51}

    3217÷6=3217÷61=3217×16\displaystyle \frac{32}{17} \div 6 = \frac{32}{17} \div \frac{6}{1} = \frac{32}{17} \times \frac{1}{6}

    =1651\displaystyle = \frac{16}{51}

  23. The greatest among 15,12,122,115\displaystyle \frac{1}{5}, \frac{1}{2}, \frac{1}{22}, \frac{1}{15} is
    Answer and solution

    Answer: (D) 12\displaystyle \frac{1}{2}

    2<5<15<222 < 5 < 15 < 22 (all have the same sign)

    ⇒12>15>115>122\displaystyle \Rightarrow \frac{1}{2} > \frac{1}{5} > \frac{1}{15} > \frac{1}{22}

    So the greatest is 12\displaystyle \frac{1}{2}.

  24. If 1<101 < 10, then multiplying both sides by −9-9 gives
    Answer and solution

    Answer: (B) −9>−90-9 > -90

    Rule: a<b⇒ma>mba < b \Rightarrow ma > mb if m<0m < 0 (the sign turns round).

    −9×1=−9-9 \times 1 = -9, −9×10=−90-9 \times 10 = -90, so −9>−90-9 > -90

  25. The part of the number line from 00 to 11 is divided into 1212 equal parts. The 11th point to the right of 00 is
    Answer and solution

    Answer: (A) 1112\displaystyle \frac{11}{12}

    Each part =112\displaystyle = \frac{1}{12}.

    1111 parts to the right of 00: 1112\displaystyle \frac{11}{12}