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4.E: Sehemu ndogo (Mazoezi)

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    4.1 - Tazama sehemu ndogo

    Katika mazoezi yafuatayo, jina la sehemu ya kila takwimu iliyofunikwa.

    1. Mduara unaonyeshwa. Imegawanywa katika vipande 8 sawa. Vipande 5 vimevuliwa.
    2. Mraba inavyoonyeshwa. Imegawanywa katika vipande 9 sawa. Vipande 5 vimevuliwa.

    Katika mazoezi yafuatayo, jina la sehemu zisizofaa. Kisha kuandika kila sehemu isiyofaa kama nambari iliyochanganywa.

    1. Viwanja viwili vinaonyeshwa. Wote wamegawanywa katika vipande vinne sawa. Mraba upande wa kushoto una vipande vyote vinne vilivyovuliwa. Mraba upande wa kulia una kipande kimoja kivuli.
    2. Duru mbili zinaonyeshwa. Wote wamegawanywa katika vipande viwili sawa. Mduara upande wa kushoto una vipande vyote viwili vimevuliwa. Mduara upande wa kulia una kipande kimoja kivuli.

    Katika mazoezi yafuatayo, kubadilisha sehemu isiyofaa kwa nambari iliyochanganywa.

    1. \(\dfrac{58}{15}\)
    2. \(\dfrac{63}{11}\)

    Katika mazoezi yafuatayo, kubadilisha nambari iliyochanganywa kwa sehemu isiyofaa.

    1. \(12 \dfrac{1}{4}\)
    2. \(9 \dfrac{4}{5}\)
    3. Kupata sehemu tatu sawa na\(\dfrac{2}{5}\). Onyesha kazi yako, kwa kutumia takwimu au algebra.
    4. Kupata sehemu tatu sawa na\(− \dfrac{4}{3}\). Onyesha kazi yako, kwa kutumia takwimu au algebra.

    Katika mazoezi yafuatayo, Pata namba kwenye mstari wa nambari.

    1. \(\dfrac{5}{8}, \dfrac{4}{3}, 3 \dfrac{3}{4}\), 4
    2. \(\dfrac{1}{4}, − \dfrac{1}{4}, 1 \dfrac{1}{3}, −1 \dfrac{1}{3}, \dfrac{7}{2}, − \dfrac{7}{2}\)

    Katika mazoezi yafuatayo, tengeneza kila jozi ya namba, ukitumia < or >.

    1. -1___\(− \dfrac{2}{5}\)
    2. \(−2 \dfrac{1}{2}\)___1-3

    4.2 - Kuzidisha na Gawanya vipande

    Katika mazoezi yafuatayo, kurahisisha.

    1. \(− \dfrac{63}{84}\)
    2. \(− \dfrac{90}{120}\)
    3. \(− \dfrac{14a}{14b}\)
    4. \(− \dfrac{8x}{8y}\)

    Katika mazoezi yafuatayo, ongeze.

    1. \(\dfrac{2}{5} \cdot \dfrac{8}{13}\)
    2. \(− \dfrac{1}{3} \cdot \dfrac{12}{7}\)
    3. \(\dfrac{2}{9} \cdot \left(− \dfrac{45}{32}\right)\)
    4. 6m\(\cdot \dfrac{4}{11}\)
    5. \(− \dfrac{1}{4}\)(-32)
    6. \(3 \dfrac{1}{5} \cdot 1 \dfrac{7}{8}\)

    Katika mazoezi yafuatayo, pata usawa.

    1. \(\dfrac{2}{9}\)
    2. \(\dfrac{15}{4}\)
    3. 3
    4. \(− \dfrac{1}{4}\)
    5. Jaza chati.
    Kinyume Thamani kamili kurudisha nyuma
    \(- \dfrac{5}{13}\)      
    \(\dfrac{3}{10}\)      
    \(\dfrac{9}{4}\)      
    -12      

    Katika mazoezi yafuatayo, ugawanye.

    1. \(\dfrac{2}{3} \div \dfrac{1}{6}\)
    2. \(\left(− \dfrac{3x}{5}\right) \div \left(− \dfrac{2y}{3}\right)\)
    3. \(\dfrac{4}{5} \div\)3
    4. 8\(\div 2 \dfrac{2}{3}\)
    5. \(8 \dfrac{2}{3} \div 1 \dfrac{1}{12}\)

    4.3 - Kuzidisha na Gawanya Hesabu Mchanganyiko na sehemu ndogo

    Katika mazoezi yafuatayo, fanya operesheni iliyoonyeshwa.

    1. \(3 \dfrac{1}{5} \cdot 1 \dfrac{7}{8}\)
    2. \(−5 \dfrac{7}{12} \cdot 4 \dfrac{4}{11}\)
    3. 8\(\div 2 \dfrac{2}{3}\)
    4. \(8 \dfrac{2}{3} \div 1 \dfrac{1}{12}\)

    Katika mazoezi yafuatayo, tafsiri maneno ya Kiingereza katika kujieleza kwa algebraic.

    1. quotient ya 8 na y
    2. quotient ya V na tofauti ya h na 6

    Katika mazoezi yafuatayo, kurahisisha sehemu tata.

    1. \(\dfrac{\dfrac{5}{8}}{\dfrac{4}{5}}\)
    2. \(\dfrac{\dfrac{8}{9}}{−4}\)
    3. \(\dfrac{\dfrac{n}{4}}{\dfrac{3}{8}}\)
    4. \(\dfrac{−1 \dfrac{5}{6}}{− \dfrac{1}{12}}\)

    Katika mazoezi yafuatayo, kurahisisha.

    1. \(\dfrac{5 + 16}{5}\)
    2. \(\dfrac{8 \cdot 4 − 5^{2}}{3 \cdot 12}\)
    3. \(\dfrac{8 \cdot 7 + 5(8 − 10)}{9 \cdot 3 − 6 \cdot 4}\)

    4.4 - Ongeza na Ondoa Fractions na Denominators ya kawaida

    Katika mazoezi yafuatayo, ongeza.

    1. \(\dfrac{3}{8} + \dfrac{2}{8}\)
    2. \(\dfrac{4}{5} + \dfrac{1}{5}\)
    3. \(\dfrac{2}{5} + \dfrac{1}{5}\)
    4. \(\dfrac{15}{32} + \dfrac{9}{32}\)
    5. \(\dfrac{x}{10} + \dfrac{7}{10}\)

    Katika mazoezi yafuatayo, toa.

    1. \(\dfrac{8}{11} − \dfrac{6}{11}\)
    2. \(\dfrac{11}{12} − \dfrac{5}{12}\)
    3. \(\dfrac{4}{5} − \dfrac{y}{5}\)
    4. \(− \dfrac{31}{30} − \dfrac{7}{30}\)
    5. \(\dfrac{3}{2} − \left(\dfrac{3}{2}\right)\)
    6. \(\dfrac{11}{15} − \dfrac{5}{15} − \left(− \dfrac{2}{15}\right)\)

    4.5 - Ongeza na Ondoa sehemu ndogo na Denominators tofauti

    Katika mazoezi yafuatayo, pata denominator ya kawaida.

    1. \(\dfrac{1}{3}\)na\(\dfrac{1}{12}\)
    2. \(\dfrac{1}{3}\)na\(\dfrac{4}{5}\)
    3. \(\dfrac{8}{15}\)na\(\dfrac{11}{20}\)
    4. \(\dfrac{3}{4}, \dfrac{1}{6}\), na\(\dfrac{5}{10}\)

    Katika mazoezi yafuatayo, mabadiliko ya vipande sawa kwa kutumia LCD iliyotolewa.

    1. \(\dfrac{1}{3}\)na\(\dfrac{1}{5}\), LCD = 15
    2. \(\dfrac{3}{8}\)na\(\dfrac{5}{6}\), LCD = 24
    3. \(− \dfrac{9}{16}\)na\(\dfrac{5}{12}\), LCD = 48
    4. \(\dfrac{1}{3}, \dfrac{3}{4}\)na\(\dfrac{4}{5}\), LCD = 60

    Katika mazoezi yafuatayo, fanya shughuli zilizoonyeshwa na uwezesha.

    1. \(\dfrac{1}{5} + \dfrac{2}{3}\)
    2. \(\dfrac{11}{12} − \dfrac{2}{3}\)
    3. \(− \dfrac{9}{10} − \dfrac{3}{4}\)
    4. \(− \dfrac{11}{36} − \dfrac{11}{20}\)
    5. \(− \dfrac{22}{25} + \dfrac{9}{40}\)
    6. \(\dfrac{y}{10} − \dfrac{1}{3}\)
    7. \(\dfrac{2}{5} + \left(− \dfrac{5}{9}\right)\)
    8. \(\dfrac{4}{11} \div \dfrac{2}{7d}\)
    9. \(\dfrac{2}{5} + \left(− \dfrac{3n}{8}\right) \left(− \dfrac{2}{9n}\right)\)
    10. \(\dfrac{\left(\dfrac{2}{3}\right)^{2}}{\left(\dfrac{5}{8}\right)^{2}}\)
    11. \(\left(\dfrac{11}{12} + \dfrac{3}{8}\right) \div \left(\dfrac{5}{6} − \dfrac{1}{10}\right)\)

    Katika mazoezi yafuatayo, tathmini.

    1. y -\(\dfrac{4}{5}\) wakati (a) y =\(− \dfrac{4}{5}\) (b) y =\(\dfrac{1}{4}\)
    2. 6mn 2 wakati m =\(\dfrac{3}{4}\) na n =\(− \dfrac{1}{3}\)

    4.6 - Ongeza na Ondoa Hesabu Mchanganyiko

    Katika mazoezi yafuatayo, fanya operesheni iliyoonyeshwa.

    1. \(4 \dfrac{1}{3} + 9 \dfrac{1}{3}\)
    2. \(6 \dfrac{2}{5} + 7 \dfrac{3}{5}\)
    3. \(5 \dfrac{8}{11} + 2 \dfrac{4}{11}\)
    4. \(3 \dfrac{5}{8} + 3 \dfrac{7}{8}\)
    5. \(9 \dfrac{13}{20} − 4 \dfrac{11}{20}\)
    6. \(2 \dfrac{3}{10} − 1 \dfrac{9}{10}\)
    7. \(2 \dfrac{11}{12} − 1 \dfrac{7}{12}\)
    8. \(8 \dfrac{6}{11} − 2 \dfrac{9}{11}\)

    4.7 - Tatua equations na FRACTIONS

    Katika mazoezi yafuatayo, onyesha kama namba ya kila ni suluhisho la equation iliyotolewa.

    1. x -\(\dfrac{1}{2}\) =\(\dfrac{1}{6}\):
      1. x = 1
      2. x =\(\dfrac{2}{3}\)
      3. x =\(− \dfrac{1}{3}\)
    2. y +\(\dfrac{3}{5}\) =\(\dfrac{5}{9}\):
      1. y =\(\dfrac{1}{2}\)
      2. y =\(\dfrac{52}{45}\)
      3. y =\(− \dfrac{2}{45}\)

    Katika mazoezi yafuatayo, tatua equation.

    1. n +\(\dfrac{9}{11}\) =\(\dfrac{4}{11}\)
    2. x -\(\dfrac{1}{6}\) =\(\dfrac{7}{6}\)
    3. h -\(\left(- \dfrac{7}{8}\right)\) =\(− \dfrac{2}{5}\)
    4. \(\dfrac{x}{5}\)= -10
    5. -z = 23

    Katika mazoezi yafuatayo, kutafsiri na kutatua.

    1. Jumla ya theluthi mbili na n ni\(− \dfrac{3}{5}\).
    2. Tofauti ya q na moja ya kumi ni\(\dfrac{1}{2}\).
    3. Quotient ya p na -4 ni -8.
    4. Tatu na nane ya y ni 24.

    MTIHANI WA MAZOEZI

    Badilisha sehemu isiyofaa kwa nambari iliyochanganywa.

    1. \(\dfrac{19}{5}\)

    Badilisha nambari iliyochanganywa kwa sehemu isiyofaa.

    1. \(3 \dfrac{2}{7}\)

    Pata namba kwenye mstari wa nambari.

    1. \(\dfrac{1}{2}, 1 \dfrac{2}{3}, −2 \dfrac{3}{4}\), na\(\dfrac{9}{4}\)

    Katika mazoezi yafuatayo, kurahisisha.

    1. \(\dfrac{5}{20}\)
    2. \(\dfrac{18r}{27s}\)
    3. \(\dfrac{1}{3} \cdot \dfrac{3}{4}\)
    4. \(\dfrac{3}{5} \cdot\)15
    5. -36u\(\left(− \dfrac{4}{9}\right)\)
    6. \(−5 \dfrac{7}{12} \cdot 4 \dfrac{4}{11}\)
    7. \(− \dfrac{5}{6} \div \dfrac{5}{12}\)
    8. \(\dfrac{7}{11} \div \left(− \dfrac{7}{11}\right)\)
    9. \(\dfrac{9a}{10} \div \dfrac{15a}{8}\)
    10. \(−6 \dfrac{2}{5} \div\)4
    11. \(\left(−15 \dfrac{5}{6}\right) \div \left(−3 \dfrac{1}{6}\right)\)
    12. \(\dfrac{−6}{\dfrac{6}{11}}\)
    13. \(\dfrac{\dfrac{p}{2}}{\dfrac{q}{5}}\)
    14. \(\dfrac{− \dfrac{4}{15}}{−2 \dfrac{2}{3}}\)
    15. \(\dfrac{9^{2} − 4^{2}}{9 − 4}\)
    16. \(\dfrac{2}{d} + \dfrac{9}{d}\)
    17. \(− \dfrac{3}{13} + \left(− \dfrac{4}{13}\right)\)
    18. \(− \dfrac{22}{25} + \dfrac{9}{40}\)
    19. \(\dfrac{2}{5} + \left(− \dfrac{7}{5}\right)\)
    20. \(− \dfrac{3}{10} + \left(- \dfrac{5}{8}\right)\)
    21. \(− \dfrac{3}{4} \div \dfrac{x}{3}\)
    22. \(\dfrac{2^{3} − 2^{2}}{\left(\dfrac{3}{4}\right)^{2}}\)
    23. \(\dfrac{\dfrac{5}{14} + \dfrac{1}{8}}{\dfrac{9}{56}}\)

    Tathmini.

    1. x +\(\dfrac{1}{3}\) wakati (a) x =\(\dfrac{2}{3}\) (b) x =\(− \dfrac{5}{6}\)

    Katika mazoezi yafuatayo, tatua equation.

    1. y +\(\dfrac{3}{5}\) =\(\dfrac{7}{5}\)
    2. a -\(\dfrac{3}{10}\) =\(− \dfrac{9}{10}\)
    3. f +\(\left(− \dfrac{2}{3}\right)\) =\(\dfrac{5}{12}\)
    4. \(\dfrac{m}{−2}\)= -16
    5. \(− \dfrac{2}{3}\)c = 18
    6. Tafsiri na kutatua: Quotient ya p na -4 ni -8. Tatua kwa p.

    Wachangiaji na Majina