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Two boys and a girl shared some money. The elder boy got 4/9 of it, the younger boy got 2/5 of the remainder and the girl got the rest. Find the percentage share of the younger boy to the girl's share.

Mathematics

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Answers

4 parts
3

−1.375\mathbf{-1.375}

4

1.5\mathbf{1.5}

5

130\mathbf{\frac{1}{30}}

6

66.67%\mathbf{66.67\%}

Step-by-step solution

13 steps

Part 3· 3 steps

Tathmini usemi ufuatao:

(81÷9)−(−15)+20−24+(12÷3)×(−2)\frac{(81 \div 9) - (-15) + 20}{-24 + (12 \div 3) \times (-2)}
  1. Tathmini nambari ya juu (numerator).

    Kwanza, fanya mgawanyiko: 81÷9=981 \div 9 = 9.
    Kisha, fanya kutoa na kujumlisha: 9−(−15)+20=9+15+20=24+20=449 - (-15) + 20 = 9 + 15 + 20 = 24 + 20 = 44.

  2. Tathmini nambari ya chini (denominator).

    Kwanza, fanya mgawanyiko: 12÷3=412 \div 3 = 4.
    Kisha, fanya kuzidisha: 4×(−2)=−84 \times (-2) = -8.
    Mwisho, fanya kujumlisha: −24+(−8)=−24−8=−32-24 + (-8) = -24 - 8 = -32.

  3. Gawanya nambari ya juu kwa nambari ya chini.

    44−32=−118\frac{44}{-32} = -\frac{11}{8}

    Unaweza pia kuandika kama desimali: −118=−1.375-\frac{11}{8} = -1.375.
    Jibu ni: −1.375\boxed{\mathbf{-1.375}}

Part 4

1.5\mathbf{1.5}

Tumia jedwali la namba tete (reciprocal table) pekee kutathmini 10.325\frac{1}{0.325}. Kisha, tathmini 0.250.325\frac{\sqrt{0.25}}{0.325} kwa tarakimu 1 ya desimali.

  1. Tathmini 10.325\frac{1}{0.325} kwa kutumia jedwali la namba tete.

    Tunaweza kuandika 10.325=13.25×10−1=13.25×101\frac{1}{0.325} = \frac{1}{3.25 \times 10^{-1}} = \frac{1}{3.25} \times 10^1.
    Kutoka jedwali la namba tete, 13.25≈0.30769\frac{1}{3.25} \approx 0.30769.
    Hivyo, 10.325≈0.30769×10=3.0769\frac{1}{0.325} \approx 0.30769 \times 10 = 3.0769.

  2. Tathmini 0.250.325\frac{\sqrt{0.25}}{0.325}.

    Kwanza, tafuta 0.25=0.5\sqrt{0.25} = 0.5.
    Hivyo, usemi unakuwa 0.50.325\frac{0.5}{0.325}.
    Hii inaweza kuandikwa kama 0.5×10.3250.5 \times \frac{1}{0.325}.
    Kutumia matokeo ya Hatua ya 1: 0.5×3.0769=1.538450.5 \times 3.0769 = 1.53845.

  3. Zungusha jibu kwa tarakimu 1 ya desimali.

    1.53845≈1.51.53845 \approx 1.5.
    Jibu ni: 1.5\boxed{\mathbf{1.5}}

Part 5

130\mathbf{\frac{1}{30}}

Tathmini usemi ufuatao:

12 of 34+112(12−23)34 of 212÷12\frac{\frac{1}{2} \text{ of } \frac{3}{4} + 1\frac{1}{2} \left(\frac{1}{2} - \frac{2}{3}\right)}{\frac{3}{4} \text{ of } 2\frac{1}{2} \div \frac{1}{2}}
  1. Tathmini nambari ya juu (numerator).

    • 12 of 34=12×34=38\frac{1}{2} \text{ of } \frac{3}{4} = \frac{1}{2} \times \frac{3}{4} = \frac{3}{8}.
    • Ndani ya mabano: 12−23=36−46=−16\frac{1}{2} - \frac{2}{3} = \frac{3}{6} - \frac{4}{6} = -\frac{1}{6}.
    • Zidisha 1121\frac{1}{2} na matokeo ya mabano: 112=321\frac{1}{2} = \frac{3}{2}. Hivyo, 32×(−16)=−312=−14\frac{3}{2} \times \left(-\frac{1}{6}\right) = -\frac{3}{12} = -\frac{1}{4}.
    • Jumlisha sehemu za nambari ya juu: 38+(−14)=38−28=18\frac{3}{8} + \left(-\frac{1}{4}\right) = \frac{3}{8} - \frac{2}{8} = \frac{1}{8}.
  2. Tathmini nambari ya chini (denominator).

    • 34 of 212\frac{3}{4} \text{ of } 2\frac{1}{2}: Badilisha 2122\frac{1}{2} kuwa sehemu isiyofaa: 212=522\frac{1}{2} = \frac{5}{2}.
    • Zidisha: 34×52=158\frac{3}{4} \times \frac{5}{2} = \frac{15}{8}.
    • Gawanya: 158÷12=158×21=308=154\frac{15}{8} \div \frac{1}{2} = \frac{15}{8} \times \frac{2}{1} = \frac{30}{8} = \frac{15}{4}.
  3. Gawanya nambari ya juu kwa nambari ya chini.

    18154=18×415=4120=130\frac{\frac{1}{8}}{\frac{15}{4}} = \frac{1}{8} \times \frac{4}{15} = \frac{4}{120} = \frac{1}{30}

    Jibu ni: 130\boxed{\mathbf{\frac{1}{30}}}

Part 6

66.67%\mathbf{66.67\%}

Wavulana wawili na msichana waligawana pesa. Kijana mkubwa alipata 49\frac{4}{9} ya pesa zote, kijana mdogo alipata 25\frac{2}{5} ya salio, na msichana alipata zilizobaki. Tafuta asilimia ya sehemu ya kijana mdogo kwa sehemu ya msichana.

  1. Tafuta sehemu ya kijana mkubwa na salio.

    Acha jumla ya pesa iwe PP.
    Sehemu ya kijana mkubwa = 49P\frac{4}{9} P.
    Salio baada ya kijana mkubwa = P−49P=59PP - \frac{4}{9} P = \frac{5}{9} P.

  2. Tafuta sehemu ya kijana mdogo.

    Sehemu ya kijana mdogo = 25\frac{2}{5} ya salio = 25×59P=29P\frac{2}{5} \times \frac{5}{9} P = \frac{2}{9} P.

  3. Tafuta sehemu ya msichana.

    Jumla ya sehemu za wavulana = 49P+29P=69P=23P\frac{4}{9} P + \frac{2}{9} P = \frac{6}{9} P = \frac{2}{3} P.
    Sehemu ya msichana = P−23P=13PP - \frac{2}{3} P = \frac{1}{3} P.

  4. Tafuta asilimia ya sehemu ya kijana mdogo kwa sehemu ya msichana.

    Uwiano wa sehemu ya kijana mdogo kwa sehemu ya msichana ni:

    Sehemu ya kijana mdogoSehemu ya msichana=29P13P=29÷13=29×31=69=23\frac{\text{Sehemu ya kijana mdogo}}{\text{Sehemu ya msichana}} = \frac{\frac{2}{9} P}{\frac{1}{3} P} = \frac{2}{9} \div \frac{1}{3} = \frac{2}{9} \times \frac{3}{1} = \frac{6}{9} = \frac{2}{3}

    Ili kupata asilimia, zidisha kwa 100%:

    23×100%=66.666...%\frac{2}{3} \times 100\% = 66.666...\%

    Zungusha kwa tarakimu 2 za desimali: 66.67%66.67\%.
    Jibu ni: 66.67%\boxed{\mathbf{66.67\%}}

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