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Swali la 3: Tathmini usemi ufuatao: ((81 ÷ 9) - (-15) + 20)/(-24 + (12 ÷ 3) × (-2)) Hatua ya 1: Tathmini nambari ya juu (numerator). Kwanza, fanya mgawanyiko: 81 ÷ 9 = 9. Kisha, fanya kutoa na kujumlisha: 9 - (-15) + 20 = 9 + 15 + 20 = 24 + 20 = 44. Hatua ya 2: Tathmini nambari ya chini (denominator). Kwanza, fanya mgawanyiko: 12 ÷ 3 = 4. Kisha, fanya kuzidisha: 4 × (-2) = -8. Mwisho, fanya kujumlisha: -24 + (-8) = -24 - 8 = -32. Hatua ya 3: Gawanya nambari ya juu kwa nambari ya chini. (44)/(-32) = -(11)/(8) Unaweza pia kuandika kama desimali: -(11)/(8) = -1.375. Jibu ni: -1.375 Swali la 4: Tumia jedwali la namba tete (reciprocal table) pekee kutathmini (1)/(0.325). Kisha, tathmini sqrt(0.25)0.325 kwa tarakimu 1 ya desimali. Hatua ya 1: Tathmini (1)/(0.325) kwa kutumia jedwali la namba tete. Tunaweza kuandika (1)/(0.325) = (1)/(3.25 × 10^-1) = (1)/(3.25) × 10^1. Kutoka jedwali la namba tete, (1)/(3.25) ≈ 0.30769. Hivyo, (1)/(0.325) ≈ 0.30769 × 10 = 3.0769. Hatua ya 2: Tathmini sqrt(0.25)0.325. Kwanza, tafuta sqrt(0.25) = 0.5. Hivyo, usemi unakuwa (0.5)/(0.325). Hii inaweza kuandikwa kama 0.5 × (1)/(0.325). Kutumia matokeo ya Hatua ya 1: 0.5 × 3.0769 = 1.53845. Hatua ya 3: Zungusha jibu kwa tarakimu 1 ya desimali. 1.53845 ≈ 1.5. Jibu ni: 1.5 Swali la 5: Tathmini usemi ufuatao: (1)/(2) of (3)/(4) + 1(1)/(2) ((1)/(2) - (2)/(3))(3)/(4) of 2(1)/(2) ÷ (1)/(2) Hatua ya 1: Tathmini nambari ya juu (numerator). • (1)/(2) of (3)/(4) = (1)/(2) × (3)/(4) = (3)/(8). • Ndani ya mabano: (1)/(2) - (2)/(3) = (3)/(6) - (4)/(6) = -(1)/(6). • Zidisha 1(1)/(2) na matokeo ya mabano: 1(1)/(2) = (3)/(2). Hivyo, (3)/(2) × (-(1)/(6)) = -(3)/(12) = -(1)/(4). • Jumlisha sehemu za nambari ya juu: (3)/(8) + (-(1)/(4)) = (3)/(8) - (2)/(8) = (1)/(8). Hatua ya 2: Tathmini nambari ya chini (denominator). • (3)/(4) of 2(1)/(2): Badilisha 2(1)/(2) kuwa sehemu isiyofaa: 2(1)/(2) = (5)/(2). • Zidisha: (3)/(4) × (5)/(2) = (15)/(8). • Gawanya: (15)/(8) ÷ (1)/(2) = (15)/(8) × (2)/(1) = (30)/(8) = (15)/(4). Hatua ya 3: Gawanya nambari ya juu kwa nambari ya chini. (1)/(8)(15)/(4) = (1)/(8) × (4)/(15) = (4)/(120) = (1)/(30) Jibu ni: (1)/(30) Swali la 6: Wavulana wawili na msichana waligawana pesa. Kijana mkubwa alipata (4)/(9) ya pesa zote, kijana mdogo alipata (2)/(5) ya salio, na msichana alipata zilizobaki. Tafuta asilimia ya sehemu ya kijana mdogo kwa sehemu ya msichana. Hatua ya 1: Tafuta sehemu ya kijana mkubwa na salio. Acha jumla ya pesa iwe P. Sehemu ya kijana mkubwa = (4)/(9) P. Salio baada ya kijana mkubwa = P - (4)/(9) P = (5)/(9) P. Hatua ya 2: Tafuta sehemu ya kijana mdogo. Sehemu ya kijana mdogo = (2)/(5) ya salio = (2)/(5) × (5)/(9) P = (2)/(9) P. Hatua ya 3: Tafuta sehemu ya msichana. Jumla ya sehemu za wavulana = (4)/(9) P + (2)/(9) P = (6)/(9) P = (2)/(3) P. Sehemu ya msichana = P - (2)/(3) P = (1)/(3) P. Hatua ya 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 = (2)/(9) P(1)/(3) P = (2)/(9) ÷ (1)/(3) = (2)/(9) × (3)/(1) = (6)/(9) = (2)/(3) Ili kupata asilimia, zidisha kwa 100%: (2)/(3) × 100\% = 66.666...\% Zungusha kwa tarakimu 2 za desimali: 66.67\%. Jibu ni: 66.67\% Tuma swali linalofuata 📸