This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Sawa Sewercydaa, hebu tuendelee na maswali haya. Swali la 1: Rahisisha usemi ufuatao: ((11)/(2) - (1)/(3)) of (3)/(4)1(1)/(4) + (1)/(2) of 2(1)/(2) Hatua ya 1: Tathmini nambari ya juu (numerator). • Kwanza, fanya kutoa ndani ya mabano: 1(1)/(2) - (1)/(3). Badilisha 1(1)/(2) kuwa sehemu isiyofaa: (3)/(2). (3)/(2) - (1)/(3) = (9)/(6) - (2)/(6) = (7)/(6). • Kisha, zidisha matokeo kwa (3)/(4): (7)/(6) × (3)/(4) = (21)/(24). • Rahisisha sehemu: (21)/(24) = (7)/(8). Hivyo, nambari ya juu ni (7)/(8). Hatua ya 2: Tathmini nambari ya chini (denominator). • Kwanza, zidisha: (1)/(2) of 2(1)/(2). Badilisha 2(1)/(2) kuwa sehemu isiyofaa: (5)/(2). (1)/(2) × (5)/(2) = (5)/(4). • Kisha, jumlisha matokeo na 1(1)/(4). Badilisha 1(1)/(4) kuwa sehemu isiyofaa: (5)/(4). (5)/(4) + (5)/(4) = (10)/(4). • Rahisisha sehemu: (10)/(4) = (5)/(2). Hivyo, nambari ya chini ni (5)/(2). Hatua ya 3: Gawanya nambari ya juu kwa nambari ya chini. (7)/(8)(5)/(2) = (7)/(8) ÷ (5)/(2) = (7)/(8) × (2)/(5) = (14)/(40) Rahisisha jibu: (14)/(40) = (7)/(20). Jibu ni: (7)/(20) Swali la 2: Namba ya tarakimu mbili ni kwamba jumla ya tarakimu zake ni 11. Wakati tarakimu zinapobadilishwa, namba mpya inayoundwa ni 27 kubwa kuliko namba ya asili. Tafuta namba hiyo. Hatua ya 1: Unda milinganyo. Acha namba ya asili iwe 10t + u, ambapo t ni tarakimu ya makumi na u ni tarakimu ya mamoja. Kutoka taarifa ya kwanza: t + u = 11 (Mlinganyo 1). Namba mpya baada ya kubadilisha tarakimu ni 10u + t. Kutoka taarifa ya pili: 10u + t = (10t + u) + 27 (Mlinganyo 2). Hatua ya 2: Rahisisha Mlinganyo 2. 10u + t = 10t + u + 27 10u - u + t - 10t = 27 9u - 9t = 27 Gawanya pande zote mbili kwa 9: u - t = 3 (Mlinganyo 3). Hatua ya 3: Tatua mfumo wa milinganyo. Tuna milinganyo miwili: 1) t + u = 11 3) u - t = 3 Jumlisha Mlinganyo 1 na Mlinganyo 3: (t + u) + (u - t) = 11 + 3 2u = 14 u = 7. Hatua ya 4: Tafuta thamani ya t. Badilisha u = 7 katika Mlinganyo 1: t + 7 = 11 t = 11 - 7 t = 4. Hatua ya 5: Tafuta namba ya asili. Namba ya asili ni 10t + u = 10(4) + 7 = 40 + 7 = 47. Jibu ni: 47 3 done, 2 left today. You're making progress.