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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Huu hapa ni ufumbuzi wa swali la kwanza: Tunahitaji kurahisisha usemi ufuatao: ((13)/(7) - (5)/(8)) + (2)/(3) of 1(1)/(5)(3)/(4) + 1(5)/(7) ÷ (4)/(7) of 2(1)/(3) Hatua ya 1: Rahisisha namba ya juu (numerator). Kwanza, badilisha namba mchanganyiko kuwa sehemu zisizofaa: 1(3)/(7) = (1 × 7 + 3)/(7) = (10)/(7) 1(1)/(5) = (1 × 5 + 1)/(5) = (6)/(5) Sasa, fanya hesabu ndani ya mabano: (10)/(7) - (5)/(8) = (10 × 8 - 5 × 7)/(56) = (80 - 35)/(56) = (45)/(56) Kisha, fanya hesabu ya 'of' (kuzidisha): (2)/(3) of 1(1)/(5) = (2)/(3) × (6)/(5) = (12)/(15) = (4)/(5) Jumlisha matokeo haya mawili ili kupata namba ya juu: (45)/(56) + (4)/(5) = (45 × 5 + 4 × 56)/(280) = (225 + 224)/(280) = (449)/(280) Hivyo, namba ya juu ni (449)/(280). Hatua ya 2: Rahisisha namba ya chini (denominator). Kwanza, badilisha namba mchanganyiko kuwa sehemu zisizofaa: 1(5)/(7) = (1 × 7 + 5)/(7) = (12)/(7) 2(1)/(3) = (2 × 3 + 1)/(3) = (7)/(3) Sasa, fanya hesabu ya 'of' kwanza: (4)/(7) of 2(1)/(3) = (4)/(7) × (7)/(3) = (28)/(21) = (4)/(3) Kisha, fanya hesabu ya kugawanya: 1(5)/(7) ÷ (4)/(3) = (12)/(7) ÷ (4)/(3) = (12)/(7) × (3)/(4) = (36)/(28) = (9)/(7) Jumlisha matokeo haya mawili ili kupata namba ya chini: (3)/(4) + (9)/(7) = (3 × 7 + 9 × 4)/(28) = (21 + 36)/(28) = (57)/(28) Hivyo, namba ya chini ni (57)/(28). Hatua ya 3: Gawanya namba ya juu kwa namba ya chini. (449)/(280)(57)/(28) = (449)/(280) ÷ (57)/(28) Ili kugawanya kwa sehemu, zidisha kwa kinyume chake: (449)/(280) × (28)/(57) Rahisisha kwa kugawanya 280 kwa 28 (ambayo ni 10): (449)/(10 × 57) = (449)/(570) Jibu la mwisho ni: (449)/(570) Tuma swali linalofuata 📸