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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Ili kutatua tatizo hili, tutafuata utaratibu wa shughuli (BODMAS/PEMDAS), tukianza na mabano ya ndani kabisa. (2)/(5) of (6(2)/(5) - (1)/(2)(1(2)/(3) + (1)/(3)) × (1)/(5)) Kumbuka kuwa "of" inamaanisha kuzidisha. Step 1: Tatua mabano ya ndani kabisa. Kwanza, badilisha namba mchanganyiko kuwa sehemu isiyofaa: 1(2)/(3) = (1 × 3 + 2)/(3) = (5)/(3). Sasa jumlisha sehemu ndani ya mabano: 1(2)/(3) + (1)/(3) = (5)/(3) + (1)/(3) = (6)/(3) = 2 Step 2: Badilisha matokeo ya Step 1 kwenye usemi mkuu na ufanye kuzidisha ndani ya mabano makubwa. (1)/(2) × 2 × (1)/(5) Zidisha kutoka kushoto kwenda kulia: (1)/(2) × 2 = 1 Kisha: 1 × (1)/(5) = (1)/(5) Step 3: Badilisha matokeo ya Step 2 kwenye mabano makubwa na ufanye kutoa. Kwanza, badilisha namba mchanganyiko 6(2)/(5) kuwa sehemu isiyofaa: 6(2)/(5) = (6 × 5 + 2)/(5) = (30 + 2)/(5) = (32)/(5). Sasa toa: (32)/(5) - (1)/(5) = (31)/(5) Step 4: Hatimaye, zidisha matokeo ya Step 3 na (2)/(5). (2)/(5) × (31)/(5) Zidisha namba za juu na namba za chini: (2 × 31)/(5 × 5) = (62)/(25) Step 5: Badilisha sehemu isiyofaa kuwa namba mchanganyiko. (62)/(25) = 2(12)/(25) Jibu la mwisho ni: 2(12)/(25) Last free one today — make it count tomorrow, or type /upgrade for unlimited.