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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Haya hapa masuluhisho ya maswali yako: 6) Kuzidisha namba nzima na sehemu: Step 1: Andika namba nzima kama sehemu. 6 × (5)/(3) = (6)/(1) × (5)/(3) Step 2: Zidisha namba za juu (numerators) na namba za chini (denominators). (6 × 5)/(1 × 3) = (30)/(3) Step 3: Rahisisha sehemu. (30)/(3) = 10 The answer is 10. 7) Kupata sehemu ya namba: Step 1: "of" inamaanisha kuzidisha. (8)/(9) of 40 = (8)/(9) × 40 Step 2: Andika namba nzima kama sehemu na zidisha. (8)/(9) × (40)/(1) = (8 × 40)/(9 × 1) = (320)/(9) Step 3: Badilisha kuwa namba mchanganyiko (optional, but good practice for improper fractions). (320)/(9) = 35 (5)/(9) The answer is (320)/(9) or 35 (5)/(9). 8) Kuzidisha sehemu mbili: Step 1: Zidisha namba za juu (numerators). (7)/(8) × (3)/(5) = (7 × 3)/(8 × 5) Step 2: Zidisha namba za chini (denominators). (21)/(40) The answer is (21)/(40). 9) Kujumlisha sehemu mbili: Step 1: Tafuta kigawo cha kawaida (common denominator) cha 2 na 8, ambacho ni 8. (1)/(2) + (7)/(8) Step 2: Badilisha (1)/(2) kuwa sehemu yenye kigawo cha 8. (1)/(2) = (1 × 4)/(2 × 4) = (4)/(8) Step 3: Jumlisha sehemu hizo mbili. (4)/(8) + (7)/(8) = (4+7)/(8) = (11)/(8) Step 4: Badilisha kuwa namba mchanganyiko. (11)/(8) = 1 (3)/(8) The answer is (11)/(8) or 1 (3)/(8). That's 2 down. 3 left today — send the next one.