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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1. Badilisha masaa yafuatayo kuwa dakika. Tunajua kuwa saa 1 ina dakika 60. a) 2(1)/(2) hours Step 1: Badilisha masaa kamili kuwa dakika. 2 hours = 2 × 60 minutes = 120 minutes Step 2: Badilisha sehemu ya saa kuwa dakika. (1)/(2) hour = (1)/(2) × 60 minutes = 30 minutes Step 3: Jumlisha dakika zote. 120 minutes + 30 minutes = 150 minutes Jibu: 150 minutes b) 1(1)/(2) hours Step 1: Badilisha masaa kamili kuwa dakika. 1 hour = 1 × 60 minutes = 60 minutes Step 2: Badilisha sehemu ya saa kuwa dakika. (1)/(2) hour = (1)/(2) × 60 minutes = 30 minutes Step 3: Jumlisha dakika zote. 60 minutes + 30 minutes = 90 minutes Jibu: 90 minutes c) 3(1)/(2) hours Step 1: Badilisha masaa kamili kuwa dakika. 3 hours = 3 × 60 minutes = 180 minutes Step 2: Badilisha sehemu ya saa kuwa dakika. (1)/(2) hour = (1)/(2) × 60 minutes = 30 minutes Step 3: Jumlisha dakika zote. 180 minutes + 30 minutes = 210 minutes Jibu: 210 minutes d) 3(3)/(4) hours Step 1: Badilisha masaa kamili kuwa dakika. 3 hours = 3 × 60 minutes = 180 minutes Step 2: Badilisha sehemu ya saa kuwa dakika. (3)/(4) hour = (3)/(4) × 60 minutes = 3 × 15 minutes = 45 minutes Step 3: Jumlisha dakika zote. 180 minutes + 45 minutes = 225 minutes Jibu: 225 minutes 2. Badilisha dakika zifuatazo kuwa masaa. Tunajua kuwa dakika 60 ni sawa na saa 1. Ili kubadilisha dakika kuwa masaa, tunagawanya kwa 60. a) 240 minutes Step 1: Gawanya dakika kwa 60. 240 minutes60 minutes/hour = 4 hours Jibu: 4 hours b) 120 minutes Step 1: Gawanya dakika kwa 60. 120 minutes60 minutes/hour = 2 hours Jibu: 2 hours c) 180 minutes Step 1: Gawanya dakika kwa 60. 180 minutes60 minutes/hour = 3 hours Jibu: 3 hours d) 270 minutes Step 1: Gawanya dakika kwa 60. 270 minutes60 minutes/hour = (27)/(6) hours Step 2: Rahisisha sehemu na ubadilishe kuwa namba mchanganyiko. (27)/(6) hours = (9)/(2) hours = 4(1)/(2) hours Jibu: 4(1)/(2) hours 3. Fanya hesabu zifuatazo (Kujumlisha masaa na dakika). a) Hours mins: 4 50 + 3 30 Step 1: Jumlisha dakika. 50 mins + 30 mins = 80 mins Step 2: Badilisha dakika kuwa masaa na dakika zilizobaki (kumbuka dakika 60 = saa 1). 80 mins = 1 hour 20 mins Step 3: Jumlisha masaa. 4 hours + 3 hours + 1 hour (kutoka dakika) = 8 hours Jibu: 8 hours 20 minutes b) Hours mins: 3 40 + 5 30 Step 1: Jumlisha dakika. 40 mins + 30 mins = 70 mins Step 2: Badilisha dakika kuwa masaa na dakika zilizobaki. 70 mins = 1 hour 10 mins Step 3: Jumlisha masaa. 3 hours + 5 hours + 1 hour (kutoka dakika) = 9 hours Jibu: 9 hours 10 minutes 4. Toa zifuatazo (Kutoa masaa na dakika). a) Hours mins: 5 20 - 2 40 Step 1: Huwezi kutoa dakika 40 kutoka dakika 20. Azima saa 1 (dakika 60) kutoka kwenye masaa. 5 hours → 4 hours 20 mins + 60 mins = 80 mins Step 2: Toa dakika. 80 mins - 40 mins = 40 mins Step 3: Toa masaa. 4 hours - 2 hours = 2 hours Jibu: 2 hours 40 minutes b) Hours mins: 6 30 - 2 50 Step 1: Huwezi kutoa dakika 50 kutoka dakika 30. Azima saa 1 (dakika 60) kutoka kwenye masaa. 6 hours → 5 hours 30 mins + 60 mins = 90 mins Step 2: Toa dakika. 90 mins - 50 mins = 40 mins Step 3: Toa masaa. 5 hours - 2 hours = 3 hours Jibu: 3 hours 40 minutes 5. Fanya hesabu (Kujumlisha na kutoa wiki na siku). Tunajua kuwa wiki 1 ina siku 7. a) Weeks days: 4 4 + 5 5 Step 1: Jumlisha siku. 4 days + 5 days = 9 days Step 2: Badilisha siku kuwa wiki na siku zilizobaki (kumbuka siku 7 = wiki 1). 9 days = 1 week 2 days Step 3: Jumlisha wiki. 4 weeks + 5 weeks + 1 week (kutoka siku) = 10 weeks Jibu: 10 weeks 2 days b) Weeks days: 4 4 - 1 5 Step 1: Huwezi kutoa siku 5 kutoka siku 4. Azima wiki 1 (siku 7) kutoka kwenye wiki. 4 weeks → 3 weeks 4 days + 7 days = 11 days Step 2: Toa siku. 11 days - 5 days = 6 days Step 3: Toa wiki. 3 weeks - 1 week = 2 weeks Jibu: 2 weeks 6 days Tuma swali linalofuata 📸