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 master, hapa kuna masuluhisho ya maswali yako: 1. Workout (2.7 × 4.8)/(2.4 × 3.6) Umeanza vizuri kwa kuzidisha nambari za juu na chini. Step 1: Zidisha nambari za juu (numerator). 2.7 × 4.8 = 12.96 Step 2: Zidisha nambari za chini (denominator). 2.4 × 3.6 = 8.64 Step 3: Gawanya matokeo ya numerator kwa matokeo ya denominator. (12.96)/(8.64) Ili kurahisisha hesabu, unaweza kuzidisha nambari zote mbili kwa 100 ili kuondoa desimali: (12.96 × 100)/(8.64 × 100) = (1296)/(864) Sasa gawanya: (1296)/(864) = 1.5 Jibu la mwisho: 1.5 2. Simplify: 1(1)/(6) × 1(1)/(4) ÷ 2(1)/(3) Kwanza, badilisha nambari mchanganyiko kuwa sehemu zisizofaa. Step 1: Badilisha nambari mchanganyiko kuwa sehemu zisizofaa. 1(1)/(6) = ((1 × 6) + 1)/(6) = (7)/(6) 1(1)/(4) = ((1 × 4) + 1)/(4) = (5)/(4) 2(1)/(3) = ((2 × 3) + 1)/(3) = (7)/(3) Step 2: Andika upya usemi kwa kutumia sehemu zisizofaa. (7)/(6) × (5)/(4) ÷ (7)/(3) Step 3: Badilisha mgawanyiko kuwa kuzidisha kwa kutumia kinyume (reciprocal) cha sehemu ya mwisho. (7)/(6) × (5)/(4) × (3)/(7) Step 4: Zidisha sehemu zote na kurahisisha. Unaweza kufuta nambari zinazofanana kabla ya kuzidisha. 76 × (5)/(4) × (3)/(7) = (1)/(6) × (5)/(4) × (3)/(1) Sasa, rahisha 3 na 6: = (1)/(6)_2 × (5)/(4) × 3_11 = (1)/(2) × (5)/(4) × (1)/(1) = (1 × 5 × 1)/(2 × 4 × 1) = (5)/(8) Jibu la mwisho: (5)/(8) 3 done, 2 left today. You're making progress.