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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Tutatafuta thamani kamili (absolute value) ya kila usemi. a) (3)/(8) - (1)/(16) + (5)/(4) Step 1: Tafuta denominator ya kawaida (LCM) kwa 8, 16, na 4, ambayo ni 16. Badilisha sehemu zote kuwa na denominator 16. (3)/(8) = (3 × 2)/(8 × 2) = (6)/(16) (5)/(4) = (5 × 4)/(4 × 4) = (20)/(16) Step 2: Fanya hesabu ya kujumlisha na kutoa. (6)/(16) - (1)/(16) + (20)/(16) = (6 - 1 + 20)/(16) = (5 + 20)/(16) = (25)/(16) Step 3: Tafuta thamani kamili. | (25)/(16) | = (25)/(16) b) 1(2)/(3) + 2(3)/(4) + 3(4)/(5) Step 1: Badilisha namba mchanganyiko kuwa sehemu zisizofaa. 1(2)/(3) = (1 × 3 + 2)/(3) = (5)/(3) 2(3)/(4) = (2 × 4 + 3)/(4) = (11)/(4) 3(4)/(5) = (3 × 5 + 4)/(5) = (19)/(5) Step 2: Tafuta denominator ya kawaida (LCM) kwa 3, 4, na 5, ambayo ni 60. Badilisha sehemu zote kuwa na denominator 60. (5)/(3) = (5 × 20)/(3 × 20) = (100)/(60) (11)/(4) = (11 × 15)/(4 × 15) = (165)/(60) (19)/(5) = (19 × 12)/(5 × 12) = (228)/(60) Step 3: Fanya hesabu ya kujumlisha. (100)/(60) + (165)/(60) + (228)/(60) = (100 + 165 + 228)/(60) = (493)/(60) Step 4: Tafuta thamani kamili. | (493)/(60) | = (493)/(60) d) 62.15 - 88.765 + 45.678 Step 1: Fanya hesabu ya kutoa na kujumlisha. 62.15 - 88.765 = -26.615 -26.615 + 45.678 = 19.063 Step 2: Tafuta thamani kamili. |19.063| = 19.063 e) 2(1)/(3) + 4(1)/(5) - (1)/(2) Step 1: Badilisha namba mchanganyiko kuwa sehemu zisizofaa. 2(1)/(3) = (2 × 3 + 1)/(3) = (7)/(3) 4(1)/(5) = (4 × 5 + 1)/(5) = (21)/(5) Step 2: Tafuta denominator ya kawaida (LCM) kwa 3, 5, na 2, ambayo ni 30. Badilisha sehemu zote kuwa na denominator 30. (7)/(3) = (7 × 10)/(3 × 10) = (70)/(30) (21)/(5) = (21 × 6)/(5 × 6) = (126)/(30) (1)/(2) = (1 × 15)/(2 × 15) = (15)/(30) Step 3: Fanya hesabu ya kujumlisha na kutoa. (70)/(30) + (126)/(30) - (15)/(30) = (70 + 126 - 15)/(30) = (196 - 15)/(30) = (181)/(30) Step 4: Tafuta thamani kamili. | (181)/(30) | = (181)/(30) Tuma swali linalofuata 📸