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 majibu ya maswali yako: c) Fractions 1. Arrange the following fractions in descending order: (3)/(4), (5)/(6), (7)/(12), (1)/(2). Step 1: Tafuta kigawo kidogo zaidi cha pamoja (LCM) cha madhehebu (4, 6, 12, 2). LCM ni 12. Step 2: Badilisha kila sehemu kuwa na dhehebu la 12. (3)/(4) = (3 × 3)/(4 × 3) = (9)/(12) (5)/(6) = (5 × 2)/(6 × 2) = (10)/(12) (7)/(12) (tayari ina dhehebu la 12) (1)/(2) = (1 × 6)/(2 × 6) = (6)/(12) Step 3: Panga sehemu hizi kwa mpangilio wa kushuka (kutoka kubwa hadi ndogo). (10)/(12), (9)/(12), (7)/(12), (6)/(12) Step 4: Rudisha sehemu kwenye umbo lake la asili. (5)/(6), (3)/(4), (7)/(12), (1)/(2) Mpangilio wa kushuka ni: (5)/(6), (3)/(4), (7)/(12), (1)/(2) 2. Calculate the sum: (1)/(25) + (3)/(4). Step 1: Tafuta kigawo kidogo zaidi cha pamoja (LCM) cha madhehebu (25 na 4). LCM ni 100. Step 2: Badilisha sehemu zote mbili kuwa na dhehebu la 100. (1)/(25) = (1 × 4)/(25 × 4) = (4)/(100) (3)/(4) = (3 × 25)/(4 × 25) = (75)/(100) Step 3: Jumuisha sehemu hizo. (4)/(100) + (75)/(100) = (4 + 75)/(100) = (79)/(100) Jumla ni: (79)/(100) 3. Calculate the product: (5)/(8) × (2)/(32). Step 1: Zidisha namba za juu (numerator) na namba za chini (denominator). (5)/(8) × (2)/(32) = (5 × 2)/(8 × 32) Step 2: Fanya kuzidisha. (10)/(256) Step 3: Rahisisha sehemu kwa kugawanya namba ya juu na ya chini kwa kigawo cha kawaida (2). (10 ÷ 2)/(256 ÷ 2) = (5)/(128) Bidhaa ni: (5)/(128) 4. Identify the reciprocal of the mixed number 3/47. Kumbuka: "3/47" si nambari mchanganyiko, ni sehemu halisi. Tutachukulia inamaanisha sehemu (3)/(47). Step 1: Ili kupata kinyume (reciprocal) cha sehemu, geuza namba ya juu na ya chini. Kinyume cha (3)/(47) ni (47)/(3). Step 2: Badilisha sehemu isiyofaa kuwa nambari mchanganyiko. (47)/(3) = 15 (2)/(3) Kinyume ni: 15 (2)/(3) 5. A piece of ribbon (9)/(10) metres long is cut into pieces, each (3)/(20) metres long. How many pieces of ribbon are there? Step 1: Gawanya urefu wote wa utepe kwa urefu wa kila kipande. Idadi ya vipande = (9)/(10) ÷ (3)/(20) Step 2: Ili kugawanya sehemu, zidisha sehemu ya kwanza na kinyume cha sehemu ya pili. (9)/(10) × (20)/(3) Step 3: Rahisisha kabla ya kuzidisha. (9)/(3) × (20)/(10) = 3 × 2 Step 4: Fanya kuzidisha. 3 × 2 = 6 Kuna vipande: 6 6. What are the next two terms in the number sequence: (1)/(3), (2)/(3), 1, 1(1)/(3), ? Step 1: Tambua muundo wa mfuatano. (1)/(3) (2)/(3) 1 = (3)/(3) 1(1)/(3) = (4)/(3) Inaonekana kila nambari inayofuata inapatikana kwa kuongeza (1)/(3) kwa nambari iliyopita. Step 2: Pata nambari ya tano. 1(1)/(3) + (1)/(3) = (4)/(3) + (1)/(3) = (5)/(3) = 1(2)/(3) Step 3: Pata nambari ya sita. 1(2)/(3) + (1)/(3) = (5)/(3) + (1)/(3) = (6)/(3) = 2 Nambari mbili zinazofuata ni: 1(2)/(3), 2 7. A student requires 3 metres of fabric for one uniform. If they have 541 metres of fabric, how many full uniforms can they make? Step 1: Gawanya jumla ya urefu wa kitambaa kwa urefu wa kitambaa kinachohitajika kwa sare moja. Idadi ya sare = Jumla ya kitambaaKitambaa kwa sare moja Idadi ya sare = 541 m3 m/sare Step 2: Fanya mgawanyiko. 541 ÷ 3 = 180 na baki 1 Mwanafunzi anaweza kutengeneza sare kamili 180. Idadi ya sare kamili ni: 180 d) Decimals 1. State the place value and the total value of the digit 6 in the decimal 3.1468. Step 1: Tambua nafasi ya tarakimu 6. Tarakimu 6 iko katika nafasi ya elfu (thousandths). Step 2: Hesabu thamani kamili ya tarakimu 6. Thamani kamili ni 6 × 0.001 = 0.006. Nafasi ya thamani ni elfu na thamani kamili ni: 0.006 2. Multiply 14.7 by 5. Step 1: Fanya kuzidisha. 14.7 × 5 Step 2: Hesabu bidhaa. 14.7 × 5 = 73.5 Bidhaa ni: 73.5 3. Calculate the product: 2.4 × 0.15. Step 1: Fanya kuzidisha. 2.4 × 0.15 Step 2: Hesabu bidhaa. 2.4 × 0.15 = 0.36 Bidhaa ni: 0.36 4. Divide 7.2 by 0.9. Step 1: Ili kugawanya desimali, badilisha kigawanyo kuwa nambari kamili kwa kuzidisha namba zote mbili kwa 10. (7.2)/(0.9) = (7.2 × 10)/(0.9 × 10) = (72)/(9) Step 2: Fanya mgawanyiko. (72)/(9) = 8 Jibu ni: 8 Last free one today — make it count tomorrow, or type /upgrade for unlimited.