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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10. John sold 833kg of sugar in 119 days. How many kilograms of sugar did the shopkeeper sell each day? Ili kupata kiasi cha sukari alichouza kila siku, tunagawanya jumla ya sukari kwa idadi ya siku. Step 1: Gawanya jumla ya sukari kwa idadi ya siku. 833 kg119 days Step 2: Fanya hesabu. 833 ÷ 119 = 7 Muuzaji aliweza kuuza kilo 7 za sukari kila siku. The shopkeeper sold: 7 kg 11. Work out; 648 ÷ 12 × 126 + 2,436 - 7,245 Tutatumia utaratibu wa shughuli (BODMAS/PEMDAS): Mabano, Amri (nguvu na mizizi), Gawanya na Zidisha (kutoka kushoto kwenda kulia), Ongeza na Toa (kutoka kushoto kwenda kulia). Step 1: Fanya mgawanyiko kwanza. 648 ÷ 12 = 54 Step 2: Fanya kuzidisha. 54 × 126 = 6,804 Step 3: Fanya kujumlisha. 6,804 + 2,436 = 9,240 Step 4: Fanya kutoa. 9,240 - 7,245 = 1,995 The result is: 1,995 12. Find the L.C.M of 12, 18 and 24. Tutapata L.C.M (Kigawo Kidogo Zaidi cha Pamoja) kwa kutumia njia ya vigawo vikuu. Step 1: Tafuta vigawo vikuu vya kila nambari. 12 = 2 × 2 × 3 = 2^2 × 3^1 18 = 2 × 3 × 3 = 2^1 × 3^2 24 = 2 × 2 × 2 × 3 = 2^3 × 3^1 Step 2: Chagua nguvu ya juu zaidi ya kila kigawo kikuu kinachoonekana. Kwa kigawo kikuu 2, nguvu ya juu zaidi ni 2^3. Kwa kigawo kikuu 3, nguvu ya juu zaidi ni 3^2. Step 3: Zidisha nguvu hizi za juu zaidi pamoja ili kupata L.C.M. L.C.M = 2^3 × 3^2 = 8 × 9 = 72 The L.C.M is: 72 13. Work out; (1)/(4) + (1)/(10) + (3)/(5)= Ili kujumlisha sehemu hizi, tunahitaji kupata kigawo cha kawaida (L.C.M) cha madhehebu (4, 10, 5). L.C.M ya 4, 10, na 5 ni 20. Step 1: Badilisha kila sehemu kuwa na dhehebu la 20. (1)/(4) = (1 × 5)/(4 × 5) = (5)/(20) (1)/(10) = (1 × 2)/(10 × 2) = (2)/(20) (3)/(5) = (3 × 4)/(5 × 4) = (12)/(20) Step 2: Jumlisha sehemu zote. (5)/(20) + (2)/(20) + (12)/(20) = (5 + 2 + 12)/(20) Step 3: Fanya hesabu ya nambari za juu. (19)/(20) The sum is: (19)/(20) 14. Obiero was offered a job at Karatina Primary School to paint a class wall, which was 6 (3)/(4) metres long. He painted 4 (1)/(2) meters by midday and the rest in the afternoon. What length of the wall did he paint in the afternoon? Ili kupata urefu wa ukuta aliochora alasiri, tunatoa urefu aliochora mchana kutoka urefu wote wa ukuta. Step 1: Badilisha nambari mchanganyiko kuwa sehemu zisizofaa. 6 (3)/(4) = ((6 × 4) + 3)/(4) = (24 + 3)/(4) = (27)/(4) m 4 (1)/(2) = ((4 × 2) + 1)/(2) = (8 + 1)/(2) = (9)/(2) m Step 2: Tafuta kigawo cha kawaida cha madhehebu (4 na 2), ambacho ni 4. (9)/(2) = (9 × 2)/(2 × 2) = (18)/(4) m Step 3: Toa urefu aliochora mchana kutoka urefu wote. (27)/(4) - (18)/(4) = (27 - 18)/(4) = (9)/(4) m Step 4: Badilisha sehemu isiyofaa kuwa nambari mchanganyiko. (9)/(4) = 2 (1)/(4) m Obiero painted: 2 (1)/(4) metres 15. Convert (8)/(25) to a percentage. Ili kubadilisha sehemu kuwa asilimia, tunazidisha sehemu hiyo kwa 100%. Step 1: Zidisha sehemu kwa 100%. (8)/(25) × 100\% Step 2: Fanya hesabu. (8 × 100)/(25)\% = (800)/(25)\% Step 3: Gawanya. 800 ÷ 25 = 32 The percentage is: 32\% 16. What is the place value of digit 5 in the number 4,964,751? Tutachunguza nafasi ya kila tarakimu katika nambari 4,964,751. Step 1: Tambua nafasi ya tarakimu 5. Nambari ni 4,964,751. • 1 iko katika nafasi ya mamoja. • 5 iko katika nafasi ya makumi. • 7 iko katika nafasi ya mamia. • 4 iko katika nafasi ya maelfu. • 6 iko katika nafasi ya makumi elfu. • 9 iko katika nafasi ya mamia elfu. • 4 iko katika nafasi ya mamilioni. The place value of digit 5 is: Makumi (Tens) 17. Joan travelled 5.6752km. How many kilometres did she travel to the nearest tenth? Ili kuzungusha nambari hadi sehemu ya kumi iliyo karibu, tunatazama tarakimu iliyo upande wa kulia wa sehemu ya kumi. Step 1: Tambua tarakimu katika nafasi ya kumi. Katika 5.6752, tarakimu katika nafasi ya kumi ni 6. Step 2: Angalia tarakimu iliyo kulia kwake (nafasi ya mia). Tarakimu iliyo kulia kwa 6 ni 7. Step 3: Kwa kuwa 7 ni kubwa kuliko au sawa na 5, tunazungusha tarakimu ya kumi juu kwa 1. 6 inakuwa 7. The distance rounded to the nearest tenth is: 5.7 km 18. A water tank had 6,448.048 litres of water. A farmer used 2,139.986km. How many litres of water remained? Kuna makosa ya kitengo katika swali hili. Inaonekana "2,139.986km" inapaswa kuwa "2,139.986 litres" ili hesabu iwe na maana. Nitachukulia kuwa mkulima alitumia lita 2,139.986 za maji. Step 1: Toa kiasi cha maji kilichotumika kutoka kiasi cha awali cha maji. 6,448.048 litres - 2,139.986 litres Step 2: Fanya hesabu ya kutoa. 6,448.048 2,139.986 1.5cm0.4pt 4,308.062 The amount of water remained is: 4,308.062 litres Tuma swali linalofuata 📸