Two alarms ring at 7:00 AM. One rings every 15 minutes, and the other rings every 25 minutes. At what time will they both ring together again?

Haya hapa majibu ya maswali yako: WEEK 6. Two alarms ring at 7:00 AM. One rings every 15 minutes, and the other rings every 20 minutes. At what time will they both ring together again? Step 1: Tafuta Kigawo Kidogo Zaidi cha Pamoja (LCM) cha 15 na 20 ili kujua baada ya muda gani zitalia pamoja tena. Vigawo vya 15: 15, 30, 45, 60, 75, ... Vigawo vya 20: 20, 40, 60, 80, ... LCM ya 15 na 20 ni 60. Hii inamaanisha zitalia pamoja baada ya dakika 60. Step 2: Ongeza dakika 60 (saa 1) kwenye muda wa kuanzia wa 7:00 AM. 7:00 AM + 1 saa = 8:00 AM Zitalia pamoja tena saa: 8:00 AM 7. A carpenter has three planks of wood with lengths 18m, 24m, and 30m. He wants to cut them into pieces of equal length without any remainder. What is the greatest possible length of each piece? Step 1: Tafuta Kigawo Kikubwa Zaidi cha Pamoja (GCF) cha 18, 24, na 30. Vigawo vya 18: 1, 2, 3, 6, 9, 18 Vigawo vya 24: 1, 2, 3, 4, 6, 8, 12, 24 Vigawo vya 30: 1, 2, 3, 5, 6, 10, 15, 30 Kigawo kikubwa zaidi cha kawaida ni 6. Urefu mkubwa zaidi unaowezekana wa kila kipande ni: 6 m 8. Using prime factorization, determine the GCD of 42 and 63. Step 1: Tafuta vigawo vikuu vya 42. 42 = 2 × 21 = 2 × 3 × 7 Step 2: Tafuta vigawo vikuu vya 63. 63 = 3 × 21 = 3 × 3 × 7 Step 3: Tambua vigawo vikuu vya kawaida na uzizidishe. Vigawo vikuu vya kawaida ni 3 na 7. GCD = 3 × 7 = 21 GCD ya 42 na 63 ni: 21 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 Umefanya vizuri! Tuma swali linalofuata 📸