Time Chapter Eleven PDF

FOR ONLINE USE ONLY DO NOT DUPLICATE Chapter Eleven Time...

FOR ONLINE USE ONLY DO NOT DUPLICATE Chapter Eleven Time Introduction In Standard Four, you learnt how to read, write, add and subtract time in LY terms of hours and minutes. In this chapter, you will learn to change, multiply and divide time measurements. You will also learn to construct a calendar. This competence will help you in scheduling and controlling your time when N performing different activities. For example, it will help you adhere to school time table, transport time table, appointments and general proper time O management. Exercise 1: Revision SE Answer the following questions: U 1. Write the time in words and numerals for each of the following clocks: (a) 12 (b) 12 (c) 12 11 1 11 1 11 1 E 10 2 10 2 10 2 9 3 9 3 9 3 N 8 4 8 4 8 4 7 5 7 5 7 5 6 6 6 LI N _________ _________ _________ (d) (e) (f) O 12 12 12 11 1 11 1 11 1 10 2 10 2 10 2 9 3 9 3 9 3 R 8 4 8 4 8 4 7 5 7 5 7 5 6 6 6 FO _________ _________ _________ 173 MATH std 5.indd 173 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 2. For each of the following questions, draw a clock face with the hour and minute hands showing the following times: (a) Quarter past twelve (12:15) (b) Four o’clock (4:00) (c) Half past eight (8:30) (d) Quarter to ten (9:45) (e) Five minutes past eleven (11:05) LY 3. Write the following times in words: (a) 2:15 (b) 7:20 N (c) 5:30 (d) 8:45 O 4. hours minutes 5. hours minutes 6. hours minutes 2 10 9 44 3 10 + 4 25 + 1 SE 10 + 5 50 7. hours minutes 8. hours minutes 9. hours minutes U 4 30 8 48 6 30 – 2 20 – 3 40 + 4 40 E N 10. hours minutes 11. hours minutes 12. hours minutes 3 32 9 00 7 46 LI – 2 05 – 5 30 – 1 22 N O 13. hours minutes 5 12 + 1 49 R FO 14. The candidates started the examination at 9:15 in the morning and finished at 10.45 in the morning. What time did the candidates use for the examination? 174 MATH std 5.indd 174 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 15. An athlete sprinter started to run at 8.55 in the morning. If he used one hour and forty minutes to finish, at what time did he finish running? Constructing an annual calendar An annual calendar displays dates, weeks, months and year. It also indicates dates for national and international public holidays. Carefully study the following LY calendar, then identify the features you have observed. 2019 CALENDAR JANUARY FEBRUARY N Monday Tuesday Wes-day Thursday Friday Saturday Sunday Monday Tuesday Wes-day Thursday Friday Saturday Sunday 1 2 3 4 5 6 1 2 3 7 8 9 10 11 12 13 4 5 6 7 8 9 10 O 14 15 16 17 18 19 20 11 12 13 14 15 16 17 21 22 23 24 25 26 27 18 19 20 21 22 23 24 28 29 30 31 25 26 27 28 MARCH APRIL Monday 4 11 18 Tuesday 5 12 19 Wes-day 6 13 20 Thursday 7 14 21 Friday 1 8 15 22 Saturday 2 9 16 23 Sunday 3 10 17 24 SE Monday 1 8 15 22 Tuesday 2 9 16 23 Wes-day 3 10 17 24 Thursday 4 11 18 25 Friday 5 12 19 26 Saturday 6 13 20 27 Sunday 7 14 21 28 25 26 27 28 29 30 31 29 30 U MAY JUNE Monday Tuesday Wes-day Thursday Friday Saturday Sunday Monday Tuesday Wes-day Thursday Friday Saturday Sunday 1 2 3 4 5 1 2 6 7 8 9 10 11 12 3 4 5 6 7 8 9 E 13 14 15 16 17 18 19 10 11 12 13 14 15 16 20 21 22 23 24 25 26 17 18 19 20 21 22 23 27 28 29 30 31 24 25 26 27 28 29 30 N JULY AUGUST Monday Tuesday Wes-day Thursday Friday Saturday Sunday Monday Tuesday Wes-day Thursday Friday Saturday Sunday 1 2 3 4 5 6 7 1 2 3 4 LI 8 9 10 11 12 13 14 5 6 7 8 9 10 11 15 16 17 18 19 20 21 12 13 14 15 16 17 18 22 23 24 25 26 27 28 19 20 21 22 23 24 25 N 29 30 31 26 27 28 29 30 31 SEPTEMBER OCTOBER O Monday Tuesday Wes-day Thursday Friday Saturday Sunday Monday Tuesday Wes-day Thursday Friday Saturday Sunday 1 1 2 3 4 5 6 2 3 4 5 6 7 8 7 8 9 10 11 12 13 9 10 11 12 13 14 15 14 15 16 17 18 19 20 16 17 18 19 20 21 22 21 22 23 24 25 26 27 R 23 24 25 26 27 28 29 28 29 30 31 30 DECEMBER NOVEMBER FO Monday Tuesday Wes-day Thursday Friday Saturday Sunday Monday Tuesday Wes-day Thursday Friday Saturday Sunday 1 1 2 3 2 3 4 5 6 7 8 4 5 6 7 8 9 10 9 10 11 12 13 14 15 11 12 13 14 15 16 17 16 17 18 19 20 21 22 18 19 20 21 22 23 24 23 24 25 26 27 28 29 25 26 27 28 29 30 30 31 175 MATH std 5.indd 175 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 1. An annual calendar displays twelve months. 2. The names of the twelve months are: January, February, March, April, May, June, July, August, September, October, November and December. 3. There are months with 31, 30, 28 or 29 days. There are two types of years; a short year and a leap year. A short year is the year with 28 days in February, and a leap year is the year with 29 days in February. A leap year is divisible by 4, whereas, a short year is not divisible LY by 4. For example, the year 2016 was a leap year because it is divisible by 4 (2016 ÷ 4 = 504), but the year 2017 was a short year because the number N 2017 is not divisible by 4, that is, 2017 ÷ 4 = 504 remainder 1. O Reading an annual calendar and writing dates Reading a calendar Example 1 SE U Write the names of the months with 30 days. Answer E The names of the months with 30 days are; April, June, September and N November. LI Example 2 N Write the names of the days of a week. O Answer The names of the days in the week are; Monday, Tuesday, Wednesday, R Thursday, Friday, Saturday and Sunday. FO 176 MATH std 5.indd 176 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Writing dates A date is written using either words or by separating the numbers which represent the day, month and year with a full stop (.), a forward slash (/) or a horizontal dash (-) and other recognized formats. Example 1 LY Write the date 1/1/2018 in words. N Answer: First of January two thousand and eighteen. O Example 2 SE Write the date: 20th February, 2018 by separating numbers using full stops. U Answer: 20.2.2018. E Example 3 N Write the date 20.2.2018 using forward slashes. LI Answer: 20/2/2018. N O Example 4 Write the following date using dashes: Third of May, two thousand and R nineteen. FO Answer: 3 – 5 – 2019. 177 MATH std 5.indd 177 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 2 Answer the following questions: 1. Write down the names of the months with 31 days. 2. How many Sundays does the current year have? LY 3. Write in words the date of the first Monday of the month of July of the current year. N 4. Use dashes to write the date of the last Wednesday of the month of O January of the current year. SE 5. Which day is the date 28/2 of this year? Constructing and reading a monthly calendar U Of all months of a year, February has exactly 4 weeks in a short year. The other months have 4 weeks and few days. Each week has 7 days. The days of a week are: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday E and Sunday. These days of a week form a calendar for one month. N Use the following steps to construct a one month calendar. LI Steps: 1. Draw a rectangle. N 2. Inside the rectangle, draw seven vertical and six horizontal lines. These O divide the rectangle into a number of smaller rectangles. 3. Write along the first row of small rectangles from left to right, the names of days, starting from Monday to Sunday. R 4. Find out on what day of the week was the last date of the previous month. FO 5. Start by writing the digit 1 for the first day of the current month. 6. Continue writing the day numbers up to the last day of the month. 178 MATH std 5.indd 178 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE The following table illustrates a monthly calendar: Wesnesday Thursday Saturday Tuesday Monday Sunday Friday 1 2 3 4 5 6 LY 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 N 28 29 30 31 O Exercise 3 Answer the following questions: SE 1. Construct a Calendar for the month of November this year and use it to answer the following questions: U (a) Which day is 30th of the month? (b) What is the date of the first Sunday of the month? E 2. Construct a calendar for the month of March this year and use it to N answer the following questions: (a) Which day is 28th of the month? LI (b) Write the date for the second Friday of the month. N 3. Lilian is a nurse at a Mawenzi hospital. She started her annual leave O on 28/5/2018 and returned to work on 25/6/2018. How many days was her annual leave? R 4. For the years, 1996, 1997, 1998, 1999, 2000, 2001, 2002, FO 2003, and 2004: (a) What were the leap years? (b) What were the short years? 179 MATH std 5.indd 179 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 5. Adamu attended a six months training programme on environmental care. If the training started on 1/2/2015, on what date did he finish the training programme? Converting time measurements In time measurement conversions, you must consider the relationship between time measurements. LY Relationship between different time measurements: N 1 Hour = 60 minutes 1 Day = 24 hours O 1 Week = 7 days 1 Month = 28 days for February of the short year, SE 29 days for February of the leap year and 30 or 31 days for the other months. 1 Year = 12 months U 1 Leap year = 366 days 1 Short year = 365 days E Remark: The relationship between months and weeks vary depending on N the given month. LI Example 1 N How many days are there in 72 hours? O Solution 1 day has 24 hours R 72 hours = 72 ÷ 24 = 3 days. FO Therefore, there are 3 days in 72 hours. 180 MATH std 5.indd 180 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 2 How many weeks are there in 91 days? Solution 1 week has 7 days. 91 days = 91 ÷ 7 = 13 weeks. LY Therefore, there are 13 weeks in 91 days. N Example 3 O How many days are there in 3 leap years? Solution 1 leap year has 366 days. SE 3 leap years have 3 × 366 = 1 098 days. U Therefore, 3 leap years have 1 098 days. E Example 4 N Juma walked 1000 metres in 15 minutes. Convert the minutes into hours. LI Solution N 60 minutes are the same as 1 hour. _15 O 15 minutes are the same as 15 ÷ 60 = ​​  ​​ hour. 60 15 _ 1 _ Simplification gives ​​   ​ = ​   ​​. R 60 4 1 _ FO Therefore, 15 minutes are the same as ​​   ​​ of an hour. 4 181 MATH std 5.indd 181 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 4 Answer the following questions: 1. How many weeks and days are there in the following number of days? (a) 48 (b) 60 (c) 19 (d) 112 (e) 705 2. Convert each of the following time into days: (a) 12 weeks and 1 day (b) 36 weeks and 6 days LY (c) 72 weeks and 4 days (d) 80 weeks N 3. A bridge was constructed in 34 days. How many weeks and days did it take to construct the bridge? O 4. If it takes 72 hours for a bus to travel from one city to another. How SE many days does this bus take to travel to its destination? 5. The green vegetables in the garden took 30 days to mature. Convert U this time into weeks and days. 6. Change 360 minutes into hours. E N 7. How many minutes are there in one day? LI 8. Convert 28 hours into days. N 9. Convert 70 hours into minutes. O 10. How many hours are there in 10 days? R Multiplication of time measurements FO When multiplying time measurement by the given number, start by multiplying the smaller time measurement followed by the larger time measurement. 182 MATH std 5.indd 182 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Multiplication of hours and minutes When multiplying hours and minutes, remember that 1 hour = 60 minutes. Start by multiplying minutes followed by hours. Example 1 hours minutes LY 2 10 × 3 N O Solution Steps: 1. Multiply minutes: ​3 × 10 = 30​ SE hours minutes minutes. Write 30 in the minutes 2 10 U position. × 3 30 E 2. Multiply hours: ​3 × 2 = 6​ hours minutes N hours. Write 6 in the hours 2 10 position. LI × 3 6 30 N Therefore, the answer is 6 hours and 30 minutes. O Example 2 R hours minutes FO 7 21 × 4 183 MATH std 5.indd 183 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution Steps: 1. Multiply minutes: ​4 ×   21 = 84​ minutes. 1 hour = 60 minutes. hours minutes Therefore, 84 minutes = 1 hour 7 21 and 24 minutes. Write 24 in the × 4 minutes position and add 1 hour 24 LY to the product of hours. 2. Multiply hours: ​4 × 7 = 28​hours. hours minutes N Add 1 hour to the product of 28 7 21 hours to get 29 hours. Write 29 × 4 O in the hours position. 29 24 SE Therefore, the answer is 29 hours and 24 minutes. Example 3 U hours minutes 5 16 E × 6 N LI Solution N hours minutes O 5 16 × 6 R 31 36 FO Therefore, the answer is 31 hours and 36 minutes. 184 MATH std 5.indd 184 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 5 Answer the following questions: 1. hours minutes 2. hours minutes 3. hours minutes 4 10 3 15 6 13 LY × 2 × 3 × 5 N 4. hours minutes 5. hours minutes 6. hours minutes O 7 23 4 16 1 05 × 4 × 6 × 8 SE U 7. hours minutes 8. hours minutes 9. hours minutes 6 20 2 12 7 05 × 3 × 9 × 3 E N 10. hours minutes LI 10 00 × 2 N O Multiplication of days and hours R When multiplying days and hours, you have to remember that 1 day = 24 hours. Start by multiplying hours followed by days. FO 185 MATH std 5.indd 185 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 1 days hours 4 3 × 7 LY Solution Steps: N 1. Multiply hours: 7 × 3 = 21 hours. days hours O Write 21 in the hours position. 4 3 × 7 SE 21 2. Multiply days: 7 × 4 = 28 days. days hours U Write 28 in the days position. 4 3 × 7 28 21 E N Therefore, the answer is 28 days and 21 hours. LI Example 2 N days hours O 6 12 × 4 R FO 186 MATH std 5.indd 186 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 1. Multiply hours: 4 × 12 = 48 hours. But 1 day = 24 hours. Therefore, days hours 48 hours = 2 days. Write 0 in the 6 12 hours position, and add 2 days × 4 to the product of days. 0 2. Multiply days, 4 × 6 = 24 days. LY Add the 2 days converted from days hours hours to 24 days to get 26 days. 6 12 Write 26 in the days position. × 4 N 26 0 O Therefore, the answer is 26 days. Example 3 SE U days hours Solution 8 20 days hours E × 2 8 20 × 2 N 17 16 LI Therefore, the answer is 17 days and 16 hours. N Exercise 6 O Answer the following questions: R 1. days hours 2. days hours 3. days hours FO 5 10 11 9 8 11 × 2 × 3 × 5 187 MATH std 5.indd 187 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 4. days hours 5. days hours 6. days hours 24 5 15 15 10 10 × 4 × 3 × 6 7. days hours 8. days hours 9. days hours LY 8 22 7 7 11 1 × 10 × 7 × 15 N O 10. days hours 20 4 × 9 SE U Multiplication of weeks and days When multiplying weeks and days, you have to remember that, 1 week = 7 days. Start by multiplying days followed by weeks. E N Example 1 LI N weeks days 2 2 O × 3 R FO 188 MATH std 5.indd 188 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution Steps: 1. Multiply days: 3 × 2 = 6 days. weeks days Write 6 in the days’ position. 2 2 × 3 6 LY 2. Multiply weeks: 3 × 2 = 6 weeks. weeks days Write 6 in the weeks’ position. 2 2 N × 3 6 6 O Therefore, the answer is 6 weeks and 6 days. Example 2 SE U weeks days 5 3 × 4 E N Solution LI Steps: N 1. Multiply days: 4 × 3 = 12 days. But 1 weeks days O week = 7 days. Therefore, 12 days = 1 week and 5 days. Write 5 in the 5 3 days position, and then add 1 week × 4 R to the product of weeks. 5 FO 189 MATH std 5.indd 189 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 2. Multiply weeks: 4 × 5 = 20 weeks. weeks days Add 1 week converted from days 5 3 to 20 weeks to get 21 weeks. × 4 Write 21 in the weeks’ position. 21 5 Therefore, the answer is 21 weeks and 5 days. LY Example 3 Solution N weeks days weeks days O 10 6 × 6 10 6 × 6 SE 65 1 Exercise 7 U Answer the following questions: E 1. weeks days 2. weeks days 3. weeks days 7 1 3 3 5 4 N × 6 × 3 × 7 LI N 4. weeks days 5. weeks days 6. weeks days 11 6 17 2 10 5 O × 2 × 3 × 4 R 7. weeks days 8. weeks days 9. weeks days FO 7 4 12 4 2 2 × 6 × 5 × 9 190 MATH std 5.indd 190 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 10. weeks days 1 5 × 5 Multiplication of years and weeks LY When multiplying years and weeks, you have to remember that 1 year = 52 weeks. Start by multiplying weeks followed by years. N Example 1 O years weeks 8 6 × 5 SE U Solution Steps: E 1. Multiply weeks: 5 × 6 = 30 weeks. N years weeks Write 30 in the weeks position. 8 6 LI × 5 30 N 2. Multiply years: 5 × 8 = 40 years. years weeks O Write 40 in the years position. 8 6 × 5 R 40 30 FO Therefore, the answer is 40 years and 30 weeks. 191 MATH std 5.indd 191 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 2 years weeks 5 21 × 4 LY Solution Steps: N 1. Multiply weeks: 21 × 4 = 84 weeks. O But 1 year = 52 weeks. So, 84 weeks years weeks = 1 year and 32 weeks. Write 32 in 5 21 the weeks position, and add 1 year to the product of years. SE × 4 32 U 2. Multiply years: 5 × 4 = 20 years. Add the converted 1 year to the 20 years to get 21 years. Write 21 in years weeks E the years position. 5 21 N × 4 21 32 LI N Therefore, the answer is 21 years and 32 weeks. O Example 3 R years weeks FO 3 25 × 4 192 MATH std 5.indd 192 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution years weeks 3 25 × 4 13 48 LY Therefore, the answer is 13 years and 48 weeks. N Exercise 8 O Answer the following questions: 1. years weeks 2. years weeks 3. years weeks × 10 10 14 5 × SE 7 34 8 × 5 5 U 4. years weeks 5. years weeks 6. years weeks E 25 30 35 4 24 15 × 6 × 8 × 6 N LI 7. years weeks 8. years weeks 9. years weeks N 15 15 175 1 1 50 0 O × 5 × 4 × 4 R 10. years weeks FO 20 6 × 9 193 MATH std 5.indd 193 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Multiplication of years and months When multiplying years and months, you have to remember that 1 year = 12 months. Start by multiplying months followed by years. Example 1 LY years months 1 4 × 2 N O Solution Steps: 1. Multiply months: 2 × 4 = 8 months. SE years months Write 8 in the months position. 1 4 U × 2 8 E 2. Multiply years: 2 × 1 = 2 years. years months N Write 2 years in the years position. 1 4 LI × 2 2 8 N Therefore, the answer is 2 years and 8 months. O Example 2 R years months FO 3 2 × 8 194 MATH std 5.indd 194 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution Steps: 1. Multiply months: 8 × 2 = 16 months. years months But 1 year = 12 months. 3 2 So, 16 months = 1 year and 4 LY × 8 months. Write 4 in the months 4 position, and add 1 year to the N product of years. O 2. Multiply years: 8 × 3 = 24 years. Add the converted 1 year to 24 years to get 25 years. Write 25 SE years 3 months 2 in the years position. × 8 U 25 4 E N Therefore, the answer is 25 years and 4 months. LI Example 3 N years months Solution O 6 5 years months × 6 6 5 R × 6 38 6 FO Therefore, the answer is 38 years and 6 months. 195 MATH std 5.indd 195 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 9 Answer the following questions: 1. years months 2. years months 3. years months 5 2 11 8 9 3 LY × 4 × 2 × 7 N 4. years months 5. years months 6. years months O 15 10 22 11 18 8 × 6 × 3 × 8 7. years months SE 8. years months 9. years months U 20 7 16 4 12 10 × 5 × 4 × 2 E 10. years months N 30 1 LI × 6 N O Division of time measurements Division of hours and minutes R In dividing hours and minutes, remember that 1 hour = 60 minutes. Start by dividing hours, then divide minutes. FO 196 MATH std 5.indd 196 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 1 hours minutes 3 12 45 1. Divide 12 hours by 3 to get 4 hours. hours minutes Write 4 in the hours position. LY 3 12 45 4 N 2. Divide 45 minutes by 3 to get hours minutes 15 minutes. Write 15 in the minutes 3 12 45 O position. 4 15 SE Therefore, the answer is 4 hours and 15 minutes. Example 2 U hours minutes 3 22 24 E N Solution Steps: LI 1. Divide 22 hours by 3 to get 7 hours N and 1 hour remainder. Change the 1 hours minutes O hour remainder into minutes, that is, 3 22 24 1 hour = 60 minutes. 7 R 2. Add the minutes that is, hours minutes FO 60 + 24 = 84 minutes. 3 21 84 7 197 MATH std 5.indd 197 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 3. Divide 84 minutes by 3 to get hours minutes 28 minutes. Write 28 in the minutes 3 21 84 position. 7 28 Therefore, the answer is 7 hours and 28 minutes. Example 3 LY hours minutes 7 30 20 N O Solution hours minutes 7 30 20 4 20 SE U Therefore, the answer is 4 hours and 20 minutes. Exercise 10 E Answer the following questions: N LI 1. hours minutes 2. hours minutes 3. hours minutes 5 15 20 3 14 15 12 125 24 N O 4. hours minutes 5. hours minutes 6. hours minutes 5 10 40 4 30 20 5 44 15 R FO 7. hours minutes 8. hours minutes 7 47 50 5 24 40 198 MATH std 5.indd 198 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Division of days and hours In dividing days and hours, remember that 1 day = 24 hours. Start dividing the days followed by hours. Example 1 days hours 5 15 20 LY N Solution Steps: O 1. Divide 15 days by 5 to get 3 days. days hours Write 3 in the days position. 5 15 20 SE 2. Divide 20 hours by 5 to get 4 hours. 3 days hours U Write 4 in the hours position. 5 15 20 3 4 E Therefore, the answer is 3 days and 4 hours. N LI Example 2 N days hours O 4 38 4 R FO 199 MATH std 5.indd 199 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution Steps: 1. Divide 38 days by 4 to get 9 days days hours and 2 days remainder. Write 9 in 4 38 4 the days position. Change 2 days 9 remainder into hours, that is, 1 day = 24 hours. Thus, 2 days = 2 x 24 hours = 48 hours. LY 2. Add the hours, that is, days hours 48 + 4 = 52 hours. 4 36 52 N 9 O 3. Divide 52 hours by 4 to get 13 hours. days hours Write 13 in the hours position. 4 36 52 SE 9 13 U Therefore, the answer is 9 days and 13 hours. Example 3 E N days hours 5 85 15 LI N Solution O days hours 5 85 15 R 17 3 FO Therefore, the answer is 17 days and 3 hours. 200 MATH std 5.indd 200 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 11 Answer the following questions: 1. days hours 2. days hours 3. days hours 4 8 12 5 10 5 8 15 16 LY 4. days hours 5. days hours 6. days hours N 5 14 9 7 15 18 13 18 10 O 7. days hours 8. days hours 9. days hours 6 15 0 10 24 SE 4 8 32 8 10. days hours U 7 18 9 E Division of weeks and days N In dividing time involving weeks and days, remember that 1 week = 7 days. LI Always start dividing weeks followed by days. N Example 1 O R weeks days FO 4 48 4 201 MATH std 5.indd 201 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution Steps: 1. Divide 48 weeks by 4 to get 12 weeks. weeks days Write 12 in the weeks position. 4 48 4 12 2. Divide 4 days by 4 to get 1 day. Write 1 weeks days LY in the days position. 4 48 4 12 1 N Therefore, the answer is 12 weeks and 1 day. O Example 2 weeks days SE 10 51 3 U Solution E Steps: 1. Divide 51 weeks by 10. You weeks days N will get 5 weeks and 1 week 10 51 3 LI remainder. Write 5 in the weeks 5 position. Change 1 week N remainder into days, that is, 1 week = 7 days. Add 7 days to O 3 days to get 10 days. 2. Divide 10 days by 10 to get weeks days R 1 day. Write 1 in the days position. 10 50 10 FO 5 1 Therefore, the answer is 5 weeks and 1 day. 202 MATH std 5.indd 202 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Example 3 weeks days 5 16 13 Solution LY weeks days 5 16 13 N 3 4 O Therefore, the answer is 3 weeks and 4 days. Exercise 12 SE Answer the following questions: U 1. weeks days 2. weeks day 3. weeks days E 3 33 3 5 45 5 17 72 6 N 4. weeks days 5. weeks days 6. weeks days LI 9 16 5 8 35 3 6 13 5 N O 7. weeks days 8. weeks days 9. weeks days 9 28 2 4 30 6 15 240 0 R FO 10. weeks days 20 142 6 203 MATH std 5.indd 203 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Division of years and weeks In dividing time involving years and weeks, remember that 1 year = 52 weeks. Always, start dividing years followed by weeks. Example 1 LY years weeks 6 24 12 N O Solution Steps: 1. Divide 24 years by 6. You will SE years weeks get 4 years. Write 4 in the 6 24 12 U years position. 4 2. Divide 12 weeks by 6. You will years weeks E get 2 weeks. Write 2 in the weeks 6 24 12 N position. 4 2 LI Therefore, the answer is 4 years and 2 weeks. N O Example 2 R years weeks FO 6 99 12 204 MATH std 5.indd 204 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution Steps: 1. Divide 99 years by 6 to get 16 years weeks years and 3 years remainder. 6 99 12 Write 16 in the years position. 16 Change the 3 years remainder into weeks, that is, 3 × 52 = 156 weeks. LY Add weeks: 12 + 156 = 168 weeks. 2. Divide 168 weeks by 6 to get years weeks N 28 weeks. Write 28 in the weeks 6 96 168 position. O 16 28 SE Therefore, the answer is 16 years and 28 weeks. U Example 3 E years weeks N 5 44 12 LI N Solution years weeks O 5 44 12 8 44 R Therefore, the answer is 8 years and 44 weeks. FO 205 MATH std 5.indd 205 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Exercise 13 Answer the following questions: 1. years weeks 2. years weeks 3. years weeks 2 74 42 6 480 18 4 17 8 LY 4. years weeks 5. years weeks 6. years weeks 52 104 0 47 124 38 8 60 0 N O 7. years weeks 8. years weeks 9. years weeks 5 54 12 11 670 30 12 125 4 10. years weeks SE 17 365 9 U E Division of Years and months In dividing time measurements that involve years and months, remember N that, 1 year = 12 months. Always, start dividing years followed by months. LI Example 1 N O years months 2 6 8 R FO 206 MATH std 5.indd 206 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Solution Steps: 1. Divide 6 years by 2 to get years months 3 years. Write 3 in the years 2 6 8 position. 3 2. Divide 8 years by 2 to get years months LY 4 months. Write 4 in the months 2 6 8 position. 3 4 N Therefore, the answer is 3 years and 4 months. O Example 2 SE years months U 5 98 4 Solution E Steps: N 1. Divide 98 years by 5 to get years months 19 years and 3 years remainder. Write 5 98 4 LI 19 in the years position. Change the 19 N 3 years remainder into months, that is, 1 year = 12 months. Thus, O 3 years = 3 x 12 months = 36 months. Add the obtained 36 months to the 4 R months to get 40 months. FO 207 MATH std 5.indd 207 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 2. Divide 40 months by 5 to get 8 months. years months Write 8 in the months position. 5 95 40 19 8 Therefore, the answer is 19 years and 8 months. LY Example 3 years months N 9 98 3 O Solution 9 years 98 3 months SE U 10 11 Therefore, the answer is 10 years and 11 months. E N Exercise 14 LI Work out the following questions: N 1. years months 2. years months 3. years months O 7 98 7 8 87 4 5 98 9 R 4. years months 5. years months 6. years months FO 10 105 10 15 51 3 11 115 6 208 MATH std 5.indd 208 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 7. years months 8. years months 9. years months 18 216 0 21 127 9 8 1866 8 10. years months 11 440 0 LY Exercise 15 N Answer the following questions: O 1. days hours 2. days hours 3. weeks days × 4 2 10 4 × SE15 2 2 × 5 6 U 4. weeks days 5. years weeks 6. years weeks E 12 14 17 19 20 40 × 5 × 13 × 10 N LI 7. days hours N 5 16 11 O 8. Change each of the following times into minutes: 1 1 R (a) 7 hours (b) 4 _ ​ ​ hours (c) 2 _ ​ ​ hours 2 2 FO 9. Which of the following years is a leap year: 2008, 2009, 2010 and 2011? 209 MATH std 5.indd 209 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE 10. Change 48 hours into days. 11. Change 124 hours into days and hours. 12. Lusia visited her sister Fausta. She stayed with her for 144 hours. How many days did she stay with her sister? LY 13. Write the total numbers of days for the months of June, July and August. N 14. How many years and months are there in 65 months? O 15. A student was required to study Mathematics at school for the whole SE year 2017. If the student was on leave in June and December, how many days was the student at school during that year? U 16. A year in which February has 29 days is known as a _____ year. E 17. In a normal cycle of one year, which months follow each other and N have 31 days? LI 18. How many weeks and days are there in April? N O 19. Which among the two years, 2000 and 2006 had fewer days than the other? R 20. A train left Dar es Salaam to Mwanza on Thursday afternoon at 2.00 FO p.m. If the train travelled for 58 hours, on which day did the train arrive in Mwanza? 210 MATH std 5.indd 210 30/07/2021 14:49  FOR ONLINE USE ONLY DO NOT DUPLICATE Summary 1. In multiplying time measurements by a number, start by multiplying the smaller measurement. When the product of the smaller unit is larger than 1 unit of the larger time measurement, convert it into the larger unit and write the remainder in the smaller time unit. LY 2. In dividing time measurements by a number, start by dividing the larger measurements, followed by smaller time measurements. 3. In multiplying or dividing time measurements by a number, take note of N the relationship that exists between the given time measurement units. 4. A year which is divisible by 4 is known as a leap year. In a leap year, O February has 29 days. 5. A year which is not divisible by 4 is known as a short year. In a short year, February has 28 days. SE U E N LI N O R FO 211 MATH std 5.indd 211 30/07/2021 14:49