6 . 5 8 3 3 3 3 3 ° ' " ° ' " ° ' " ° ' " 15 min 6 h 20 min 6 h 15 min 20 min 6 h 35 min
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C H A P T E R 1 W O R K I N G M A T H E M A T I C A L LY, P R O B L E M S O LV I N G A N D N U M B E R
Convert this calculator answer (in hours) into an answer in hours and minutes by pressing:
˝ ˝ ˝
6 h 35 min 0 s
the total time is 6 h 35 min.
Note: Many calculators automatically give the final answer in hours
and minutes.
Check your manual to determine which keys you need to press.
●
2 Convert 372 min into hours and minutes.Method 1 Method 2
As 1 h 60 min: 372 min36702h
6 h (6 60) min 61620h
360 min 6 h 12 min
So 372 min (360 12) min Note: 61620h 615h
6 h 12 min However, in this case the
answer is required in hours and minutes, so we do not simplify the fraction.
Method 3: Calculator method
372 min36702h
On a calculator, press 372 60
˝
decimal hours
To convert this answer (in hours) into an answer in hours and minutes, press:
˝ ˝ ˝
6 h 12 min 0 s
372 min 6 h 12 min
Note: With some calculators, you may need to press
Check your manual to determine which keys you need to press.
° ' " INV 6 ° I 2 ° 0 ° ' " 6 . 2 6 ° 3 5 ° 0 ° ' " INV 6.2 h 615h 6 h (15 60) min 6 h 12 min
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7 Express in 24-hour time:a 5 am b 8 pm c 6:55 am d 7:15 pm
e 11:20 am f 11:20 pm g 3:36 pm h 11:59 pm
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8 Write each time in 12-hour time. Remember to put am or pm.a 0700 h b 1300 h c 1600 h d 0305 h
e 1854 h f 2345 h g 2010 h h 0011 h
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9 How long is it from:a 5 am to noon? b 6:30 pm to midnight? c 9 am to 1:45 pm?
d 0215 h to 1345 h? e 1405 h to 1950 h? f 2130 h to 0420 h?
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10 What is the time 1 h 15 min:a after 6 pm? b before 11 pm? c after 2:30 pm?
d before 0710 h? e after 1150 h? f before 0025 h?
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11 Find the sum of:a 38 min and 22 min b 17 min and 55 min
c 1 h 17 min and 54 min d 2 h 34 min and 3 h 49 min
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12 Find:a 2 (4 h 13 min) b 3 (5 h 26 min)
c 5 (3 h 25 min) d 7 (2 h 32 min)
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13 How many minutes are there in:a one day? b one week?
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14 How many seconds are there in:a one day? b one week?
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15 Convert into hours and minutes:a 87 min b 190 min c 135 min d 270 min
e 450 min f 249 min g 357 min h 700 min
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16 Adelchi worked from 7:30 am to 4:15 pm. How long is this?■
17 Elena slept 8 h 10 min each night for a week. How much sleep did she get altogether?■
18 If the walk to school takes 19 min, at what time must I leave home to get to school at 8:15 am?■
19 Ada arrived at the station at 9:25 am. The next train arrived at 8 min to 10. How many minutes did she wait for the next train?■
20 A heart beats 76 times every minute. How many times does it beat in a week?■
21 Margaret and Harold left Bundanoon at 20 to 11 in the morning and arrived in Blaxland 212h later. What was their time of arrival?■
22 Colin is booked to leave on an overseas flight on 4 July. He must pay his fare at least 21 days before departure.To find the sum of 2 or more numbers,
■
23 Copy and complete the table below for the settings on a DVD player that uses a 24-hour display:■
24 This table shows the arrival times at different wharves of a ferry that leaves Circular Quay at 7:35 am.How long would it take to travel from:
a Circular Quay to Greenwich?
b Circular Quay to Gladesville?
c Greenwich to Gladesville?
d Long Nose Point to Valentia Street?
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25 The table shows the times that trains leave Blacktown station and when they arrive in the city.Greg missed the 9:19 am train by 5 min and waited for the next train. How long did it take him to travel to the city from the time he arrived at Blacktown station?
37
C H A P T E R 1 W O R K I N G M A T H E M A T I C A L LY, P R O B L E M S O LV I N G A N D N U M B E R 1910 in 24-hour time is often displayed as: I 9 : I 0Program Timer settings Length of time
(12-hour time) (24-hour time) (in hours and minutes)
a 9:00 am to 11:30 am b 8:45 am to 12:45 pm c 1:20 pm to 8:50 pm d 3:30 pm to 11:45 pm e 0215 to 1000 f 0620 to 1910 g 0008 to 0815 h 11:45 am to … 1 h 25 min i … to 12:05 pm 2 h 50 min j … to 2210 3 h 17 min
Wharf Time of arrival
Circular Quay Departs 7:35 am
Long Nose Point 7:47 am
Greenwich 7:50 am
Cockatoo Island 7:53 am Valentia Street 7:56 am Gladesville 8:04 am
Depart Blacktown Arrive in city
9:04 am 9:56 am 9:19 am 10:09 am 9:27 am 10:15 am 9:46 am 10:39 am
W O R K I N G M A T H E M A T I C A L L Y
Assignment
Calendars
■
1 Investigate the Chinese year and calendar.■
2 The length of the tropical year (or correct year) is measured from the spring equinox in the northern hemisphere. Investigate this and find the possible dates for it. Similarly, investigate the autumn equinox.■
3 The month of January was named after the two-faced Roman god Janus. Investigate the origins of the names of other months.■
4 Sunday was originally so namedbecause it was the first day of the week and was considered sacred to the sun. It was observed as a day of rest and worship. Investigate the origins of the names of other days of the week.
■
5 Why was Stonehenge built? Where is it? How are the giant stones arranged? When was it built?■
6 Why is the International Date Line important in time-keeping?■
7 What amazing things are carved in the Aztec calendar (or ‘Sunstone’)? How did it tell time? What is in its centre? What do the different symbols mean?Suggestions
Work in small groups and assign different topics from the above list to each member of your group.
Research the topics at your school or
local library, on computer CD encyclopaedia packages, or on the Internet.
Present your assignment on one A4 page. The Aztec calendar stone was quarried from a rock weighing 50 tonnes! It was only unearthed in 1790.
The Mayans had a sun calendar and used special numerals shaped like human faces for their records of dates. These were carved on stone columns called steles.
P R O B L E M S O L V I N G 1
39
C H A P T E R 1 W O R K I N G M A T H E M A T I C A L LY, P R O B L E M S O LV I N G A N D N U M B E R
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1 A clock takes 3 seconds to strike 3 o’clock. How long does it take to strike 6 o’clock?■
2 When doing a calculator question, Tania cubed 1.1 instead of squaring it. How much greater was her answer than it should have been?■
3 A 2-digit number with identical digits is multiplied by 99. What is the answer when the third digit from the left is 5?■
4 Twelve tickets (numbered 1–12) were folded up and put in a box. They were then drawn out in pairs, and the total of each pair was written down. These totals were 4, 6, 13, 14, 20 and 21. What were the numbers on the pairs of tickets?■
5 Working backwardsThree young children were playing a game that involved trying to throw round lollies into a mug. If a player missed, he or she gave the other two children enough lollies to double the number they already held. Each child had one turn. Each child missed. They then counted the number of lollies they had—all three children had
40 lollies each.
How many did each one have to start, if they all had different amounts?
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6 Systematic countingA local council decided to issue its residents with new luminous house numbers.
a How many digits are needed for the 269 houses in Ozone Street?
b How many of each digit (0 to 9) are needed?
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7 What two numbers, one 2-digit and one 3-digit, both made of odd digits, give the greatest product?■
8 a Write as many facts as you can about the numbers 2004 and 2005. Include their factors.b Write 2001 as the sum of two numbers.
i What is the greatest possible difference of two such numbers? ii What is the greatest possible product?
c Write 2001 as the sum of three numbers. What is the greatest product of three such numbers?
■
9 A single-digit number, when added to another single-digit number, gives a single-digit answer. Zero cannot be used. A number can be used more than once.a What is the smallest possible sum?
b What is the largest?
c How many different ways are there of getting a single-digit answer?
d How many ways are there of adding a 2-digit number to a 2-digit number to get a 2-digit answer? Check that you have them all!
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