Logical Class

Class 5 / Mathematics Course Book 2 / Distance, Time and Temperature / Distance, Time and Temperature

Distance, Time and Temperature

Distance

Distance is a numerical description of how far apart objects are.

Conversion of Units of Lengths

We can covert the unit of distance from one unit to another using the given chart.

Kilometres to metres

We can convert Kilometres to metres by multiplying the kilometres with 1000.

For example, 3 km = 3 × 1000 = 3000 m

For changing metres to kilometres we divide the metres by 1000.

For example, 21000 m = \(21000\over 1000\) = 21 km

Metres to centimeters

We can convert metres to centimetres by multiplying the metres with 100.

For example, 2.5 m = 2.5 × 100 = 250 cm. For changing centimetres to metres we divide the centimetres by 100.

For example,

3500 cm = \(3500 \over 100\) = 35 m

Centimetres to millimeters

We can convert centimetres to millimetres by multiplying the centimetres with 10.

For example, 6 cm = 6 × 10 = 60 mm. For changing millimetres to centimetres we divide the millimetres by 10.

For example,

500 mm = \(500 \over10\) = 50 cm

Example 1 Convert 25 km to metres.

Solution

25 kilometres

∴ 1 kilometre = 1000 metres.

25 kilometres = 25 × 1000 m

= 25,000 metres

Example 2 Convert 15 metres to centimetres.

Solution 15 metres

∴ 1 metre = 100 centimetre

15 metres = 15 × 100 cm

= 1500 cm

Example 3 Convert 5 centimetres to millimetres.

Solution 5 centimetres

∴ centimetre = 10 mm

5 centimetres = 5 × 10 mm

= 50 mm

Distance, Time and Temperature

Time

Time is measured using seconds, minutes, hours, days, weeks, months and years. Clocks measure time in seconds, minutes, hours. Calendars are used to keep the records of days, weeks, months and years.

Conversion of hours to minutes, minutes to seconds and vice versa

In our daily life we need to perform conversions between seconds, minutes and hours. Now we will learn how to. perform these conversions. For converting, units of time chart given is helpful.

Conversion of hours to minutes

As 1 hour = 60 minutes so to convert hours to minutes we multiply number of hours by 60. Following examples show how to convert hours to minutes

Example 1 Convert the following hours to minutes:

i. 3 hours ii. 11 hours 55 minutes iii. 2\(1 \over 4\) hours

Solution
1. 3 hours = 3 × 60 = 180 minutes.
2. 11 hours 55 minutes = 11 × 60 + 55 = 660 + 55 = 715 minutes.
3. 2\(1 \over 4\) hours =\(9 \over 4\) × 60 = 9 × 15 = 135 minutes.
Conversion of minutes to hours

As 60 minutes = 1 hour or 1 minute = so to convert minutes to hours we divide number of minutes by 60. Following examples show how to convert minutes to hours.

Example Convert the following minutes to hours:

i. 900 minutes ii. 350 minutes iii. 90 minutes

Solution
1. 900 minutes = \(900 \over60 \)= 15 hours
2. 350 minutes = \(350 \over60 \) = 5 \(50 \over60 \)= 5 hours and 50 minutes
3. 90 minutes = \(90 \over60 \) = 1 \(30 \over60 \)= 1 hour and 30 minutes
Conversion of minutes to seconds

As 1 minute = 60 seconds so to convert minutes to seconds we multiply number of minutes by 60. Following examples show how to convert minutes to seconds.

Example Convert the following minutes to seconds

1. 10 minutes ii. 48 minutes

Solution
1. 10 minutes = 10 × 60 = 600 seconds
2. 48 minutes = 48 × 60 = 2880 seconds
Conversion of seconds to minutes

As 60 seconds = 1 minute or 1 second =\(1 \over60\) so to convert seconds to minutes we divide number of seconds by 60. Following examples show how to convert seconds to minutes

Example Convert the following seconds to minutes

i. 600 seconds ii. 540 seconds

iii. 350 seconds iv. 90 seconds

Solution

600 seconds = \(600 \over 60\) = 10 minutes

540 seconds = \(540 \over60\)= 9 minutes

350 seconds = \(350\over 60\)= 5\(50\over 60\)

= 5 minutes and 50 seconds

90 seconds = \(90\over60\)=1\(30 \over 60\)

= 1 minute and 30 seconds

Addition and subtraction of units of time with carrying / borrowing

Addition of Units of Time with carrying

Example Add.
1. 55 minutes, 45 minutes
2. 2 hours 30 minutes, 3 hours 58 minutes
3. 8 hours 45 minutes 40 seconds, 7 hours 21 minutes 35 seconds
4. 9 hours 30 minutes 47 seconds, 3 hours 47 minutes 58 seconds
5. 18 hours 45 minutes 50 seconds, 15 hours 55 seconds, 10 hours 40 minutes
Subtraction of Units of Time with Borrowing

The process of subtraction is illustrated in the following example.

Example Subtract.
1. 4 hour 10 minutes from 6 hour 25 minutes
2. 1 hour 35 minutes from 2 hour 18 seconds
3. 2 hour 52 minutes 24 seconds from 4 hour 10 minutes 20 seconds
4. 1 hour 5 minutes 35 seconds from 8 hour 5 minutes
Solution

4 hour 10 minutes from 6 hour 25 minutes

1 hour 35 minutes from 2 hour 18 seconds

2 hour 52 minutes 24 seconds from 4 hour 10 minutes 20 seconds

1 hour 5 minutes 35 seconds from 8 hour 5 minutes

Conversion of years to months, months to days, weeks to days and vice versa

Now we learn to perform conversion between days, weeks, months and years

Conversion of years to months

Following example shows how to convert years to months

Example Convert:

i. 15 years to months ii. 10 years 11 months to months

Solution 1 year = 12 months
1. 15 years = 15 × 12 = 180 months
2. 10 years 11 months = 10 × 12 + 11 = 120 + 11 = 131 months
Conversion of months to years

Following example shows how to convert months to years

Example Convert:

1. 132 months to years ii. 85 months to months and years

Solution 1 month =\(1\over 12\) year
1. 132 months = \(132\over 12\)= 11 years
2. 85 months = \(85\over 12\)= 7\(1\over 12\) = 7 years 1 month
Conversion of months to days

Following example shows how to convert months to days.

Example Convert:

i.4 months to days ii. 20 months 15 days to days

Solution

1 month = 30 days
1. 4 months= 4 × 30 = 120 days
2. ii. 20 months 15 days = 20 × 30 + 15 = 600 + 15 = 615 days
Conversion of days to months

Following example shows how to convert days to months.

Example Convert:

i. 480 days to months ii. 760 days to months and days

Solution 1 day = \(1\over 30\)months
1. 480 days = \(480\over 30\) = 16
2. 760 days = \(760\over 30\)= 25 \(10\over 30\)= 25 months 10 days
Conversion of weeks to day

Following example shows how to convert weeks to days

Example Convert

1. 18 weeks to days ii. 20 weeks 15 days to days

Solution 1 week = 7 days
1. 18 weeks = 18 × 7 = 126 days
2. 20 weeks 15 days = 20 × 7 + 15 = 140 + 15 = 155 days.
Conversion of days to weeks

Following example shows how to convert days to weeks.

Example Convert

1. 168 days to weeks ii. 750 days to weeks and days

Solution 1 day =\(1\over 7\) week
1. 168 days =\(168\over 7\) = 24 weeks
2. 750 days = \(750\over 7\)= 107\(1\over 7\) = 107 weeks 1 day

Distance, Time and Temperature

Temperature

Temperature is one of the basic physical quantities of science. It’s a numerical representation of how cold or hot an object is. Temperature is defined as the degree of heat present in an object, measured by a thermometer

Recognition of units of temperature in Fahrenheit and Celsius

The following two basic temperature scales are commonly used:

• Celsius or Centigrade (C)

• Fahrenheit (F)

• Celsius Scale: The basic unit of temperature for everyday applications and use is Celsius scale, in which 0°C corresponds to the freezing point of water and 100°C is its boiling point. It is widely known as centigrade scale because the distance between melting point and boiling point of water is divided into 100 equal intervals called degrees centigrade(°C).

• Fahrenheit Scale: The second basic unit for measuring temperature is Fahrenheit. In Fahrenheit scale 32°F is freezing point and 212°F is the boiling point of water. In Fahrenheit temperature scale, the distance between melting point and boiling point of water is divided in 180 equal intervals called degrees Fahrenheit (°F).

Solution of real life problems involving conversion, addition and subtraction of units of temperature

In daily life to convert Celsius scale temperature to Fahrenheit scale temperature or vice versa, following steps are taken:

• To convert Celsius to Fahrenheit we multiply the given temperature by \(9 \over 5\)and add 32 to the product [or F =\(9 \over 5\) × C + 32] where F is Fahrenheit temperature and C is Celsius temperature.

• To convert Fahrenheit to Celsius we subtract 32 from Fahrenheit temperature and multiply the difference by \(5 \over9 \)

[or C = (F - 32) × \(5 \over9 \)] where C is Celsius temperature and F is Fahrenheit temperature.

Example

Convert: i. 32°F to Celsius scale

ii. 212°F to Celsius scale

iii. 35° C to Fahrenheit scale

iv. 102° C to Fahrenheit scale

Solution

1)32°F to Celsius scale

Subtract 32 from Fahrenheit temperature = 32 — 32 = 0

Multiply the difference with \(5 \over 9\) = \(5 \over 9\)× 0 = 0°C

Thus, 32°F = 0 °C

2) 212°F to Celsius scale

Subtract 32 from Fahrenheit temperature = 212 — 32 = 180

Multiply the difference with \(5 \over 9\)= \(5 \over 9\)× 180 = 100°C

Thus, 212°F = 100°C

iii. 35°C to Fahrenheit scale

Multiply the Celsius scale temperature by \(9 \over5\)= 35 ×\(9 \over5\) = 63

Add 32 to the product = 63 + 32 = 95°F

Thus, 35°C = 95 °F

iv. 102° C to Fahrenheit scale

Multiply the Celsius scale temperature by \(9 \over5\) = 102 ×\(9 \over5\) = 183.6

Add 32 to the product = 183.6 + 32 =215.6°F

Thus, 102°C = 215.6 °F

Example 1

The melting point of a metal is 263°C. If another metal is amalgam (mixed) in it then its melting point is increased by 25°C. Find the new melting point of the mixture.

Solution Melting point of pure metal = 263°C

Increase in melting point = 25°C

Thus, melting point of mixture is = 263° + 25° = 288°C