Measurement of Long Distance
The distance between two cities in a country is very long as compare to the distance between two walls of a room, therefore, long distance is measured in kilometres. Bigger unit of length can be converted into smaller unit and smaller into bigger.
Numbers for the representation of big length in small unit takes more space and it is a long process, therefore, bigger length is expressed in big units.
Conversion between Kilometres and Metres
The following steps are used for the conversion of kilometres into metres:
Step 1: Convert kilometres into metres by multiplying the number of kilometers by 1,000 (1 km = 1,000 metres).
Step 2: Convert the kilometres and metres into metres by multiplying the number of kilometres by 1,000 and then add the number of metres.
The distance between two colonies in a city is 15 km 540 m. express the length in metres?
(a) 13,204 m
(b) 15,540 m
(c) 2,304 m
(d) None of these
(e) All of these
Answer (b)
Explanation:
Conversion of Metres into Kilometres
The following steps are used for the conversion of metres into kilometres
Step 1: Divide the number of metres by one thousand.
Step 2: Place decimal point among the digits if required.
Step 3: Write resulting decimal with three decimal places.
The length of a fly over 1s 250 m- lf a truck covers the distance of 1200 km excluding the length of fly over then what is the total distance covered by truck including the length of the fly over ?
(a) 1200.260km
(b) 1200.255km
(c) 1200. 250km
(d) None of these
(e) all of these
Answer (c)
Explanation
The length of the fly over is 250 m. Hence, the total distance covered by the truck = 1200 km + 250 m = 1200 km 
1200 km + 0. 25 km = 1200.25 km =1200 km 250m. 
Measurement of Short Length
The shape and size of everything are measured by a measuring instrument. Rulers are well known devices for the measurement of the length. Measured lengths are expressed in units. The units for measured length are kilometre, metre, centimeter and millimetre. Sl unit for the measured length is metre. Small lengths are measured in metre, centimetre and millimetre. The length of our one finger is measured in inches or in centimetre or in millimetre but the length between two city is measured in kilometres. 1 metre = 100 cm and 1000 m = 1 kilometer.
Units are given in the options for the measurement of the length. Which one of the following units is not used for the measurement of the length?
(a) Centimeters
(b) Kilometers
(c) Kilograms
(d) None of these
(e) All of these
Answer (c)
Explanation
Kilogram is the Sl unit of mass hence, this is not used for the measurement of length.
Conversion Table
| 10 millimetres (mm) | 1 centimetre (cm) |
| 10 centimetres | 1 decimetre (dm) |
| 10 decimetres | 1 metre (m) |
| 10 metres | 1 decimetre (dm) |
| 10 decimetres | 1 hectometre (hm) |
| 10 hectometres | 1 kilometre (km) |
Convert more... 
Introduction
Measurement is the elementary information about everything. Length, width, height and volume of a thing are measured in appropriate units. The term measurement is derived from the Latin word mensura. Sl unit stands for International system for units. This is also known as metric system. In this chapter we will learn about the concept of measurement.
Read the following about the Sl units:
| Sr.Number | Measurement | SI Units |
| 1 | Length | Meter |
| 2 | Time | Seconds |
| 3 | Mass | Kilogram |
Introduction
Unitary method is self-indicating that this is the method for finding the value of unit article if the values of two or more articles is given. This method is widely used for the simplification of word based problems in arithmetic and geometry. In this chapter we will learn about the concept and use of unitary method.
Unitary Method and Its Use
Unitary method is used for solving the problems if there are variation in the given quantity. In this method different quantities are converted into single unit and required unit is obtained by arithmetic operations. If a car travels 20 km in 15 minutes and it is required to find the distance travelled by car in 60 minutes then distance travelled by the car in 1 minute must be carried out, that is obtained by the division of 
TTherefore, the distance travelled by the car in 60 minutes is obtained by multiplying the distance travelled in 1 minute by 
kilometres.
The weight of 4 coins is 150 grams. What is the weight of 10 such coins?
(a) 380 grams
(b) 400 grams
(c) 500 grams
(d) 1500 grams
(e) None of these
Answer (a)
Explanation The weight of 4 coins = 150 grams therefore, the weight of 1 coin 
grams i.e, the weight of 10 coins 
gram.
Applications of Unitary Method
The given number of articles is converted into single unit and the value of required number of articles is obtained. The cost of 7 articles is Rs 686, for finding the cost of one article Rs 686 is divided by 7. Therefore, the cost of one article, 
and the cost of 12 such articles
A company buys 45 computers. If the cost of total number of hard disks isB 84330, then what will be the cost of 96 such hard disks?
(a) Rs 179908
(b) Rs 179904
(c) Rs 179910
(d) Rs 170000
(e) None of these
Answer (b)
Explanation
The cost of 45 hard disks is? 84330. Therefore, the cost off one hard disk 
The cost of 96 such hard disks
The cost of 96 such hard disk 
The total length of 6 equal plane figures is 54 metres. What will be the total length of 9 such plane figures?
(a) 82 metres
(b) 80 metres
(c) 81 more... 
Addition of Money
Whenever money is paid against the cost of two or more things, the value of total money that have to be paid is obtained by addition of the cost of the purchased items or things.
The following steps are used for the addition of money:
Step 1: Arrange the money vertically, rupees under rupees column and paise under paise column.
Step 2: Add the money from right or paise.
Step 3: If carry is generated then add the carry to the next addition.
Step 4: The resulting value of money is their addition.
For example Addition of Rs 18 and 20 paise and Rs 20 and 40 paise is given below.
| Rupess | Paise | ||
| 18 | . | 20 | |
| + 20 | . | 80 | = Rs 39.00. |
| 39 | . | 00 |
Find the total cost if the cost of 12 kg rice is Rs 450 and 50 p, 5 l of vegetable oil is Rs 454 and 75 p and the cost of one piece of coconut is Rs 30 and 50 p.
(a) Rs 935 and 75 paise
(b) Rs 936 and 75 paise
(c) Rs 900 and 75 paise
(d) Rs 845 and 65 paise
(e) None of these
Answer (a)
Explanation
| Rupees | Paise | more...
 Introduction
Money is defined as the equivalent of the cost of a thing. In ancient world coins were made up of gold and silver. Now a day money is available in two form coins and notes. Coins are metallic form and notes are paper form of money. Most of the money which is derived today is originated from Roman originals. Paper money was first introduced in China 15 century AD. Denomination of currency is the proper description of money. Each and every country in the world has self-denominated money. In this chapter we will learn about the money.
Identification of Indian Money
Money is paid against purchasing the things from shops or markets. The value of money is denominated on the notes or coins. Therefore, money is circulated in the form of notes and coins. Money is identified by its different design. Every country in the world has self-designed notes and coins. The important identifying part of notes and coins are its value those are written on the notes and coins in words and in numbers. In India the denominated coins are 5 paise, 10 paise, 20 paise, 25 paise, 50 paise, Rs 1, Rs 2, Rs 5 Rs 10 and denominated notes are Rs 1, Rs 2, Rs 5, Rs 10, Rs 20,Rs 50, Rs 100, Rs 500, Rs 1000. Rs 1 = 100 paise. Indian rupee is called INR (Indian national rupee). The symbol for the notation of rupee is Rs. and paise is P.Rupees 60 and 70 paise can be written as Rs 60 and 70 P or Rs 60.70. Therefore, rupees and paise are separated by a dot (.). Rupees 8 and 5 paise are written as Rs.8.05. Rs 8.5 is rupees 8 and 50 paise.
Look at the following pictures of denominated Indian coins:
Look at the following pictures of denominated Indian rupees:
|
Calendar
The name of days and months are arranged in a proper way in a calendar and name of the days and dates of months are shown by the calendar. The name of the days are arranged in upper row for every month in the year. In the above picture a calendar for the year2013 has been shown. From the above picture, we get following information, 7 days = 1 week, 30 days = 1 month, 12 months = 1 year. Every year which is divisible by 4 such as 1992 is called a leap year and during the leap year the month of February is increased by one and the total number of days of the year is also increased by one which is from 365 days to 366 days.
There are seven days in a week, i.e. Sunday, Monday, Tuesday, Wednesday, and Thursday Friday and Saturday. Monday is the first day of the week.
The following are the months of the year, its Latin name and number of days:
Introduction
There are various unit by which the time can be denoted. The Sl unit (Standard International unit) of time is second. Hour and minute are calculated along with the Sl unit of time. The format of numbers that we use today for time is based on60. We know that 60 seconds is equal to 1 minute and 60 minutes is equal to 1hour. Calendar that we use today is actually adopted from Gregorien calendar. Calendar always starts from 1 January. If the year is exactly divisible by 4 then the year is called leap year and a leap year contains 29 days of February. The name ofthe months is based on Latin words.
In the above figure a watch is shown. The biggest hand is its seconds indicating hand. It moves faster as compare to the movement of other two hands. In the watch, the hour hand can be easily identified by its speed of rotation. Minute hand moves one small division on one complete rotation of the second hand. The second biggest hand of the arm is its minute hand and hour hand moves to one big division by one complete rotation of the minute hand. Therefore, if minute hand rotates one complete rotation then the hour hand moves from one big division of one hour to another big division of second hour.
Look at the following picture of division of minutes and hour in the watch:
Conversion of Time
One minute is equal to 60 seconds and one hour is equal to 60 minutes, therefore,one unit can be converted into another. 110 minutes is converted into hour as 60minutes + 50 minutes = 1 hour 50 minutes.
Time conversion table
Multiplication and division of Fractions
Multiplication of two or more fractions is the multiplication of its numerators and denominators. Therefore, the multiplication of the given fractions:
The division of two fractions is obtained by multiplying the reciprocal of the fraction
Hence, division of the fractions 
is 
The lowest term of the fraction 9 is Stained by dividing the numerator and denominator with a common divisor3.
Note: Every fraction can be reduced into its lowest term if the highest common factor of numerator and denominator is not 1
Find the lowest term of the fraction 
?
(a) 
(b) 
(d) 
(e) None of these
Answer (c)
Explanations: 5 are the common divisor of the given fraction. Hence, the lowest term of 
Find the crossed part of the following whole figure.
(a) 
(b) 
(c) 
(d) All of these
(e) None of these
Answer (a)
Explanations: Crossed part is one fourth of whole figure.
(a) 2
(b) 1
(c) 3
(d) 4
(e) None of these
Answer (b)
Explanation: 
on the given number lines?
(a)
(b) 
(c) 
Introduction
Division is the basic arithmetic operation and this the inverse process of multiplications. The symbol for the notation of division is 
.
The symbol for the notation of division is also known as obelus. Obelus means a line between two dots. In this chapter we will learn about the division on various type of numbers.
Division is the inverse process of multiplication and repeated subtraction. It determines the one value is how many times greater than another value. It is expressed in the form of 
where a is the dividend and denoted by capital latter of English alphabet D and b is divisor denoted by small letter d. The number which tells how many times the division has been carried out is called the Quotient and denoted by 'Q’. The number which is left after the division is called the remainder and denoted by ‘R. The symbol for the notation of division is 
.
The division of x by y is represented by:
(a) 
(b) 
(c) 
(d) Both A and B
(e) None of these
Answer (d)
Explanation: The division of x by y is represented by either 
