Data Handling

Shape and Space

 

 

 

Symmetry:

• The quality of being made up of exactly similar parts facing each other or around an axis.
• Exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a center or an axis.

Length

Various instruments are used to measure length. For example:

• Rulers and tape measures are marked in millimetres or centimetres to measure shorter lengths accurately. 
• A trundle wheel is used to measure length to the nearest metre. Note that a counter may be attached to the trundle wheel to count metres. 
• A car's odometer often measures distance in tenths of a kilometre.

To convert length from a larger unit into a smaller unit, multiply by the relevant power of 10.
To convert length from a smaller unit into a larger unit, divide by the relevant power of 10.

Example.
Convert the following measurements to the units indicated:
a. 7 cm to mm
b. 8 m to cm
c. 9 km to m

Solution: 

Time

Whole Number: Division

• In mathematics, especially in elementary arithmetic, division (÷) is an arithmetic operation. 
• Another basic view of division is sharing equally.

Example:
Danesse has 3 friends. She has 12 cookies to share with them. How many cookies does each of the four people get? 

• Danesse probably shared her cookies by saying one for you, one for you, so on. Thus the 12 cookies are shared equally by four people, and each gets three cookies.  
• Or, you might say that the 12 cookies have been partitioned into four sets of the same size.

Exercises:

1.  21 ÷ 3 = ________
2.  24 ÷ 4 = ________
3.  42 ÷ 7 = ________
4.  32 ÷ 8 = ________
5.  24 ÷ 8 = ________
6.  54 ÷ 6 = ________
7.  72 ÷ 6 = ________
8.  27 ÷ 9 = ________
9.  72 ÷ 9 = ________
10.  56 ÷ 7 = ________

Fractions

• A fraction is a number that is written in the form:

or a/b

• The a is the numerator, and the b is the denominator.
• The line separating the numerator and denominator is a fraction bar.
• Fractions are used when representing numbers that describe the parts of a whole. The fraction a/b also can be read as "a out of b" ,"a over b" or "a divided by b."

There are some restrictions on a and b:

• Both a and b must be integers, meaning positive and negative whole numbers. 
• The denominator, or b, cannot be zero. This is because one cannot divide by zero.

Example:
If there are 18 students in a classroom, and 6 of the students wear glasses, what fraction of the students wear glasses?

 

• A fraction can be thought of as "a out of b." 
• Total number of students is 18. 
• Number of students with glasses is 6.
• Number of students with glasses out of the whole class is 6/18.

Whole Numbers: Multiplication

• Multiplication (often denoted by the cross symbol "×") is the mathematical operation of scaling one number by another.
• Whole-number products greater than 1 can be computed by repeated addition;

for example:

• 7 multiplied by 3 (often said as "7 times 3") can be calculated by adding 7 copies of 3 together:    7 x 3 = 3 + 3 + 3 + 3 + 3 + 3 + 3 = 21
• Here 7 and 3 are the "factors" and 21 is the "product".
• 7 multiplied by 3 can also be calculated by adding 3 copies of 7 together: 7 x 3 = 7 + 7 + 7 = 21

Exercises:

1. 7 x 1 =
2. 6 x 5 =
3. 7 x 8 =
4. 3 x 9 =
5. 6 x 6 =
6. 9 x 8 =
7. 5 x 7 =
8. 6 x 9 =
9. 2 x 8 =
10. 9 x 9 =

Whole Number : Subtraction

How to subract number:


Example: 99876 -57894 = ?

• Line up the numbers:

   9|9|8|7|6|
-  5|7|8|9|4|
________

• Subtract the numbers starting from place value ones to ten thousands:

         8 17 17
   9|9|8|7|6|
-  5|7|8|9|4|
   4 1 9 8 2

Exercises:

1. 203 - 35 =
2. 72 - 16 =
3. 2180 - 726 =
4. 62731 - 12735 =
5. 7261 - 3815 =
6. 92 - 25 =
7. 18 - 10 =
8. 8271 - 941 =
9. 51426 - 903 =
10. 6251 - 170 =

Whole Numbers: Addition

First, we need to work on place values:

45 971
|  |  | | |___ Ones 1's
|  |  | |____ Tens 10's
|  |  |_____ Hundreds 100's
|  |_______Thousands 1 000's
|_________Ten Thousands 10 000's


If we expand this out, we get:

45971 = 40 000 + 5 000 + 900 + 70 + 1


Write this from up to down:

   4|0|0|0|0|
     |5|0|0|0|
        |9|0|0|
           |7|0|
 +           |1|
   4 5 9 7 1



How to add up numbers:

Example: 53 681 + 7927 = ?

• Line up the numbers:

   5|3|6|8|1|
+   |7|9|2|7|
________

• Add up the numbers starting from place value ones to ten thousands:

      1  1  1
   5|3|6|8|1|
+   |7|9|2|7|
   6 1 6 0 8

Whole Numbers

Whole Numbers

• Whole Numbers are simply the numbers 0, 1, 2, 3, 4, 5, … (and so on) 

 

No fraction!

Counting Numbers

• Counting Numbers are Whole Numbers, but without the zero. Because you can't "count" zero. So they are 1, 2, 3, 4, 5, … (and so on).

Natural Numbers

• Mean either "Counting Numbers" {1, 2, 3, ...}, or "Whole Numbers" {0, 1, 2, 3, ...}, depending on the subject.

Place Value till Ten Thousands

• The position, or place, of a digit in a number written in standard form determines the actual value the digit represents. 
• Below shows the place value for various positions:

Place (underlined)           Name of Position
1 000                                 Ones (units) position
1 000                                 Tens
1 000                                 Hundreds
1 000                                 Thousands
10 000                               Ten Thousands
1 000 000                          Hundred Thousands
1 000 000                          Millions

Place Value

Example
The number 21,040:

• Has a 2 in the ten thousands place,
• a one in the thousands place, 
• a 4 in the tens place, 
• and a 0 in both the hundreds and ones place.
• Can be written as twenty-one thousand and forty.