Natural Numbers - Mathematics Form 1 Notes

• Introduction
  • Place Value
  • Total Value
  • Billions
• Rounding Off
• Operations on Whole Numbers
  • Addition
  • Subtraction
  • Multiplication
  • Division
  • Word Problem
• Even Number
• Odd Number
• Prime Number
• Past KCSE Questions on the Topic

Introduction

Place Value

• A digit can have a different value in a number because of its position in a number. The position of a digit in a number is called its place value.

Total Value

• This is the product of the digit and its place value.

Example

- A place value chart can be used to identify both place value and total value of a digit in a number. The place value chart is also used in writing numbers in words.

Example

• Three hundred and forty five million, six hundred and seventy eight thousand, nine hundred and one.
• Seven hundred and sixty nine million, Three hundred and one thousand, eight hundred and fifty four.

Billions

• A billion is one thousands million, written as 1, 000, 000,000.There are ten places in a billion.
  
  Example
  What is the place value and total value of the digits below?
  1. 47,397,263,402 (place value 7 and 8).
  2. 389,41 0 ,000,245 ( place 3 and 9)
  
  Solution
  
  1. The place value for 6 is ten thousands. Its total value is 60,000.
  2. The place value of 3 is hundred billions. Its total value is 300,000,000,000.

Rounding Off

• When rounding off to the nearest ten, the ones digit determines the ten i.e. if the ones digit is 1 , 2, 3, or 4 the nearest ten is the ten number being considered.
• If the ones digit is 5 or more the nearest ten is the next ten or rounded up.
• Thus 641 to the nearest ten is 640, 31 89 to the nearest is 31 90.
• When rounding off to the nearest 1 00, then the last two digits or numbers end with 1 to 49 round off downwards.
• Number ending with 50 to 99 are rounded up.
• Thus 641 to the nearest hundred is 600, 31 89 is 3200.
  
  Example
  Rounding off each of the following numbers to the nearest number indicated in the bracket:
  1. 473,678 ( 1 00)
  2. 524,239 (1 000)
  3. 2,499 (1 0)
  
  Solution
  
  1. 473,678 is 473,700 to the nearest 100.
  2. 524,239 is 524,000 to the nearest 1000
  3. 2,499 is 2500 to the nearest 10.

Operations on Whole Numbers

Addition

Example

Find out:

1. 98 + 6734 + 348
2. 6349 + 259 +7954

Solution

1. Arrange the numbers in vertical forms
       98
   6734
   +348
   71 80
2.     6349
         259
   +79542
     86150

Subtraction

Example

Find: 73469 – 8971

Solution

73469
-8971
64498

Multiplication

• The product is the result of two or more numbers.

Example

Work out: 469 x 63

Solution

     469
     ×63
    1407 → 469 x 3 = 1407
+28140→469 x 60 = 28140
  29547

Division

• When a number is divided by the result is called the quotient. The number being divided is the divided and the number dividing is the divisor.

Example

Find: 6493 ÷ 14

Solution

We get 463 and 1 1 is the remainder

Note:
6493 = (463 x 14) + 1 1

In general, dividend = quotient x division + remainder.

Word Problem

• In working the word problems, the information given must be read and understood well before attempting the question.
• The problem should be broken down into steps and identify each other operations required.

Example

Otego had 3469 bags of maize, each weighing 90 kg. He sold 2654 of them.

1. How many kilogram of maize was he left with?
2. If he added 468 more bags of maize, how many bags did he end up with?

Solution

1. One bag weighs 90 kg.
   3469 bags weigh 3469 x 90 = 31 2,21 0 kg
   2654 bags weigh 2654 x 90 = 238,860 kg
   Amount of maize left = 31 2,21 0 – 238,860
   = 73,350 kg.
2. Number of bags = 81 5 + 468
   =1 283

Even Number

• A number which can be divided by 2 without a remainder E.g. 0,2,4,6 0 or 8 
  3600, 7800, 806, 78346

Odd Number

• Any number that when divided by 2 gives a remainder. E.g. 471 ,1 23, 1 1 97,71 29.The numbers ends with the following digits 1 , 3, 5,7 or 9.

Prime Number

• A prime number is a number that has only two factors one and the number itself.
• For example, 2, 3, 5, 7, 1 1 , 1 3, 1 7 and 1 9.
  Note:
  1. is not a prime number.
  2. is the only even number which is a prime number.

Past KCSE Questions on the Topic

1. Write 27707807 in words
2. All prime numbers less than ten are arranged in descending order to form a number
   1. Write down the number formed
   2. What is the total value of the second digit?
   3. Write the number formed in words