Mathematics Form 1-4: CHAPTER ONE – NATURAL NUMBERS

Specific Objectives

By the end of this topic, the learner should be able to:

1. Identify, read, and write natural numbers in symbols and words;
2. Round off numbers to the nearest tens, hundreds, thousands, millions, and billions;
3. Classify natural numbers as even, odd, or prime;
4. Solve word problems involving natural numbers.

Content

1. Place values of numbers
2. Rounding off numbers to the nearest tens, hundreds, thousands, millions, and billions
3. Odd numbers
4. Even numbers
5. Prime numbers
6. Word problems involving natural numbers

Introduction

Place Value

A digit has a different value in a number depending on its position within the number. This position is called the place value of the digit. Understanding place value is fundamental to reading, writing, and working with numbers effectively.

Total Value

The total value of a digit is the product of the digit itself and its place value. This helps in understanding the actual contribution of each digit to the overall number.

Example

A place value chart is a useful tool to identify both the place value and total value of each digit in a number. It also assists in writing numbers in words accurately.

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 equal to one thousand million, written numerically as 1,000,000,000. There are ten place values in a billion, extending the place value chart further to accommodate larger numbers.

Example

What is the place value and total value of the digits below?

1. 47,397,263,402 (place value of digits 7 and 8).
2. 389,410,000,245 (place value of digits 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 whether to round down or up. If the ones digit is 1, 2, 3, or 4, the number rounds down to the nearest ten. If the ones digit is 5 or more, the number rounds up to the next ten.

For example, 641 rounded to the nearest ten is 640, while 3189 rounded to the nearest ten is 3190.

When rounding off to the nearest hundred, numbers ending with digits 1 to 49 round down, while those ending with 50 to 99 round up.

For example, 641 rounded to the nearest hundred is 600, and 3189 rounded to the nearest hundred is 3200.

Example

Round off each of the following numbers to the nearest value indicated in the bracket:

1. 473,678 (nearest 100)
2. 524,239 (nearest 1000)
3. 2,499 (nearest 10)

Solution

1. 473,678 rounds to 473,700 to the nearest 100.
2. 524,239 rounds to 524,000 to the nearest 1000.
3. 2,499 rounds to 2,500 to the nearest 10.

Operations on Whole Numbers

Addition

Example

Find the sums of the following:

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

Solution

Arrange the numbers vertically for easy addition:

98
6734
+ 348
7180

6349
259
+7954
14562

Subtraction

Example

Calculate: 73,469 – 8,971

Solution

73,469
– 8,971
64,498

Multiplication

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

Example

Calculate: 469 × 63

Solution

469
× 63
1,407
+28,140
29,547

Division

When a number is divided, the result is called the quotient. The number being divided is the dividend, and the number dividing is the divisor.

Example

Find: 6,493 ÷ 14

Solution

The quotient is 463 with a remainder of 11.

Note:

6493 = (463 × 14) + 11

In general, dividend = quotient × divisor + remainder.

Word Problem

When working on word problems, it is important to carefully read and understand the information given before attempting to solve the question. Breaking the problem down into smaller steps and identifying the operations required will help in finding the correct solution.

Example

Otego had 3,469 bags of maize, each weighing 90 kg. He sold 2,654 of them.

1. How many kilograms 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.

   Total weight of 3,469 bags = 3,469 × 90 = 312,210 kg.

   Total weight of 2,654 bags sold = 2,654 × 90 = 238,860 kg.

   Amount of maize left = 312,210 – 238,860 = 73,350 kg.

2. Number of bags left = 3,469 – 2,654 = 815 bags.

   After adding 468 bags, total bags = 815 + 468 = 1,283 bags.

Even Number

An even number is a number that can be divided by 2 without leaving a remainder. Examples include 0, 2, 4, 6, and 8.

Examples of even numbers: 3600, 7800, 806, 78,346.

Odd Number

An odd number is any number that, when divided by 2, leaves a remainder. Examples include 471, 123, 1197, and 7129. Odd numbers end with the digits 1, 3, 5, 7, or 9.

Prime Number

A prime number is a number that has exactly two factors: one and the number itself.

Examples include 2, 3, 5, 7, 11, 13, 17, and 19.

Note:

1. 1 is not a prime number.
2. 2 is the only even number that is prime.

End of Topic

Past KCSE Questions on the Topic

1. Write 27,707,807 in words.
2. All prime numbers less than ten are arranged in descending order to form a number.
3. Write down the number formed.
4. What is the total value of the second digit?
5. Write the number formed in words.