1.1 Whole to 100 000
A Naming, writing numbers and determining their place values
1.The numbers, 0,1,2,3,4,5,6,7,8,9,10,... are called whole numbers.
2. Every digit in a whole number has a certain place value.
3. The place values of a 5-digit number include ones, tens, hundreds, thousands and ten thousands.
Partition the number 24 715.
24 715 = 20 000 + 4000 + 700 + 10 + 5
24 715 = 2 ten thousands + 4 thousands + 7 hundreds + 1 ten + 5 ones
24 715 is read as twenty-four thousand seven hundred and fifteen.
Worked Example 1
Write 45 298 in words.
B Comparing numbers
1. When comparing two 5-digit numbers, compare the digits in the ten thousands place first. Next, compare the digits in the thousands place, and so on.
2. We can use a place value chart to compare numbers.
Example:
Which number is larger, 53 926 or 32 714?
So 53 926 is larger than 32 714
Worked Example 2
Which number is smaller, 65 479 or 64 350?
So, 64 350 is smaller than 65 479.
3. We can use a number line to compare numbers.
Worked Example 3
C. Rounding Off numbers
1. Round off to the nearest ten:
Example;
2. Round off to the nearest hundred:
Example:
3. Round off to the nearest thousand
Example:
4. When rounding off a whole number, look at the first digit to the right of the place value involved.
(a) If the digit is less than 5, retain the digit at the place value involved and replaced the other digits on its right with zeros.
Example:
(b) If the digit is 5 or more, add 1 to the digits at the place value involved and replace the other digits on its right with zeros
Example:
1.2 Addition within 100 000
1. An addition is a process of finding the total of two or more numbers.
2. The total also means the sum.
Example:
Follow the steps below when carriying out an addition.
Step 1: Arrange the numbers according to their place values in vertical form.
Step 2: Add the digits from right to left.
Example:
(a) Without regrouping
(b) With regrouping
Worked Example 4
Find the sum of 26 366, 21 755 and 19 234
1.3 Subtraction within 100 000
1. A subtraction is a process of finding the difference between two numbers.
Example:
2. Follow the steps below when carrying out a subtraction.
Step 1: Arrange the numbers according to their place values in vertical form.
Step 2: Subtract the digits from right to left. Example:
(a) Without regrouping
(b) With regrouping
Worked Example 5
Find the difference between 52 524 and 29 846.
1.4 Multiplication within 100 000
1. Multiplication is a process of repeated addition.
2. The result is called the product.
Example
3. Changing the order of numbers in a multiplication does not effect the product.
Example:
8 x 6 = 6 x 8 = 48
4. When multiplying a number by 10, 100 or 1 000, add one, two or three zeros after the number.
Example:
5. When multiplying two whole numbers, the number with more digits is written on top to simplify the calculation.
Example:
Worked Example 6
Find the product of 451 and 42
1.5 Division within 100 000
1. A division is a process of sharing or grouping equally.
2. Unlike addition, subtraction and multiplication, we start dividing from the left of the number to be divided called the dividend.
Example:
If a number which ends with one zero or more than one zero is divided by 10, 100 or 1 000, the quotient is obtained just taking away the zero or zeros of the dividend itself.
Example:
Worked Example 7
Divide 7 245 by 9
1.6 Mixed Operations
1. A mixed operation is a process which involves more than one operation.
2. For mixed operations involving addition and subtraction, calculate from left to right.
Example:
Worked Example 8
Find the value of 9 624 - 5 847 + 597
1.7 Problem Solving Involving Addition, Subtraction, Multiplication, Division and Mixed Operations
1. Undestand the problem
2. Devise a plan
3. Carry out the plan.
4. Check the answer.
Worked Example 9
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