Numbers, Operations & Algebra
Working with Whole Numbers, Fractions, Decimals and Percentages
Grade 4 · Grade 5 · Grade 6
- ✓By the end of this lesson students will be able to perform basic operations (addition, subtraction, multiplication, division) with whole numbers.
- ✓By the end of this lesson students will be able to understand, compare, and perform operations with common fractions, including finding equivalent fractions.
- ✓By the end of this lesson students will be able to understand place value in decimal fractions, convert between common and decimal fractions, and perform operations with decimals.
- ✓By the end of this lesson students will be able to understand the concept of percentages and calculate simple percentages of whole numbers.
- ✓By the end of this lesson students will be able to solve word problems involving whole numbers, fractions, decimals, and percentages.
Key concepts
Whole numbers are the counting numbers starting from zero (0, 1, 2, 3, ...). We use them for counting objects and performing basic calculations. The four basic operations with whole numbers are addition (+), subtraction (-), multiplication (×), and division (÷).
A common fraction represents a part of a whole. It consists of a numerator (the top number, indicating how many parts you have) and a denominator (the bottom number, indicating how many equal parts the whole is divided into).\n\n- A **proper fraction** has a numerator smaller than its denominator (e.g., 1/2, 3/4).\n- An **improper fraction** has a numerator equal to or larger than its denominator (e.g., 5/4, 7/7).\n- A **mixed number** combines a whole number and a proper fraction (e.g., 1 1/2).\n- **Equivalent fractions** are fractions that represent the same value (e.g., 1/2 = 2/4 = 3/6).
Decimal fractions are another way to write fractions, especially those with denominators of 10, 100, 1000, and so on. They use a decimal comma (,) to separate the whole number part from the fractional part.\n\n- **Place Value**: The digits to the right of the decimal comma represent tenths, hundredths, thousandths, etc.\n- Example: 0,5 means 5 tenths (5/10). 0,25 means 25 hundredths (25/100).
The word 'percentage' means 'per hundred' or 'out of one hundred'. It is a way to express a fraction with a denominator of 100. The symbol for percentage is %.\n\n- Example: 25% means 25 out of 100, which can be written as the fraction 25/100 or the decimal 0,25.
Key facts to remember
- 1Place value is crucial: Understand the value of each digit in whole numbers and decimal fractions (units, tens, tenths, hundredths, etc.).
- 2Fractions represent parts of a whole: The denominator tells you how many equal parts the whole is divided into, and the numerator tells you how many of those parts you have.
- 3Equivalent fractions have the same value: You can create equivalent fractions by multiplying or dividing both the numerator and denominator by the same non-zero number.
- 4Always align the decimal commas when adding or subtracting decimal fractions.
- 5Percentage means 'out of 100': For example, 75% is the same as 75/100 or 0,75.
- 6You can convert between common fractions, decimal fractions, and percentages (e.g., 1/2 = 0,5 = 50%).
- 7For more complex calculations, remember the order of operations (BODMAS: Brackets, Orders, Division/Multiplication, Addition/Subtraction).
Worked examples
Example 1
A baker bakes 245 loaves of bread on Monday and 319 loaves on Tuesday. If 1/3 of the total loaves were sold by lunchtime on Wednesday, how many loaves were sold?
Answer
188 loaves were sold.
This problem combines addition of whole numbers and finding a fraction of a whole number.
Example 2
Convert 3/4 to a decimal fraction and then add it to 1,25.
Answer
2,00 (or 2)
Remember to align the decimal commas when adding or subtracting decimal fractions.
Example 3
In a class of 40 learners, 25% achieved full marks in a Mathematics test. How many learners achieved full marks?
Answer
10 learners achieved full marks.
Percentages can often be simplified by converting them to common fractions or decimal fractions before calculating.
Common mistakes
- ✗Incorrectly using place value, for example, confusing 0,5 with 0,05, or misaligning decimal commas during addition/subtraction.
- ✗Attempting to add or subtract common fractions without first finding a common denominator.
- ✗Confusing the numerator and denominator in a fraction, or misinterpreting what each number represents.
- ✗Making errors in basic whole number operations (addition, subtraction, multiplication, division), which then leads to incorrect answers in more complex problems.
- ✗Misinterpreting percentages, such as thinking 20% of 50 means 20 + 50, instead of (20/100) × 50.
Exam tips
- ★Read the question carefully: Always read the question more than once to ensure you fully understand what is being asked and what operations are required.
- ★Show all your working steps: Even if you make a calculation error, showing your steps allows the examiner to award partial marks for correct methods.
- ★Check your answer: After solving a problem, ask yourself if the answer makes sense in the context of the question. Use inverse operations to check your calculations.
- ★Practise mental maths: Knowing your multiplication tables and basic number facts will help you perform calculations more quickly and accurately, reducing errors.
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