Number & Numeration
Fractions, Decimals, Money and Percentages
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- ✓By the end of this lesson students will be able to identify and represent fractions as parts of a whole.
- ✓By the end of this lesson students will be able to convert simple fractions to decimals and vice versa.
- ✓By the end of this lesson students will be able to perform basic arithmetic operations with Nigerian currency (Naira and Kobo).
- ✓By the end of this lesson students will be able to understand and calculate simple percentages of quantities.
- ✓By the end of this lesson students will be able to solve word problems involving fractions, decimals, money, and percentages.
Key concepts
A fraction represents a part of a whole. It is written as two numbers separated by a line. The top number is called the 'numerator', and it tells us how many parts we have. The bottom number is called the 'denominator', and it tells us the total number of equal parts the whole is divided into. For example, 1/2 means one part out of two equal parts. Fractions can be proper (numerator smaller than denominator), improper (numerator larger than or equal to denominator), or mixed numbers (a whole number and a proper fraction).
Equivalent fractions are fractions that look different but represent the same value or the same part of a whole. For example, 1/2 is equivalent to 2/4 and 3/6. You can find equivalent fractions by multiplying or dividing both the numerator and the denominator by the same non-zero number.
Decimals are another way to represent parts of a whole, especially when the whole is divided into tenths, hundredths, thousandths, and so on. A decimal number has a whole number part and a fractional part, separated by a 'decimal point'. The digits after the decimal point represent fractions with denominators of 10, 100, 1000, etc. For example, 0.5 means 5 tenths (5/10), and 0.25 means 25 hundredths (25/100).
In Nigeria, our currency is the Naira (₦) and Kobo (k). One Naira is equal to one hundred Kobo. This means ₦1 = 100k. Money amounts are often written using decimals, where the digits after the decimal point represent Kobo. For example, ₦50.75 means fifty Naira and seventy-five Kobo.
A percentage means 'per hundred' or 'out of one hundred'. It is a way of expressing a number as a fraction of 100. The symbol for percentage is %. For example, 50% means 50 out of 100, which is the same as the fraction 50/100 or the decimal 0.50. To find a percentage of a number, you can convert the percentage to a fraction (over 100) or a decimal, and then multiply.
Key facts to remember
- 1A fraction represents a part of a whole, with a numerator (parts you have) and a denominator (total equal parts).
- 2Decimals use a decimal point to separate whole numbers from fractional parts (tenths, hundredths, etc.).
- 3In Nigerian currency, ₦1 (One Naira) is equal to 100k (One Hundred Kobo).
- 4A percentage means 'per hundred' and is represented by the symbol %.
- 5To add or subtract fractions with the same denominator, only add or subtract the numerators.
- 6When adding or subtracting decimals or money, always align the decimal points.
- 7To convert a fraction to a decimal, divide the numerator by the denominator.
- 8To find a percentage of a number, convert the percentage to a fraction (over 100) or a decimal, then multiply.
Worked examples
Example 1
Add 1/4 and 2/4. Then simplify your answer.
Answer
3/4
When adding or subtracting fractions with the same denominator, only add or subtract the numerators.
Example 2
A textbook costs ₦750.50 and a notebook costs ₦125.00. How much will a student pay for both items?
Answer
₦875.50
Always align the decimal points when adding or subtracting money amounts to ensure correct calculation of Naira and Kobo.
Example 3
Find 25% of ₦800.
Answer
₦200
Remember that 25% is equivalent to 1/4, 50% is 1/2, and 75% is 3/4. This can make calculations faster.
Common mistakes
- ✗Adding or subtracting both numerators and denominators when working with fractions (e.g., 1/2 + 1/2 = 2/4 instead of 1).
- ✗Not aligning decimal points correctly when adding or subtracting decimals or money, leading to incorrect place values.
- ✗Confusing Naira and Kobo, or forgetting that ₦1 = 100k when performing conversions or calculations.
- ✗Incorrectly converting percentages to fractions or decimals (e.g., treating 10% as 10 instead of 10/100 or 0.10).
- ✗Forgetting to simplify fractions to their lowest terms when required.
Exam tips
- ★Read each question carefully to understand what is being asked, especially in word problems.
- ★Show all your working steps clearly. Even if your final answer is wrong, you might get marks for correct steps.
- ★Always include the correct units (e.g., ₦, k, or %) in your final answers for money and percentage problems.
- ★Check your answers, especially for money calculations, to ensure they are reasonable and make sense in the context of the problem.
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