Section A — Chapters 1–22
Applied Arithmetic I
Junior Cycle — 1st Year
- ✓By the end of this lesson students will be able to calculate percentages of quantities.
- ✓By the end of this lesson students will be able to calculate percentage increase and decrease.
- ✓By the end of this lesson students will be able to solve problems involving VAT and household bills.
- ✓By the end of this lesson students will be able to solve problems involving ratio and proportion.
- ✓By the end of this lesson students will be able to perform simple currency conversions.
Key concepts
A percentage is a way of expressing a number as a fraction of 100. The symbol for percentage is %.
To find a percentage of a quantity, convert the percentage to a decimal or fraction and then multiply it by the quantity.
To calculate a percentage increase, find the amount of increase, divide it by the original amount, and then multiply by 100%.
To calculate a percentage decrease, find the amount of decrease, divide it by the original amount, and then multiply by 100%.
VAT is a tax added to the price of most goods and services. It is calculated as a percentage of the original price (before tax).
Household bills (e.g., electricity, gas) are calculated based on usage, unit rates, standing charges, and often include VAT.
A ratio compares two or more quantities of the same type. It shows how much of one quantity there is compared to another.
Proportion describes when two ratios are equal. It is often used to find an unknown quantity when other quantities are in a given ratio.
Currency exchange involves converting an amount of money from one currency to another using an exchange rate. The exchange rate tells you how much one unit of currency is worth in another.
Key facts to remember
- 1To convert a percentage to a decimal, divide by 100 (e.g., 25% = 0.25).
- 2To find a percentage of a quantity, multiply the quantity by the percentage (as a decimal or fraction).
- 3VAT is always added to the original price of goods or services.
- 4A ratio compares quantities of the same type (e.g., 2:3).
- 5When sharing a quantity in a ratio, first find the total number of parts.
- 6An exchange rate tells you the value of one currency in terms of another.
Worked examples
Example 1
Calculate 15% of €240.
Answer
€36
You could also convert 15% to a fraction (15/100) and multiply.
Example 2
A television costs €450 before VAT. If VAT is charged at 23%, what is the total price of the television?
Answer
€553.50
Remember to add the VAT to the original price to get the total.
Example 3
Share €180 in the ratio 4 : 5.
Answer
€80 and €100
Always check that your shares add up to the original total (€80 + €100 = €180).
Common mistakes
- ✗Forgetting to convert percentages to decimals or fractions before performing calculations.
- ✗Confusing percentage increase with percentage decrease, or vice-versa.
- ✗Adding VAT to the total price instead of the original price, or forgetting to add it at all.
- ✗Incorrectly applying exchange rates (e.g., multiplying when you should divide, or vice-versa).
- ✗Not finding the total number of parts when sharing a quantity in a ratio.
Exam tips
- ★Always show all your working steps clearly, even for simple calculations, as marks are often awarded for method.
- ★Read each question carefully to identify whether you need to calculate an increase, a decrease, or a specific part of a whole.
- ★For currency exchange, write down the exchange rate and clearly state whether you are multiplying or dividing.
- ★Practise converting between percentages, decimals, and fractions regularly to improve speed and accuracy.
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