Percentages (Junior Cert Mathematics): Revision Notes

Example: What is $24$% of $250$?

Method 1: Using a Formula

Step 1: Write the percentage as a fraction: $24$% becomes $\frac{24}{100}$.

Step 2: Multiply this fraction by the number: $\frac{24}{100} \times 250 = 60$ Answer: $24$% of $250$ is $60$.

Method 2: Using Decimals

Step 1: Convert $24$% into a decimal by moving the decimal point two places to the left. So, $24$% becomes $0.24$.

Step 2: Multiply the decimal by $250$: $0.24 \times 250 = 60$ Answer: $24$% of $250$ is $60$.

Example: $25$% of the marks in an exam are for a practical part. If there are $50$ marks for this practical, how many marks is the whole exam worth?

Step 1: Think of the total marks as a mystery number, say $x$.

Step 2: Set up the equation: $\frac{25}{100} \times x = 50$

Step 3: Solve for $x$ by multiplying both sides by $100$ and then dividing by $25$: $x = \frac{50 \times 100}{25} = 200$

Answer: The whole exam is worth $200$ marks.

Quick Check: Since $25$% means $1/4$, you could also multiply the given marks $(50)$ by $4$ to get the total: $50 \times 4 = 200$

Example: A product costs $€120$, and the price is increased by $15$%. What will the new price be? Steps:

1. Step 1: Find $15$% of $€120$ by multiplying: $\frac{15}{100} \times 120 = 18$
2. Step 2: Add this amount to the original price: $120 + 18 = 138$ Answer: The new price is $€138$.