Number - Percentages, Profit, Loss, and Simple Interest

Percentages as Fractions of 100: A percentage represents a part out of 100. Visually, this can be represented as a 10 by 10 grid where each of the 100 small squares represents $1\%$. For example, if 30 squares are shaded in the grid, it visually represents $30\%$ or $\frac{30}{100}$.

Percentage Increase and Decrease: This measures how much a value has changed relative to its original amount. Visually, imagine a bar model where the original value is a single bar representing $100\%$. An increase adds an extra block to the end of the bar, while a decrease involves 'cutting off' a portion of the original bar.

Profit and Loss: Profit occurs when the Selling Price ($SP$) is greater than the Cost Price ($CP$), while a Loss occurs if the $SP$ is less than the $CP$. In a financial ledger, profit is often represented by positive green figures, while loss is represented by negative red figures.

Simple Interest: Simple interest is a fixed amount of interest calculated only on the initial principal sum. Visually, if you plot the Total Amount ($A$) against Time ($T$) on a coordinate plane, the relationship forms a straight diagonal line (linear growth) starting from the Principal ($P$) on the y-axis.

Multipliers for Percentage Calculations: To find a percentage of a number or apply a change, we use decimal multipliers. For a $15\%$ increase, the multiplier is $1.15$ ($100\% + 15\%$); for a $15\%$ decrease, the multiplier is $0.85$ ($100\% - 15\%$). This collapses two steps of calculation into one simple multiplication.

Reverse Percentages: This concept is used to find the original value after a percentage change has already occurred. You must divide the new value by the multiplier. On a flow diagram, if going from 'Original' to 'New' involves multiplying by $1.20$, then going from 'New' back to 'Original' requires dividing by $1.20$.

Markup and Discount: Retailers use markups to ensure they make a profit over the cost price. Discounts are percentage reductions from the marked price. Visually, a discount can be seen as a 'Price Drop' tag that subtracts a slice from the total cost bar.