Multipliers

Understanding Multipliers

• A multiplier is a value by which we multiply to scale, or increase or decrease, the size of another number.
• Multipliers are used to create proportional changes – like increasing a quantity by a certain percentage.
• To create a multiplier, we convert the percentage into a decimal and add or subtract it from 1, depending on whether we are increasing or decreasing a value.
• The process can be visualised as distributing a quantity into multiple equal parts, each being a multiplier of the original quantity.

Working with Multipliers

• To increase a quantity by a certain percent, the multiplier is calculated as 1 plus the percentage as a decimal. For instance, to increase by 20%, the multiplier would be 1 + 0.20 = 1.2.
• When decreasing a quantity by a certain percent, the multiplier is 1 minus the percentage in decimal form. To decrease by 20%, the multiplier is 1 - 0.20 = 0.8.
• To use the multiplier, multiply the original quantity by the multiplier. For example, with an original quantity of 50 and a multiplier of 1.2, the new quantity would be 50 * 1.2 = 60.

Multipliers in Ratio Problems

• In ratio problems, multipliers can be used to scale up or scale down the two quantities in the ratio, without changing the ratio.
• For instance, if a ratio is given as 2:3, and we want to scale it up to represent larger quantities, we could use a multiplier of 10 to get a ratio of 20:30.
• In this case, the multiplier has allowed us to alter the quantities without changing the fundamental comparison as represented by the ratio.

Applications of Multipliers

• Multipliers find wide application in real-world scenarios including calculating discounts, profit and loss, interest rates, and other financial calculations.
• A sound understanding of multipliers is essential for confidence in proportional reasoning in both academic studies and everyday life.