A multiplier is a number you multiply by the original value to find a new value after a percentage increase or decrease. Multipliers are a faster alternative to finding the change first and then adding or subtracting it.

 
To find a multiplier for a percentage increase, add the percentage (as a decimal) to \(1\).

$$
\text{multiplier} = 1 + \frac{\text{percentage increase}}{100}
$$

For example, a 20% increase:

$$
1 + \frac{20}{100} = 1.2
$$

If a price of \(50\) increases by 20%, the new price is:

$$
50 \times 1.2 = 60
$$

 
To find a multiplier for a percentage decrease, subtract the percentage (as a decimal) from \(1\).

$$
\text{multiplier} = 1 - \frac{\text{percentage decrease}}{100}
$$

For example, a 15% decrease:

$$
1 - \frac{15}{100} = 0.85
$$

If a value of \(80\) decreases by 15%, the new value is:

$$
80 \times 0.85 = 68
$$

Multipliers can also be used for repeated changes. Each change is applied one after the other by multiplying again.

$$
100 \times 1.1 \times 1.1 = 121
$$

This represents two consecutive 10% increases, not a single 20% increase.

 
Always interpret multipliers carefully.

• A multiplier greater than \(1\) represents an increase.
• A multiplier between \(0\) and \(1\) represents a decrease.

Multipliers change the value in one step, but the original value still matters, especially when changes are repeated.