# Percentage Increases & Decreases

## Percentage Multipliers

To calculate percentage increases and decreases, we use Percentage multipliers. Percentage multipliers allow us to calculate percentage increases and percentage decreases very quickly, with one single multiplication.

By the end of this section we'll know how to find percentage multipliers as well as calculate any percentage increase, or decrease, such as:

Increasing $$48$$ by $$35\%$$ or Decreasing $$220$$ by $$40\%$$
We start by watching the following tutorial.

### Tutorial: Percentage Increases & Decreases - Percentage Multipliers

In the following tutorial we learn how to calculate percentage increases and decreases using percentage multipliers.

The method shown in the tutorial is summarized here in three steps.

## Percentages Increase & Decrease with Multipliers

To increase, or decrease a number $$N$$, by a percentage $$X\%$$ we multiply $$N$$ by a percentage multiplier (often just called multiplier).

We can calculate any percentage increase, or decrease, in three steps:

• Step 1: write $$X\%$$ in decimal form. Remember, this is done by moving the number $$X$$ back two decimal places.
Example: $$5\% = 0.05$$, $$12\% = 0.12$$, ... .
• Step 2: Calculate the percentage multiplier by adding, or subtracting, the decimal found in step 1 to, or from, $$1$$
• For percentage increases: add the decimal to $$1$$.
• For percentage decreases: subtract the decimal from $$1$$.
• Step 3: multiply the number $$N$$ by the multiplier, found in Step 2.

## Example 1

Increase $$80$$ kg by $$23\%$$.

### Solution

• Step 1: we write $$23\%$$ in decimal form: $23\% = 0.23$
• Step 2: we find the multiplier. Since we're increasing by $$23\%$$, we add $$0.23$$ to $$1$$: $1 + 0.23 = 1.23$
• Step 3: we multiply $$80$$ by the multiplier $$1.23$$: $80 \times 1.23 = 98.4$ So $$80$$kg increased by $$23\%$$ is $$98.4$$ kg.

## Example 2

Decrease $$\ \ 120$$ by $$19\%$$.

### Solution

• Step 1: we write $$19\%$$ in decimal form: $19\% = 0.19$
• Step 2: we find the multiplier. Since we're decreasing by $$19\%$$, we subtract $$0.19$$ from $$1$$: $1 - 0.19 = 0.81$
• Step 3: we multiply $$80$$ by the multiplier $$0.81$$: $120 \times 0.81 = 97.2$ So $$\ \ 120$$ decreased by $$19\%$$ is $$\ \ 97.20$$.

## Exercise 1

Find the percentage multipliers for each of the following increases and decreases:

1. Increase by $$27\%$$.

1. Decrease by $$14\%$$.

1. Increase by $$3\%$$.

1. Decrease by $$9\%$$.

1. Increase by $$118\%$$.

1. Increase by $$210\%$$.

1. Increase by $$79\%$$.

1. Increase by $$88\%$$.

1. Decrease by $$5\%$$.

1. Increase by $$0.8\%$$.

1. Decrease by $$1.5\%$$.

1. Increase by $$13.7\%$$.

Note: this exercise can be downloaded as a worksheet to practice with:

## Exercise 2

Using a percentage multiplier, and stating its value, calculate each of the following:

1. Increase $$240$$ by $$18\%$$.

1. Decrease $$820$$ by $$12\%$$.

1. Increase $$150$$ by $$6\%$$.

1. Decrease $$550$$ by $$9\%$$.

1. Increase $$70$$ by $$200\%$$

1. Increase $$68$$ by $$37\%$$.

1. Decrease $$120$$ by $$2.5\%$$

1. Decrease $$98$$ by $$14\%$$.

1. Increase $$640$$ by $$118\%$$

1. Decrease $$504$$ by $$67\%$$.

1. Increase $$49$$ by $$12.7\%$$

1. Decrease $$82$$ by $$9.9\%$$.

Note: this exercise can be downloaded as a worksheet to practice with: