Calculating Percentage Changes with Decimal Multipliers

Recommended resources

The freely available resources this lesson will direct you to.

Welcome to our next lesson in Mathematics! In our previous session, we honed your ability to estimate answers, a crucial skill for checking if your calculations are on the right track. Now, we're shifting our focus from approximation to a highly efficient method for finding exact answers in a very common real-world scenario: percentage changes.

Today's lesson is all about how to calculate a percentage increase or decrease using a decimal multiplier. This powerful technique allows you to find the new value after a percentage change in a single step, which is much faster than the traditional two-step method. This skill will be incredibly useful, especially as we move on to topics like GST, discounts, and interest later in this module.

Part 1: Two Methods for Percentage Change

When we need to increase or decrease a number by a certain percentage, there are a couple of ways to approach it. One method is very intuitive, and another, the "multiplier method," is much faster once you understand it.

The following video from Cognito clearly explains both approaches. As you watch, pay attention to the difference between them.

GCSE Maths - Percentage Increase and Decrease (Multiplier Method) (2026/27 exams)

This video covers everything you need for today's learning goal, from the basic method to the more advanced multiplier technique. First, watch the section explaining the two-step method. This involves calculating the percentage amount first, then adding or subtracting it from the original value. Notice that it takes two separate calculations. Next, watch the main part of the video which introduces the multiplier method. Focus on how a single number—the multiplier—can do the entire job in one calculation. The video will show you how to find the multiplier for both increases and decreases. It also flags a very common mistake to watch out for!

What to watch for while viewing: How an 'increase' multiplier is always greater than 1. How a 'decrease' multiplier is always less than 1. The special way to handle percentages less than 10%, like 3% or 8%.

The video you just watched demonstrated that the multiplier method is a far more efficient way to handle these problems, especially when using a calculator. Let's break down the rules for finding these multipliers.

Part 2: The Rules for Finding a Decimal Multiplier

The key idea is to think of the original amount as 100%, or as the number 1. The percentage change then adjusts this number.

For a Percentage Increase

To increase a value by a percentage, you are starting with the full 100% and adding more.

An increase of 25% means you end up with $100% + 25% = 125%$ .
To find the multiplier, you convert this new percentage to a decimal: $125 \div 100 = 1.25$ .
So, to increase an amount by 25%, you simply multiply it by 1.25.

The following resource provides a clear, concise rule for this.

Percentage Multipliers

This document from MathsPanda summarises the rule for finding an increase multiplier.

Read the section under the heading "Increase by a percentage". Focus on this example and rule, which clearly states that to find the multiplier, you add the percentage to 100% and then convert it to a decimal.

For a Percentage Decrease

To decrease a value by a percentage, you are starting with the full 100% and taking some away.

A decrease of 25% means you are left with $100% - 25% = 75%$ .
To find the multiplier, you convert this remaining percentage to a decimal: $75 \div 100 = 0.75$ .
So, to decrease an amount by 25%, you simply multiply it by 0.75.

Let's look at the rule for this in the same document.

Percentage Multipliers

Now, let's confirm the rule for decreases.

Read the section under the heading "Decrease by a percentage". Pay attention to this example and the summary rule at the end of the section. It confirms that for a decrease, you subtract the percentage from 100% before converting to a decimal.

A Crucial Tip: Single-Digit Percentages

As the Cognito video pointed out, a common trap is mishandling percentages under 10%.

An increase of 6% is $100% + 6% = 106%$ . The multiplier is 1.06, not 1.6.
A decrease of 6% is $100% - 6% = 94%$ . The multiplier is 0.94.

Always remember that the two digits immediately after the decimal point represent the percentage change relative to 1.

Part 3: Let's Practice

Now it's your turn to apply the multiplier method. For each question, determine the correct decimal multiplier and then calculate the final answer.

Questions:

Increase $150 by 25%.
Decrease $90 by 12%.
Increase $3,400 by 6%.
A phone originally costing $1,200 is discounted by 15%. What is the sale price?

Solutions:

Increase $150 by 25%
- Multiplier: An increase of 25% means we want 125% of the original value. The multiplier is 1.25.
- Calculation: $150 \times 1.25 = $187.50$
Decrease $90 by 12%
- Multiplier: A decrease of 12% means we want $100% - 12% = 88%$ of the original value. The multiplier is 0.88.
- Calculation: $90 \times 0.88 = $79.20$
Increase $3,400 by 6%
- Multiplier: An increase of 6% means we want 106% of the original value. The multiplier is 1.06.
- Calculation: $3, 400 \times 1.06 = $3, 604$
Phone discount
- Multiplier: A discount of 15% is a decrease. We are left with $100% - 15% = 85%$ of the price. The multiplier is 0.85.
- Calculation: $1, 200 \times 0.85 = $1, 020$

Key Takeaways

Excellent work! You've just learned a very efficient mathematical tool used widely in everyday life, from shopping to banking.

To calculate a percentage change in one step, use a decimal multiplier.
For an increase of $x %$ , the multiplier is $1 + (x /100)$ .
For a decrease of $x %$ , the multiplier is $1 - (x /100)$ .
Be careful with single-digit percentages: a 7% increase uses a multiplier of 1.07.

In our next lesson, we will continue exploring proportional reasoning by learning how to divide a quantity in a given part-to-part ratio. This is another fundamental skill for comparing and sharing quantities.