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# Working with Percentages: Increase and Decrease

### Working with Percentages: Increase and Decrease

Percentages increase and percentage decrease are useful ways to see how much amounts change over time.

A **percentage** shows us a proportion of a whole (100%).

What is $100\%$ of 12 cans of cola?

In this lesson, we will look at increasing or decreasing an amount by a percentage. We will need to understand multiplication and division of decimals.

Often, we need to increase or decrease an amount by a percentage, to see how it has changed.

Payrises and VAT are examples of **percentage increase**. Discounts are examples of **percentage decrease**.

You buy a car costing £900 and later decide to sell it at a price reduced by 5%. Let's have a go at finding the new price!

Find the percentage of the new price

The old price has been reduced by 5%. Therefore, the new price is $100-5=95\%$ of the old price.

Apply this percentage to the price

$95\%$ of the old price is $0.95 \times 900=855$

Nice! 🤟🏼

The new price is $\pounds855$

When you are peeling carrots, you notice that 5% of the mass is lost. How much is left from a bag containing 2.5kg?

Let's see what happens when we need to **increase** the value by a percentage.

Your bill at a restaurant is $\pounds121$. You want to add a tip of $12\%$. What is the final total?

We need to increase the price by $12\%$

Therefore, the new price is $112\%$ of the original.

What is $112\%$ as a decimal?

Multiply $\pounds121$ by $1.12$ and give your answer to 2 decimal places

The final answer is $\pounds135.52$

Nice! We've added on a tip.

You are at a sale and see a jumper with a label that says "Was $\pounds50$ - now reduced by $15\%$'

How much is the jumper now?