Calculate Percentage Increase: 40 to 45 Pesos Movie Ticket Price Change

Q: Why do I divide by the original price and not the new price?

Percentage increase compares the change to what you started with. The original price of 40 pesos is your reference point. Dividing by 45 would tell you what percent the increase is of the new price, not the increase rate.

Q: How do I remember the percentage increase formula?

Think of it as: How much did it grow compared to what I had? So it's always $ \frac{\text{increase}}{\text{original}} \times 100 $

Q: What if I get a decimal answer like 12.5%?

Decimal percentages are completely normal! 12.5% means 12.5 out of every 100, or $ \frac{1}{8} $ of the original amount.

Q: Can I use this same method for percentage decrease?

Yes! The formula works the same way. Just find the decrease amount, divide by the original value, and multiply by 100. The result will show how much it decreased as a percentage.

Q: Why do we multiply by 100 at the end?

Multiplying by 100 converts the decimal to a percentage. Without it, $ \frac{5}{40} = 0.125 $ which means the same thing as 12.5%, just in different form.

Percentage Increase with Division Method

The price of the movie ticket rose from 40 to 45 pesos. By what percentage did the price increase?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The price of the movie ticket rose from 40 to 45 pesos. By what percentage did the price increase?

Step-by-step solution

In order to answer the question we must first understand how much the ticket costs:

45-40=5

That is, the price of the ticket increased by 5$.

Now we need to determine what the percentage value of the 5 pesos increase is. In order to determine this we will divide the increase by the original price and multiply it by 100 to convert it into a percentage.

5/40 * 100

We start by converting the 100 into fraction form.

5/40 * 100/1

When there is a multiplication of fractions, we can multiply numerator by numerator and denominator by denominator.

5*100 / 40*1

500 / 40

Thus we simplify as follows:

50/4

Lastly we convert the fraction into its complete form.

50/4 = 12.5

Final Answer

12.5%

Key Points to Remember

Essential concepts to master this topic

Formula: Percentage increase = (increase ÷ original value) × 100
Technique: Find difference first: 45 - 40 = 5 pesos increase
Check: Verify: 40 + (40 × 0.125) = 40 + 5 = 45 ✓

Common Mistakes

Avoid these frequent errors

Using the new value as the base instead of original
Don't divide by the new price (45) = wrong percentage! This gives 5/45 = 11.1% which is incorrect. Always divide the increase by the original value (40) to find the true percentage increase.

Practice Quiz

Test your knowledge with interactive questions

Calculate 30 over 100 as a percentage:

FAQ

Everything you need to know about this question

Why do I divide by the original price and not the new price?

Percentage increase compares the change to what you started with. The original price of 40 pesos is your reference point. Dividing by 45 would tell you what percent the increase is of the new price, not the increase rate.

How do I remember the percentage increase formula?

Think of it as: How much did it grow compared to what I had? So it's always $\frac{\text{increase}}{\text{original}} \times 100$

What if I get a decimal answer like 12.5%?

Decimal percentages are completely normal! 12.5% means 12.5 out of every 100, or $\frac{1}{8}$ of the original amount.

Can I use this same method for percentage decrease?

Yes! The formula works the same way. Just find the decrease amount, divide by the original value, and multiply by 100. The result will show how much it decreased as a percentage.

Why do we multiply by 100 at the end?

Multiplying by 100 converts the decimal to a percentage. Without it, $\frac{5}{40} = 0.125$ which means the same thing as 12.5%, just in different form.

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