Calculate Percentage: Finding What Percent 45 is of 180

Q: Why do we use X/100 in the proportion?

The X represents the percentage we're looking for, and percentages are always 'out of 100'. So X/100 means 'X percent', which is what we want to find!

Q: Can I just divide 45 by 180 directly?

Yes! Dividing gives you the decimal: 45 ÷ 180 = 0.25. Then multiply by 100 to get the percentage: 0.25 × 100 = 25%. Both methods work!

Q: How do I remember which number goes where in the proportion?

Think of it as: 'What percent is [part] of [whole]?' So the setup is always: $ \frac{\text{unknown %}}{100} = \frac{\text{part}}{\text{whole}} $

Q: Why do we cross multiply instead of just solving normally?

Cross multiplication is just a shortcut for clearing fractions! It's the same as multiplying both sides by 100 and by 180, but faster.

Q: What does 'reduce' mean in the solution?

Reducing means simplifying by dividing both sides by a common factor. Here, 180X = 4500 becomes 18X = 450 by dividing both sides by 10.

Percentage Calculations with Cross Multiplication

Calculate 45 over 180 as a percentage:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's calculate what 45 is as a percentage of 180.

00:10 We use the formula for percentages. Ready? Here we go.

00:17 First, divide 45 by 180. Then, multiply the result by 100.

00:23 Let's break it down into simpler factors and reduce, if possible.

00:40 And that's how we find the percentage! Well done.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate 45 over 180 as a percentage:

Step-by-step solution

When calculating percentages, we need to know the following simple equation:

Percentage calculation formula

Using the two pieces of known data, we are able to calculate the percentage:

In this case, we know the percentage value - 45

And the initial quantity - 180

Therefore, we can insert this information into the formula:

X/100 = 45/180

We'll multiply by cross multiplication:

180X=45*100

180X=4500

Let's reduce:

18X=450

Divide by 18:

X=25

Hence the answer is 25%

Final Answer

25%

Key Points to Remember

Essential concepts to master this topic

Formula: Set up proportion X/100 = part/whole
Technique: Cross multiply 180X = 45 × 100 = 4500
Check: Verify 25% of 180 equals 45: 180 × 0.25 = 45 ✓

Common Mistakes

Avoid these frequent errors

Setting up the proportion incorrectly
Don't write 45/100 = X/180 = wrong percentage! This puts the part over 100 instead of the unknown percentage. Always write X/100 = part/whole where X is the unknown percentage.

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 we use X/100 in the proportion?

The X represents the percentage we're looking for, and percentages are always 'out of 100'. So X/100 means 'X percent', which is what we want to find!

Can I just divide 45 by 180 directly?

Yes! Dividing gives you the decimal: 45 ÷ 180 = 0.25. Then multiply by 100 to get the percentage: 0.25 × 100 = 25%. Both methods work!

What if I get a decimal percentage like 33.33%?

That's completely normal! Many percentage problems result in decimals or fractions. Just round to a reasonable number of decimal places as needed.

How do I remember which number goes where in the proportion?

Think of it as: 'What percent is [part] of [whole]?' So the setup is always: $\frac{\text{unknown %}}{100} = \frac{\text{part}}{\text{whole}}$

Why do we cross multiply instead of just solving normally?

Cross multiplication is just a shortcut for clearing fractions! It's the same as multiplying both sides by 100 and by 180, but faster.

What does 'reduce' mean in the solution?

Reducing means simplifying by dividing both sides by a common factor. Here, 180X = 4500 becomes 18X = 450 by dividing both sides by 10.

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