Calculate the Ratio: Converting 15 Apples and 10 Oranges to Simplified Form

Q: Why do we need to simplify ratios?

Simplifying ratios makes them easier to understand and compare. Instead of saying 15:10, we can say 3:2, which clearly shows that for every 3 apples, there are 2 oranges!

Q: What if the numbers don't have a common factor?

If the GCD is 1, the ratio is already in simplest form! For example, 7:4 cannot be simplified further because 7 and 4 share no common factors except 1.

Q: Can ratios be written as fractions?

Yes! The ratio 3:2 can also be written as the fraction $ \frac{3}{2} $. Both forms show the same relationship between the quantities.

Q: Does order matter in ratios?

Absolutely! The ratio 3:2 (apples to oranges) is completely different from 2:3 (oranges to apples). Always match the order to what the question asks for.

Ratio Simplification with Common Factors

In a basket, there are 15 apples and 10 oranges. What is the ratio of apples to oranges?

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Step-by-step written solution

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Understand the problem

In a basket, there are 15 apples and 10 oranges. What is the ratio of apples to oranges?

Step-by-step solution

To find the ratio of apples to oranges, divide the number of apples by the number of oranges.
Therefore, $\text{apples:oranges} = \frac{15}{10} = 3:2$ .
Thus, the ratio of apples to oranges is $3:2$ .

Final Answer

$3:2$

Key Points to Remember

Essential concepts to master this topic

Rule: Write ratio as first quantity to second quantity
Technique: Find GCD of 15 and 10, which is 5
Check: Verify $3 \times 5 = 15$ and $2 \times 5 = 10$ ✓

Common Mistakes

Avoid these frequent errors

Writing the ratio in reverse order
Don't write oranges to apples as 10:15 when asked for apples to oranges = wrong order! The question asks specifically for apples to oranges, so apples must come first. Always read carefully and write the first item mentioned first in your ratio.

Practice Quiz

Test your knowledge with interactive questions

What is the ratio between the orange and gray parts in the drawing?

FAQ

Everything you need to know about this question

Why do we need to simplify ratios?

Simplifying ratios makes them easier to understand and compare. Instead of saying 15:10, we can say 3:2, which clearly shows that for every 3 apples, there are 2 oranges!

How do I find the greatest common divisor (GCD)?

List the factors of both numbers and find the largest one they share. For 15: 1, 3, 5, 15. For 10: 1, 2, 5, 10. The GCD is 5 since it's the largest common factor.

What if the numbers don't have a common factor?

If the GCD is 1, the ratio is already in simplest form! For example, 7:4 cannot be simplified further because 7 and 4 share no common factors except 1.

Can ratios be written as fractions?

Yes! The ratio 3:2 can also be written as the fraction $\frac{3}{2}$ . Both forms show the same relationship between the quantities.

Does order matter in ratios?

Absolutely! The ratio 3:2 (apples to oranges) is completely different from 2:3 (oranges to apples). Always match the order to what the question asks for.

How can I check if my simplified ratio is correct?

Multiply both parts of your simplified ratio by the same number to see if you get back to the original quantities. Here: $3 \times 5 = 15$ apples and $2 \times 5 = 10$ oranges ✓

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