Reduce the Ratio 8:6: Finding the Simplest Form

Q: What if the two numbers don't have any common factors except 1?

Then the ratio is already in its simplest form! For example, $ 5:7 $ cannot be reduced further since GCD(5,7) = 1.

Q: Can I reduce ratios with more than two terms?

Yes! Find the GCD of all terms. For $ 12:18:24 $, the GCD is 6, so it becomes $ 2:3:4 $.

Q: Why is it important to reduce ratios to simplest form?

Reduced ratios are easier to understand and compare. $ 4:3 $ clearly shows the relationship better than $ 8:6 $.

Q: What's the difference between a ratio and a fraction?

A ratio compares two quantities (like $ 4:3 $), while a fraction represents part of a whole (like $ \frac{4}{7} $ of the total).

Ratio Simplification with Greatest Common Divisor

What is the reduced ratio of the ratio $8:6$ ?

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Step-by-step written solution

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Understand the problem

What is the reduced ratio of the ratio $8:6$ ?

Step-by-step solution

To solve this problem, let's reduce the ratio $8:6$ to its simplest form.

First, we need to determine the greatest common divisor (GCD) of the numbers 8 and 6. The divisors of 8 are 1, 2, 4, and 8. The divisors of 6 are 1, 2, 3, and 6. The greatest common divisor shared by both 8 and 6 is 2.

Next, we simplify the ratio by dividing both terms of the ratio by their GCD:

Divide 8 by 2: $\frac{8}{2} = 4$
Divide 6 by 2: $\frac{6}{2} = 3$

Thus, the ratio $8:6$ simplifies to $4:3$ .

Therefore, the reduced ratio of the given ratio is $4:3$ .

Final Answer

$4:3$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the GCD of both terms to simplify ratios
Technique: Divide both terms by GCD: 8÷2 = 4 and 6÷2 = 3
Check: Verify GCD is correct by confirming no common factors remain ✓

Common Mistakes

Avoid these frequent errors

Dividing by a factor that isn't the greatest common divisor
Don't divide by just any common factor like 1 instead of finding GCD = partially reduced ratio! This leaves the ratio not fully simplified. Always find the greatest common divisor first, then divide both terms by it.

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

How do I find all the divisors of a number?

Start with 1 and the number itself, then find pairs that multiply to give your number. For 8: 1×8=8 and 2×4=8, so divisors are 1, 2, 4, 8.

What if the two numbers don't have any common factors except 1?

Then the ratio is already in its simplest form! For example, $5:7$ cannot be reduced further since GCD(5,7) = 1.

Can I reduce ratios with more than two terms?

Yes! Find the GCD of all terms. For $12:18:24$ , the GCD is 6, so it becomes $2:3:4$ .

Why is it important to reduce ratios to simplest form?

Reduced ratios are easier to understand and compare. $4:3$ clearly shows the relationship better than $8:6$ .

What's the difference between a ratio and a fraction?

A ratio compares two quantities (like $4:3$ ), while a fraction represents part of a whole (like $\frac{4}{7}$ of the total).

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