How to simplify ratios?

Understand the Problem

The question is asking how to simplify ratios. Simplifying a ratio means reducing it to its simplest form, similar to simplifying a fraction. This involves dividing all parts of the ratio by their greatest common factor (GCF).

Answer

Divide all parts of the ratio by their greatest common factor (GCF). Example: $12:18:30$ simplifies to $2:3:5$.

Steps to Solve

Find the Greatest Common Factor (GCF)

Find the GCF of all the numbers in the ratio. In this case, we need more information because no numbers are in the ratio.

To illustrate with an example, consider the ratio $12:18:30$. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The greatest common factor (GCF) of 12, 18, and 30 is 6.

Divide by the GCF

Divide each number in the ratio by the GCF found in the previous step.

Using our previous example, divide each part of the ratio $12:18:30$ by 6:

$12 \div 6 = 2$

$18 \div 6 = 3$

$30 \div 6 = 5$

This gives us the simplified ratio $2:3:5$.

To simplify a ratio, divide all parts of the ratio by their greatest common factor (GCF).

For the example $12:18:30$, the simplified ratio is $2:3:5$.

More Information

Simplifying ratios is analogous to simplifying fractions. Both involve finding a common factor and dividing through to reach the simplest form. Ratios and fractions are used to represent relationships between quantities.

Tips

A common mistake is not finding the greatest common factor. If you divide by a common factor that isn't the greatest, you'll need to repeat the process until the ratio is fully simplified. For instance, if you divided $12:18:30$ by 2 initially, you'd get $6:9:15$, and you'd then need to divide by 3 to get the final simplified ratio of $2:3:5$.

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