# What is the Simplest Form of a Ratio? | Don't Memorise | Summary and Q&A

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December 17, 2014
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Infinity Learn NEET
What is the Simplest Form of a Ratio? | Don't Memorise

## TL;DR

Learn how to simplify ratios to their simplest form by dividing the numerator and denominator by their highest common factor (HCF).

## Key Insights

• 😑 Ratios can be expressed in different ways by multiplying or dividing the numerator and denominator by the same value.
• 🥳 Dividing the numerator and denominator by their HCF simplifies the ratio to its simplest form.
• 💁 Common factors help identify the values to divide the numerator and denominator by to obtain the simplest form.
• ✋ The HCF is the highest number that divides both the numerator and denominator evenly.

## Transcript

ratio of the number of chocolates gorov received to the number of chocolates J received is 2 is to 3 and that can also be written as 2x3 we have seen that 2x3 can be written in different ways we can multiply the numerator as well as the denominator by two and get 4X 6 or we can also multiply the numerator and the denominator by 3 to get 6 by 9 all ... Read More

### Q: How can we write the ratio 2:3 in different ways?

The ratio 2:3 can also be written as 4:6 or 6:9 by multiplying the numerator and denominator by 2 or 3, respectively. These ratios have the same value as 2:3.

### Q: How can we simplify the ratio 12:18?

To simplify 12:18, we divide the numerator and denominator by their highest common factor (HCF), which is 6. The simplified ratio is 2:3.

### Q: What if we have the ratio 30:50 and don't know the HCF?

In such cases, we look for the common factors of the numerator and denominator. Dividing both by the common factor(s) will simplify the ratio. In this case, dividing by 2 gives 15:25. Then, dividing by 5 gives the simplest form of 3:5.

### Q: How do we determine the HCF of a ratio?

The HCF is the highest number that divides both the numerator and denominator evenly. In the ratio 30:50, the HCF is 10 (2 * 5), which is the product of all the numbers we divided the numerator and denominator by.

## Summary & Key Takeaways

• Ratios express the relationship between two quantities and can be written in multiple ways.

• By multiplying or dividing the numerator and denominator by the same value, the ratio remains unchanged.

• To simplify a ratio, divide the numerator and denominator by their highest common factor (HCF).