Reduce the Fraction 12/15 to Its Simplest Form: Step-by-Step Solution

Q: What if I can't see the HCF right away?

Start with small common factors like 2 or 3. You can simplify step by step! For example, if you divided by 3 first, you could check if the result can be simplified further.

Q: How do I know when a fraction is fully simplified?

A fraction is in simplest form when the numerator and denominator have no common factors except 1. Check: 4 and 5 only share the factor 1, so $ \frac{4}{5} $ is fully simplified!

Q: Why is the answer 4/5 and not 4/3?

The original explanation has an error! When we divide $ \frac{12}{15} $ by 3, we get $ \frac{12÷3}{15÷3} = \frac{4}{5} $, not $ \frac{4}{3} $. Always divide both the numerator and denominator by the same number.

Fraction Simplification with Common Factor Method

Reduce the given fraction into its simplest form:

$\frac{12}{15}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduce the fraction as much as possible

00:03 Divide by the greatest common factor

00:07 Make sure to divide both numerator and denominator

00:10 Calculate the quotients

00:14 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Reduce the given fraction into its simplest form:

$\frac{12}{15}=$

Step-by-step solution

We need to identify the highest common factor (HCF): The largest number that both the numerator and the denominator can be divided by.

In this case, the number is 3, therefore:

$\frac{12:3}{15:3}=\frac{4}{3}$

Final Answer

$\frac{4}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the highest common factor (HCF) of numerator and denominator
Technique: Divide both 12 and 15 by their HCF of 3
Check: Verify $\frac{4}{5}$ cannot be simplified further ✓

Common Mistakes

Avoid these frequent errors

Dividing by different numbers for numerator and denominator
Don't divide 12 by 4 and 15 by 3 = unequal fractions like $\frac{3}{5}$ ! This changes the fraction's value completely. Always divide both numerator and denominator by the same common factor.

Practice Quiz

Test your knowledge with interactive questions

Simplify the following fraction by a factor of 4:

$\frac{4}{8}=$

FAQ

Everything you need to know about this question

How do I find the highest common factor (HCF)?

List the factors of both numbers: 12 has factors 1, 2, 3, 4, 6, 12 and 15 has factors 1, 3, 5, 15. The largest number that appears in both lists is your HCF - in this case, 3!

What if I can't see the HCF right away?

Start with small common factors like 2 or 3. You can simplify step by step! For example, if you divided by 3 first, you could check if the result can be simplified further.

How do I know when a fraction is fully simplified?

A fraction is in simplest form when the numerator and denominator have no common factors except 1. Check: 4 and 5 only share the factor 1, so $\frac{4}{5}$ is fully simplified!

What if I get the wrong HCF?

No problem! If you use a smaller common factor first, you can always continue simplifying. For instance, dividing by 1 won't change anything, and dividing by 2 would only work if both numbers are even.

Why is the answer 4/5 and not 4/3?

The original explanation has an error! When we divide $\frac{12}{15}$ by 3, we get $\frac{12÷3}{15÷3} = \frac{4}{5}$ , not $\frac{4}{3}$ . Always divide both the numerator and denominator by the same number.

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