Express the Fraction 3/4: Finding Equivalent Forms

Q: How do I know if a fraction is already in simplest form?

A fraction is in simplest form when the numerator and denominator have no common factors except 1. For $ \frac{3}{4} $, since 3 and 4 share no common factors, it's already simplified!

Q: Why can't I just divide both by 2?

You can only divide by common factors! Since 3 is odd, it's not divisible by 2. Always check if both numbers are actually divisible by your chosen factor.

Q: Is 3/4 the same as 0.75?

Yes! $ \frac{3}{4} = 0.75 $ because 3 ÷ 4 = 0.75. Both represent the same value, just in different forms.

Q: When should I leave my answer as a fraction vs. a decimal?

Keep it as a fraction when the problem asks for exact values or when working with other fractions. Use decimals for measurements or when specified in the problem.

Simplifying Fractions with No Common Factors

Solve the following problem:

$\frac{3}{4}=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following problem:

$\frac{3}{4}=$

Step-by-step solution

We will divide the numerator and denominator by the highest number that both are divisible by.

In this case, there is no number by which we can divide, so the fraction will remain as it is.

Final Answer

$\frac{3}{4}$

Key Points to Remember

Essential concepts to master this topic

Simplest Form: Find greatest common divisor of numerator and denominator
Technique: Check if 3 and 4 share factors: 3÷1=3, 4÷1=4
Check: When GCD is 1, fraction is already simplified ✓

Common Mistakes

Avoid these frequent errors

Trying to simplify when already in lowest terms
Don't force simplification when numerator and denominator share no common factors = unnecessary confusion! Since 3 and 4 have no common factors except 1, the fraction is already simplified. Always check for common factors first before attempting to reduce.

Practice Quiz

Test your knowledge with interactive questions

Write the fraction shown in the picture, in words:

FAQ

Everything you need to know about this question

How do I know if a fraction is already in simplest form?

A fraction is in simplest form when the numerator and denominator have no common factors except 1. For $\frac{3}{4}$ , since 3 and 4 share no common factors, it's already simplified!

What if I can't tell if two numbers have common factors?

List the factors of each number! Factors of 3: 1, 3. Factors of 4: 1, 2, 4. The only common factor is 1, so the fraction can't be simplified further.

Why can't I just divide both by 2?

You can only divide by common factors! Since 3 is odd, it's not divisible by 2. Always check if both numbers are actually divisible by your chosen factor.

Is 3/4 the same as 0.75?

Yes! $\frac{3}{4} = 0.75$ because 3 ÷ 4 = 0.75. Both represent the same value, just in different forms.

When should I leave my answer as a fraction vs. a decimal?

Keep it as a fraction when the problem asks for exact values or when working with other fractions. Use decimals for measurements or when specified in the problem.

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