Simplify the Fraction: Reducing 1/1 to Its Simplest Form

Fraction Simplification with Unit Fractions

Simplify the following fraction:

11= \frac{1}{1}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Reduce the fraction by 1
00:03 Divide the fraction by the given factor
00:06 Make sure to divide both numerator and denominator
00:09 Any number divided by 1 is always equal to itself
00:13 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Simplify the following fraction:

11= \frac{1}{1}=

2

Step-by-step solution

Let's reduce as follows, we'll divide both the numerator and denominator by 1:

1:11:1=11 \frac{1:1}{1:1}=\frac{1}{1}

3

Final Answer

11 \frac{1}{1}

Key Points to Remember

Essential concepts to master this topic
  • Identity Rule: Any number divided by itself equals one
  • Recognition: 11 \frac{1}{1} is already in simplest form since GCD(1,1) = 1
  • Verification: Check that 1 ÷ 1 = 1, confirming the fraction equals 1 ✓

Common Mistakes

Avoid these frequent errors
  • Trying to reduce 1/1 further
    Don't think 1/1 needs more simplification = confusion about what "simplest form" means! A fraction is simplified when numerator and denominator have no common factors other than 1. Always recognize that 1/1 is already fully simplified since GCD(1,1) = 1.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

\( 5:6= \)

FAQ

Everything you need to know about this question

Why is 1/1 already in simplest form?

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A fraction is in simplest form when the numerator and denominator have no common factors other than 1. Since both the numerator and denominator are 1, their greatest common divisor is 1, so 11 \frac{1}{1} cannot be reduced further.

Does 1/1 equal 1?

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Yes! 11=1 \frac{1}{1} = 1 because any number divided by itself equals 1. Think of it as: if you have 1 whole thing and divide it into 1 equal part, each part is the whole thing.

Is there a difference between 1 and 1/1?

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Mathematically, no difference - they represent the same value. However, 11 \frac{1}{1} is the fraction form while 1 is the whole number form. Both equal the same amount.

How do I know when a fraction is fully simplified?

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A fraction is fully simplified when the greatest common divisor (GCD) of the numerator and denominator is 1. Use the GCD to check: if it's 1, you're done!

Can 1/1 be written differently?

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Yes! 11 \frac{1}{1} can be written as 1, 22 \frac{2}{2} , 33 \frac{3}{3} , etc. But 11 \frac{1}{1} is the simplest fraction form because it uses the smallest possible numbers.

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