Solve the Fraction: Simplifying 13/13 Step by Step

Q: Does this work for any number divided by itself?

Yes! Any non-zero number divided by itself equals 1. For example: $ \frac{5}{5} = 1 $, $ \frac{100}{100} = 1 $, even $ \frac{-7}{-7} = 1 $.

Q: What if the numerator and denominator are different?

Then you need to simplify by finding the GCD. For example, $ \frac{12}{15} = \frac{12 ÷ 3}{15 ÷ 3} = \frac{4}{5} $ because GCD(12,15) = 3.

Q: How can I remember this rule?

Remember the phrase: "Same over same equals one!" Whenever you see identical numbers in numerator and denominator, the answer is always 1.

Q: What about 0/0?

$ \frac{0}{0} $ is undefined, not 1! This is a special case in mathematics. Our rule only works for non-zero numbers divided by themselves.

Fraction Simplification with Equal Numerators

Solve the following expression:

$\frac{13}{13}=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following expression:

$\frac{13}{13}=$

Step-by-step solution

First, we will divide the numerator and denominator by the highest number that both are divisible by.

In this case, the number is 13.

Then we will divide the fraction as follows:

$\frac{13:13}{13:13}=\frac{1}{1}=1$

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Fundamental Rule: Any number divided by itself always equals 1
Technique: Divide both numerator and denominator by their GCD: $\frac{13}{13} = \frac{13 ÷ 13}{13 ÷ 13} = \frac{1}{1}$
Check: Verify by multiplying: $1 × 13 = 13$ and $13 ÷ 13 = 1$ ✓

Common Mistakes

Avoid these frequent errors

Thinking the answer is the numerator value
Don't assume $\frac{13}{13} = 13$ just because you see 13 on top! This gives you 13 instead of 1. When numerator and denominator are identical, they cancel out completely. Always remember that any non-zero number divided by itself equals 1.

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

Why does 13/13 equal 1 and not 13?

Think of it this way: if you have 13 cookies and divide them into 13 equal groups, each group gets 1 cookie. The fraction $\frac{13}{13}$ means "13 divided by 13", which always equals 1!

Does this work for any number divided by itself?

Yes! Any non-zero number divided by itself equals 1. For example: $\frac{5}{5} = 1$ , $\frac{100}{100} = 1$ , even $\frac{-7}{-7} = 1$ .

What if the numerator and denominator are different?

Then you need to simplify by finding the GCD. For example, $\frac{12}{15} = \frac{12 ÷ 3}{15 ÷ 3} = \frac{4}{5}$ because GCD(12,15) = 3.

How can I remember this rule?

Remember the phrase: "Same over same equals one!" Whenever you see identical numbers in numerator and denominator, the answer is always 1.

What about 0/0?

$\frac{0}{0}$ is undefined, not 1! This is a special case in mathematics. Our rule only works for non-zero numbers divided by themselves.

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