Simplify the Fraction: 100000/100000 Using Factor Method

Fraction Simplification with Identity Factors

Simplify the following fraction by a factor of 1:

100000100000= \frac{100000}{100000}=

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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
00:07 Make sure to divide both numerator and denominator
00:13 When dividing any number by 1, the quotient is always equal to the number itself
00:20 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 by a factor of 1:

100000100000= \frac{100000}{100000}=

2

Step-by-step solution

We will reduce in the following way, divide the numerator by 1 and the denominator by 1:

100000:1100000:1=100000100000 \frac{100000:1}{100000:1}=\frac{100000}{100000}

3

Final Answer

100000100000 \frac{100000}{100000}

Key Points to Remember

Essential concepts to master this topic
  • Identity Rule: Dividing by 1 leaves any fraction unchanged
  • Factor Method: 100000100000÷11=100000100000 \frac{100000}{100000} ÷ \frac{1}{1} = \frac{100000}{100000}
  • Verification: Check that both numerator and denominator remain equal ✓

Common Mistakes

Avoid these frequent errors
  • Confusing simplification with actual reduction
    Don't think dividing by 1 should change the fraction = 100000100000 \frac{100000}{100000} becomes something different! Division by 1 is the identity operation and leaves numbers unchanged. Always remember that simplifying by a factor of 1 means the fraction stays exactly the same.

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

Why doesn't the fraction change when I divide by 1?

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Dividing by 1 is the identity operation in mathematics - it leaves any number completely unchanged! Just like 5 ÷ 1 = 5, when you divide both parts of a fraction by 1, you get the exact same fraction.

Isn't this fraction equal to 1 since the numerator and denominator are the same?

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You're absolutely right that 100000100000=1 \frac{100000}{100000} = 1 ! However, the question asks to simplify by a factor of 1, which means divide both parts by 1, keeping the fraction form unchanged.

When would I actually need to simplify by a factor of 1?

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This might seem silly, but it's important for understanding the simplification process. It shows that dividing by 1 doesn't change anything, which helps when learning to simplify by other factors like 2, 5, or 10.

How is this different from finding the GCD?

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Great question! The GCD (Greatest Common Divisor) of 100000 and 100000 is actually 100000, not 1. This problem specifically asks to use factor 1 to demonstrate the identity property, not to find the most simplified form.

What if the question asked me to simplify by a different factor?

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Then you'd divide both numerator and denominator by that factor! For example: 100000÷10000100000÷10000=1010 \frac{100000 ÷ 10000}{100000 ÷ 10000} = \frac{10}{10} . The key is using the same factor for both parts.

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