Reduce the Fraction 10/10: Step-by-Step Simplification

Q: Why does 10/10 equal 1 instead of staying as a fraction?

Any fraction where the numerator equals the denominator represents one whole unit! Think of it as having 10 pieces out of 10 total pieces - that's the complete set, which equals 1.

Q: How do I find the highest common factor when both numbers are the same?

When the numerator and denominator are identical, the HCF is simply that number itself! For $ \frac{10}{10} $, the HCF is 10.

Q: What if I had a fraction like 15/15 or 7/7?

The same rule applies! Any fraction with equal numerator and denominator simplifies to 1. So $ \frac{15}{15} = 1 $ and $ \frac{7}{7} = 1 $.

Q: How can I check that 10/10 really equals 1?

Think about division: 10 ÷ 10 = 1. Also, imagine having 10 slices of pizza out of 10 total slices - you have the whole pizza, which is 1 complete pizza!

Fraction Simplification with Equal Numerator and Denominator

Reduce the given fraction into its simplest form:

$\frac{10}{10}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's simplify the fraction as much as possible.

00:09 First, divide by the greatest common factor, or G-C-F.

00:15 Remember to divide both the top and bottom numbers.

00:19 Now, go ahead and calculate the quotients.

00:23 Remember, any number divided by itself gives you 1.

00:28 And that's how we solve this problem!

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:

$\frac{10}{10}=$

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 10, therefore:

$\frac{10:10}{10:10}=\frac{1}{1}=1$

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the highest common factor (HCF) of numerator and denominator
Technique: Divide both parts by HCF: $\frac{10÷10}{10÷10} = \frac{1}{1}$
Check: Any fraction with identical numerator and denominator equals 1 ✓

Common Mistakes

Avoid these frequent errors

Thinking the fraction cannot be simplified
Don't assume 10/10 is already in simplest form = missing that it equals 1! This happens when students don't recognize that equal numerator and denominator always simplify to 1. Always check if both numbers share a common factor, especially when they're identical.

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 does 10/10 equal 1 instead of staying as a fraction?

Any fraction where the numerator equals the denominator represents one whole unit! Think of it as having 10 pieces out of 10 total pieces - that's the complete set, which equals 1.

How do I find the highest common factor when both numbers are the same?

When the numerator and denominator are identical, the HCF is simply that number itself! For $\frac{10}{10}$ , the HCF is 10.

Is 1 really the simplest form, or should I write it as 1/1?

The simplest form is just 1 (not 1/1). When a fraction equals a whole number, we write it as that whole number rather than keeping the fraction format.

What if I had a fraction like 15/15 or 7/7?

The same rule applies! Any fraction with equal numerator and denominator simplifies to 1. So $\frac{15}{15} = 1$ and $\frac{7}{7} = 1$ .

How can I check that 10/10 really equals 1?

Think about division: 10 ÷ 10 = 1. Also, imagine having 10 slices of pizza out of 10 total slices - you have the whole pizza, which is 1 complete pizza!

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