Verify the Fraction Simplification: (6×3)/(6×3) = 1

Q: Do I need to multiply 6×3 first, or can I cancel right away?

For this verification problem, you should multiply first to get $ \frac{18}{18} $, then simplify. This shows you understand the complete process!

Q: What if the numbers were different, like 6×3 in numerator and 6×2 in denominator?

Then you'd get $ \frac{18}{12} = \frac{3}{2} $, which does not equal 1. The numerator and denominator must be exactly identical to equal 1.

Q: Is this the same as canceling common factors?

Yes! When you have $ \frac{6 \times 3}{6 \times 3} $, you can cancel both the 6's and the 3's, leaving $ \frac{1 \times 1}{1 \times 1} = 1 $.

Q: Will this always work with any identical products?

Absolutely! Whether it's $ \frac{2 \times 5}{2 \times 5} $ or $ \frac{7 \times 4 \times 9}{7 \times 4 \times 9} $, any fraction with identical numerator and denominator equals 1.

Fraction Simplification with Identical Numerators and Denominators

Determine if the simplification below is correct:

$\frac{6\cdot3}{6\cdot3}=1$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine if the reduction is correct

00:06 We'll reduce what we can, when reducing the entire fraction 1 always remains

00:12 Let's compare the expressions

00:17 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Determine if the simplification below is correct:

$\frac{6\cdot3}{6\cdot3}=1$

Step-by-step solution

We simplify the expression on the left side of the approximate equality:

$\frac{\textcolor{red}{\not{6}}\cdot\textcolor{blue}{\not{3}}}{\textcolor{red}{\not{6}}\cdot\textcolor{blue}{\not{3}}}\stackrel{?}{= }1\\ \downarrow\\ 1\stackrel{!}{= }1$ therefore, the described simplification is correct.

Therefore, the correct answer is A.

Final Answer

Correct

Key Points to Remember

Essential concepts to master this topic

Rule: Any fraction with identical numerator and denominator equals 1
Technique: Calculate 6×3 = 18, so $\frac{18}{18} = 1$
Check: Verify that numerator 6×3 and denominator 6×3 are exactly equal ✓

Common Mistakes

Avoid these frequent errors

Canceling factors before computing the products
Don't cancel 6 and 3 separately before multiplying = wrong process! This skips the actual calculation and misses the point of verifying the result. Always compute both 6×3 in numerator and 6×3 in denominator first, then simplify.

Practice Quiz

Test your knowledge with interactive questions

Determine if the simplification shown below is correct:

$\frac{7}{7\cdot8}=8$

FAQ

Everything you need to know about this question

Why does any fraction equal 1 when the top and bottom are the same?

Because division asks "how many times does the denominator fit into the numerator?" When they're identical, like $\frac{18}{18}$ , the answer is exactly once = 1!

Do I need to multiply 6×3 first, or can I cancel right away?

For this verification problem, you should multiply first to get $\frac{18}{18}$ , then simplify. This shows you understand the complete process!

What if the numbers were different, like 6×3 in numerator and 6×2 in denominator?

Then you'd get $\frac{18}{12} = \frac{3}{2}$ , which does not equal 1. The numerator and denominator must be exactly identical to equal 1.

Is this the same as canceling common factors?

Yes! When you have $\frac{6 \times 3}{6 \times 3}$ , you can cancel both the 6's and the 3's, leaving $\frac{1 \times 1}{1 \times 1} = 1$ .

Will this always work with any identical products?

Absolutely! Whether it's $\frac{2 \times 5}{2 \times 5}$ or $\frac{7 \times 4 \times 9}{7 \times 4 \times 9}$ , any fraction with identical numerator and denominator equals 1.

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