Verify the Equation: Is 7/(7·8) = 8 Correct?

Q: Why can't I just cancel the 7s and get 8?

When you cancel the 7s, you're left with 1 over 8, not just 8! The denominator still has the factor 8 remaining: $ \frac{7}{7\cdot8} = \frac{1}{8} $.

Q: How do I know what factors I can cancel?

You can only cancel identical factors that appear in both numerator and denominator. Here, the 7 appears in both places, but the 8 only appears in the denominator.

Q: What's the difference between 1/8 and 8?

$ \frac{1}{8} = 0.125 $ while 8 = 8.000. That's a huge difference! Always be careful when simplifying fractions.

Q: Can I check my answer by converting to decimals?

Yes! $ \frac{7}{7\cdot8} = \frac{7}{56} = 0.125 $. Since 0.125 ≠ 8, the original equation is incorrect.

Fraction Simplification with Common Factor Cancellation

Determine if the simplification shown below is correct:

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

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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

00:08 Let's reduce what we can

00:13 Let's compare the expressions, we'll see they are opposite

00:20 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 shown below is correct:

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

Step-by-step solution

Let's consider the fraction and break it down into two multiplication exercises:

$\frac{7}{7}\times\frac{1}{8}$

We simplify:

$1\times\frac{1}{8}=\frac{1}{8}$

Therefore, the described simplification is false.

Final Answer

Incorrect

Key Points to Remember

Essential concepts to master this topic

Rule: Cancel common factors in numerator and denominator before multiplying
Technique: Rewrite $\frac{7}{7\cdot8}$ as $\frac{7}{7} \times \frac{1}{8} = 1 \times \frac{1}{8}$
Check: Final answer $\frac{1}{8} = 0.125$ , not 8 ✓

Common Mistakes

Avoid these frequent errors

Incorrectly canceling the entire denominator
Don't cancel 7 from both numerator and 7·8, leaving just 8! This ignores the remaining factor of 8 in the denominator. Always cancel only matching factors: 7 cancels with 7, leaving 1/8.

Practice Quiz

Test your knowledge with interactive questions

Identify the field of application of the following fraction:

$\frac{7}{13+x}$

FAQ

Everything you need to know about this question

Why can't I just cancel the 7s and get 8?

When you cancel the 7s, you're left with 1 over 8, not just 8! The denominator still has the factor 8 remaining: $\frac{7}{7\cdot8} = \frac{1}{8}$ .

How do I know what factors I can cancel?

You can only cancel identical factors that appear in both numerator and denominator. Here, the 7 appears in both places, but the 8 only appears in the denominator.

What's the difference between 1/8 and 8?

$\frac{1}{8} = 0.125$ while 8 = 8.000. That's a huge difference! Always be careful when simplifying fractions.

Can I check my answer by converting to decimals?

Yes! $\frac{7}{7\cdot8} = \frac{7}{56} = 0.125$ . Since 0.125 ≠ 8, the original equation is incorrect.

What if there were no common factors to cancel?

Then you'd multiply the denominator terms together and leave the fraction as is. For example, $\frac{5}{3\cdot4} = \frac{5}{12}$ since 5 shares no factors with 3 or 4.

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