Verify the Fraction Equation: Is 4·8/4 = 1/8 Correct?

Q: Why can't I just cancel the 4s right away?

You can only cancel factors that are multiplied, not added or part of other operations. Here, the 4 in the numerator is multiplied by 8 first, so you must complete $ 4\cdot8 = 32 $ before dividing.

Q: What's the correct way to simplify this fraction?

Step 1: Calculate numerator: $ 4\cdot8 = 32 $Step 2: Divide: $ \frac{32}{4} = 8 $The correct answer is 8, not $ \frac{1}{8} $!

Q: How do I know when I can cancel terms in fractions?

You can only cancel common factors from the numerator and denominator. For example, in $ \frac{12}{16} $, both 12 and 16 have factor 4, so $ \frac{12}{16} = \frac{3}{4} $.

Q: What does 1/8 equal as a decimal?

$ \frac{1}{8} = 0.125 $, which is much smaller than 8! This huge difference should be a red flag that something went wrong in the simplification.

Q: Is there a way to check my fraction work?

Yes! Convert to decimals and see if they make sense. Also, ask yourself: does my answer seem reasonable given the original numbers?

Fraction Simplification with Order of Operations

Determine if the simplification below is correct:

$\frac{4\cdot8}{4}=\frac{1}{8}$

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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

00:04 Let's reduce what we can

00:18 Let's compare the expressions, we'll see they are opposite

00:26 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:

$\frac{4\cdot8}{4}=\frac{1}{8}$

Step-by-step solution

We will divide the fraction exercise into two multiplication exercises:

$\frac{4}{4}\times\frac{8}{1}=$

We simplify:

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

Therefore, the described simplification is false.

Final Answer

Incorrect

Key Points to Remember

Essential concepts to master this topic

Order: Perform multiplication in numerator before dividing
Technique: $\frac{4\cdot8}{4} = \frac{32}{4} = 8$ step by step
Check: Verify final answer makes sense: 8 ≠ 0.125, so equation is incorrect ✓

Common Mistakes

Avoid these frequent errors

Canceling terms incorrectly across multiplication
Don't cancel the 4s immediately to get $\frac{8}{1} = \frac{1}{8}$ = wrong answer! This ignores order of operations and creates false equality. Always complete multiplication first: $4\cdot8 = 32$ , then divide $\frac{32}{4} = 8$ .

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 can't I just cancel the 4s right away?

You can only cancel factors that are multiplied, not added or part of other operations. Here, the 4 in the numerator is multiplied by 8 first, so you must complete $4\cdot8 = 32$ before dividing.

What's the correct way to simplify this fraction?

Step 1: Calculate numerator: $4\cdot8 = 32$
Step 2: Divide: $\frac{32}{4} = 8$
The correct answer is 8, not $\frac{1}{8}$ !

How do I know when I can cancel terms in fractions?

You can only cancel common factors from the numerator and denominator. For example, in $\frac{12}{16}$ , both 12 and 16 have factor 4, so $\frac{12}{16} = \frac{3}{4}$ .

What does 1/8 equal as a decimal?

$\frac{1}{8} = 0.125$ , which is much smaller than 8! This huge difference should be a red flag that something went wrong in the simplification.

Is there a way to check my fraction work?

Yes! Convert to decimals and see if they make sense. Also, ask yourself: does my answer seem reasonable given the original numbers?

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