Verify the Fraction Simplification: 5·8/8·3 = 5/3

Q: Why can I cancel the 8s but not the other numbers?

You can only cancel numbers that are common factors - meaning they appear in both the numerator and denominator. Here, 8 appears in both $ 5 \cdot 8 $ and $ 8 \cdot 3 $, but 5 and 3 don't share any common factors.

Q: What does it mean to 'break down' the fraction?

Breaking down means separating the fraction into parts you can work with easily. Here we split $ \frac{5 \cdot 8}{8 \cdot 3} $ into $ \frac{8}{8} \times \frac{5}{3} $ to see the cancellation clearly.

Q: How do I know when a fraction is fully simplified?

A fraction is fully simplified when the numerator and denominator share no common factors other than 1. In $ \frac{5}{3} $, since 5 and 3 are both prime numbers, this fraction cannot be simplified further.

Q: Can I always rearrange multiplication like this?

Yes! The commutative property lets you rearrange multiplication in any order. So $ 5 \cdot 8 = 8 \cdot 5 $, and you can group factors however makes the cancellation easiest to see.

Q: What if there are no common factors to cancel?

If there are no common factors, the fraction is already in simplest form! Just leave it as is. Not every fraction can be simplified - that's perfectly normal.

Fraction Simplification with Common Factors

Determine if the simplification below is correct:

$\frac{5\cdot8}{8\cdot3}=\frac{5}{3}$

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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

00:07 Reduce what is possible

00:16 Compare between the expressions

00:23 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:

$\frac{5\cdot8}{8\cdot3}=\frac{5}{3}$

Step-by-step solution

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

$\frac{8}{8}\times\frac{5}{3}$

We simplify:

$1\times\frac{5}{3}=\frac{5}{3}$

Final Answer

Correct

Key Points to Remember

Essential concepts to master this topic

Cancellation Rule: Common factors in numerator and denominator can be cancelled
Technique: Factor out 8: $\frac{5 \cdot 8}{8 \cdot 3} = \frac{8}{8} \times \frac{5}{3}$
Check: Verify 8÷8 = 1, so final answer is 1 × 5/3 = 5/3 ✓

Common Mistakes

Avoid these frequent errors

Cancelling numbers that aren't common factors
Don't cancel numbers like 5 and 3 in this fraction = wrong answer! These aren't shared between numerator and denominator. Always cancel only factors that appear in both numerator and denominator.

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 I cancel the 8s but not the other numbers?

You can only cancel numbers that are common factors - meaning they appear in both the numerator and denominator. Here, 8 appears in both $5 \cdot 8$ and $8 \cdot 3$ , but 5 and 3 don't share any common factors.

What does it mean to 'break down' the fraction?

Breaking down means separating the fraction into parts you can work with easily. Here we split $\frac{5 \cdot 8}{8 \cdot 3}$ into $\frac{8}{8} \times \frac{5}{3}$ to see the cancellation clearly.

How do I know when a fraction is fully simplified?

A fraction is fully simplified when the numerator and denominator share no common factors other than 1. In $\frac{5}{3}$ , since 5 and 3 are both prime numbers, this fraction cannot be simplified further.

Can I always rearrange multiplication like this?

Yes! The commutative property lets you rearrange multiplication in any order. So $5 \cdot 8 = 8 \cdot 5$ , and you can group factors however makes the cancellation easiest to see.

What if there are no common factors to cancel?

If there are no common factors, the fraction is already in simplest form! Just leave it as is. Not every fraction can be simplified - that's perfectly normal.

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