Verify the Equation: Is (3×7)/(7×3) = 0 Correct?

Q: Why does any number divided by itself equal 1?

Think of it this way: if you have 21 cookies and divide them into groups of 21, you get exactly 1 group. That's why $ \frac{21}{21} = 1 $!

Q: What if the numbers were different, like 3×5 and 7×2?

Then you'd calculate each part separately: $ \frac{3×5}{7×2} = \frac{15}{14} $. Since 15 ≠ 14, this fraction cannot be simplified to 1.

Q: How can I tell when a fraction equals 1?

A fraction equals 1 when the numerator and denominator are identical. Always calculate both parts first, then compare: if they match, the answer is 1!

Q: Could this fraction ever equal 0?

No! A fraction only equals 0 when the numerator is 0 and the denominator is non-zero. Here, both the numerator and denominator equal 21, so the result is 1.

Q: What's the difference between 3×7 in the numerator vs denominator?

There's no difference - multiplication is commutative! So 3×7 = 7×3 = 21 whether it's on top or bottom of the fraction.

Fraction Simplification with Common Factors

Determine if the simplification below is correct:

$\frac{3\cdot7}{7\cdot3}=0$

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

00:14 Let's compare 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:

$\frac{3\cdot7}{7\cdot3}=0$

Step-by-step solution

We will divide the fraction exercise into two different multiplication exercises.

As this is a multiplication exercise, you can use the substitution property:

$\frac{7}{7}\times\frac{3}{3}=1\times1=1$

Therefore, the simplification described is false.

Final Answer

Incorrect

Key Points to Remember

Essential concepts to master this topic

Rule: Any non-zero number divided by itself equals 1
Technique: $\frac{3×7}{7×3} = \frac{21}{21} = 1$
Check: Verify multiplication gives same numerator and denominator: 21 = 21 ✓

Common Mistakes

Avoid these frequent errors

Confusing fraction simplification with subtraction
Don't think $\frac{3×7}{7×3}$ means "3×7 minus 7×3" = 0! This applies subtraction instead of division. Always remember fractions represent division, and identical values divided give 1.

Practice Quiz

Test your knowledge with interactive questions

Complete the corresponding expression for the denominator

$\frac{12ab}{?}=1$

FAQ

Everything you need to know about this question

Why does any number divided by itself equal 1?

Think of it this way: if you have 21 cookies and divide them into groups of 21, you get exactly 1 group. That's why $\frac{21}{21} = 1$ !

What if the numbers were different, like 3×5 and 7×2?

Then you'd calculate each part separately: $\frac{3×5}{7×2} = \frac{15}{14}$ . Since 15 ≠ 14, this fraction cannot be simplified to 1.

How can I tell when a fraction equals 1?

A fraction equals 1 when the numerator and denominator are identical. Always calculate both parts first, then compare: if they match, the answer is 1!

Could this fraction ever equal 0?

No! A fraction only equals 0 when the numerator is 0 and the denominator is non-zero. Here, both the numerator and denominator equal 21, so the result is 1.

What's the difference between 3×7 in the numerator vs denominator?

There's no difference - multiplication is commutative! So 3×7 = 7×3 = 21 whether it's on top or bottom of the fraction.

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