Solve: Dividing Identical Fractions (3/4 ÷ 3/4)

Fraction Division with Identical Values

3434=? \frac{\frac{3}{4}}{\frac{3}{4}}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:03 Here's a key rule to remember: when we divide any number by itself, the result is always one.
00:11 Of course, we need to make sure the denominator isn't zero, because that would be undefined. In this case, we're good to proceed!
00:20 This rule applies to all numbers, including fractions. When you divide a fraction by the exact same fraction, you'll always get one.
00:29 And there you have it! That's how we know our answer is one. Nice work following along!

Step-by-step written solution

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1

Understand the problem

3434=? \frac{\frac{3}{4}}{\frac{3}{4}}=\text{?}

2

Step-by-step solution

We will use the formula:

aa=1 \frac{a}{a}=1

Therefore the answer is 1

3

Final Answer

1 1

Key Points to Remember

Essential concepts to master this topic
  • Identity Rule: Any number divided by itself always equals 1
  • Method: Apply a/a = 1 where a ≠ 0
  • Verify: 34×1=34 \frac{3}{4} \times 1 = \frac{3}{4} confirms our answer ✓

Common Mistakes

Avoid these frequent errors
  • Converting fractions to decimals before dividing
    Don't convert 3/4 to 0.75 and divide 0.75 ÷ 0.75 = wrong approach! While you get the right answer, you're making extra work and missing the key concept. Always recognize that any non-zero number divided by itself equals 1 directly.

Practice Quiz

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FAQ

Everything you need to know about this question

Why is any number divided by itself equal to 1?

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Think of it this way: division asks "how many groups?" If you have 3/4 of a pizza and want to make groups of 3/4 pizza each, you can make exactly 1 complete group!

What if the fractions look different but are equivalent?

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Great question! 68÷34 \frac{6}{8} ÷ \frac{3}{4} also equals 1 because 6/8 = 3/4. Always check if fractions are equivalent first.

Does this work with negative fractions too?

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Yes! 3/43/4=1 \frac{-3/4}{-3/4} = 1 because negative ÷ negative = positive. Any non-zero number divided by itself equals 1.

Can I use the flip and multiply method instead?

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You could: 34÷34=34×43=1 \frac{3}{4} ÷ \frac{3}{4} = \frac{3}{4} \times \frac{4}{3} = 1 . But recognizing the identity property a ÷ a = 1 is much faster!

What happens if I divide zero by zero?

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Zero divided by zero is undefined! The identity rule a ÷ a = 1 only works when a ≠ 0. Division by zero breaks mathematical rules.

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