Compare Division 7:11: Is the Quotient Less Than 1?

Q: Why don't I need to calculate 7 ÷ 11?

The question specifically asks you to determine this without calculating! Just comparing the sizes of 7 and 11 tells you everything you need to know.

Q: What if the numerator and denominator were equal?

If the numerator equals the denominator (like $ \frac{8}{8} $), then the quotient equals exactly 1, not less than 1.

Q: Does this work for all fractions?

Yes! This rule works for all positive fractions: Proper fractions (numerator Improper fractions (numerator > denominator) are greater than 1

Q: What about negative numbers?

For negative fractions, the rule flips! If $ -7 ÷ 11 $, the result is negative, so it's definitely less than 1 (and less than 0).

Q: How is this different from regular division?

It's the same concept! $ 7:11 $ means $ 7 ÷ 11 $ or $ \frac{7}{11} $. The colon (:) is just another way to write division.

Fraction Comparison with Numerator-Denominator Analysis

Without calculating, determine whether the quotient in the division exercise is less than 1:

$7:11$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's find out if the result of this division is less than or greater than one, without doing any calculations.

00:14 Here, notice that the top number, called the numerator, is smaller than the bottom number, the denominator.

00:21 In any fraction like this, where the numerator is smaller than the denominator, the result, or quotient, is always less than one.

00:29 So, the answer to our question is clear. The quotient is less than one.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Without calculating, determine whether the quotient in the division exercise is less than 1:

$7:11$

Step-by-step solution

Note that the numerator is smaller than the denominator:

$7 < 11$

As a result, we can write it thusly:

$\frac{7}{11}<1$

Therefore, the quotient in the division exercise is indeed less than 1.

Final Answer

Less than 1

Key Points to Remember

Essential concepts to master this topic

Rule: When numerator is smaller than denominator, quotient is less than 1
Technique: Compare 7 < 11, so $\frac{7}{11} < 1$
Check: Any proper fraction has numerator smaller than denominator ✓

Common Mistakes

Avoid these frequent errors

Calculating the actual decimal value first
Don't compute 7 ÷ 11 = 0.636... to answer this question = wasted time and effort! The problem asks you to determine this WITHOUT calculating. Always compare the numerator and denominator directly first.

Practice Quiz

Test your knowledge with interactive questions

Write the fraction shown in the picture, in words:

FAQ

Everything you need to know about this question

Why don't I need to calculate 7 ÷ 11?

The question specifically asks you to determine this without calculating! Just comparing the sizes of 7 and 11 tells you everything you need to know.

What if the numerator and denominator were equal?

If the numerator equals the denominator (like $\frac{8}{8}$ ), then the quotient equals exactly 1, not less than 1.

Does this work for all fractions?

Yes! This rule works for all positive fractions:

Proper fractions (numerator < denominator) are less than 1
Improper fractions (numerator > denominator) are greater than 1

What about negative numbers?

For negative fractions, the rule flips! If $-7 ÷ 11$ , the result is negative, so it's definitely less than 1 (and less than 0).

How is this different from regular division?

It's the same concept! $7:11$ means $7 ÷ 11$ or $\frac{7}{11}$ . The colon (:) is just another way to write division.

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