Division Problem: Is 5:6 Less Than 1 Without Calculating?

Fraction Comparison with Visual Estimation

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

5:6= 5:6=

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 No need to calculate if the quotient is greater or smaller than 1?
00:04 The numerator is smaller than the denominator
00:08 Therefore the quotient must be smaller than 1
00:12 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

5:6= 5:6=

2

Step-by-step solution

Note that the numerator is smaller than the denominator:

5<6 5 < 6

As a result, we can write it thusly:

56<1 \frac{5}{6} < 1

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

3

Final Answer

Less than 1

Key Points to Remember

Essential concepts to master this topic
  • Rule: When numerator is smaller than denominator, fraction is less than 1
  • Technique: Compare 5 < 6, so 56<1 \frac{5}{6} < 1 without calculating
  • Check: Visualize: 5 out of 6 pieces is less than the whole ✓

Common Mistakes

Avoid these frequent errors
  • Calculating the decimal value first
    Don't convert 5÷6 = 0.833... to check if it's less than 1! This defeats the purpose and wastes time. Always compare numerator and denominator directly to determine if the fraction is less than, equal to, or greater than 1.

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

How can I tell if a fraction is less than 1 without calculating?

+

Simply compare the numerator and denominator! If the top number is smaller than the bottom number, the fraction is less than 1. If they're equal, it equals 1. If the top is bigger, it's greater than 1.

What if the numbers are really big? Does this rule still work?

+

Yes! Whether it's 56 \frac{5}{6} or 487523 \frac{487}{523} , the rule stays the same. As long as numerator < denominator, the fraction is less than 1.

Why is this method better than calculating the decimal?

+

It's faster and builds number sense! You can instantly see relationships between numbers without doing division. Plus, some divisions create long decimals that are harder to work with.

What does 5:6 notation mean compared to 5/6?

+

Both 5:6 and 5/6 represent the same division. The colon (:) is just another way to write division, commonly used in ratios. They both mean "5 divided by 6".

How can I visualize this to make sure I understand?

+

Think of a pizza cut into 6 slices. If you eat 5 slices, you've eaten 56 \frac{5}{6} of the pizza - that's less than the whole pizza! You still have 1 slice left.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Simple Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations