Solve for Remaining Water: 1/12 Hourly Reduction Over 4 Hours

Q: Why can't I just multiply 4 × 1/12 and subtract once?

You absolutely can! Both methods work perfectly. Subtracting $ \frac{4}{12} = \frac{1}{3} $ from 1 gives $ \frac{2}{3} $. The step-by-step approach helps you understand what happens each hour.

Q: How do I subtract fractions with different denominators?

Find a common denominator first! For example, $ \frac{3}{4} - \frac{1}{12} $ becomes $ \frac{9}{12} - \frac{1}{12} = \frac{8}{12} $, then simplify to $ \frac{2}{3} $.

Q: What does 'full bottle' mean as a fraction?

A full bottle represents the whole amount, which equals 1 or $ \frac{12}{12} $ when using twelfths. Think of it as 12 out of 12 parts!

Q: Should I always reduce fractions to lowest terms?

Yes, always simplify! $ \frac{8}{12} $ reduces to $ \frac{2}{3} $ by dividing both numerator and denominator by their greatest common factor (4).

Q: What if the problem asked about 5 hours instead?

Same process! After 5 hours: $ 1 - 5 \times \frac{1}{12} = 1 - \frac{5}{12} = \frac{7}{12} $ would remain. The pattern continues for any number of hours.

Fraction Subtraction with Repeated Operations

A full bottle of water has a small hole in it. Every hour the amount of water in the bottle decreases by $\frac{1}{12}$ .

How much water remains in the bottle after 4 hours?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Found the remaining part in the bottle after 4 hours

00:03 Given the amount that decreased after 4 hours

00:05 Therefore, subtract the given amount from the whole

00:10 Convert the whole to the appropriate fraction

00:16 Subtract in the common denominator

00:20 Calculate the numerator

00:24 Reduce the fraction as much as possible

00:27 Make sure to divide both numerator and denominator

00:34 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

A full bottle of water has a small hole in it. Every hour the amount of water in the bottle decreases by $\frac{1}{12}$ .

How much water remains in the bottle after 4 hours?

Step-by-step solution

To solve this problem, we'll subtract $\frac{1}{12}$ from the full bottle (represented as '1' or $\frac{12}{12}$ ) for each hour for a total of 4 hours:

Initially, the bottle is full: $\frac{12}{12}$ .
After 1 hour, subtract $\frac{1}{12}$ :
$\frac{12}{12} - \frac{1}{12} = \frac{11}{12}$ .
After 2 hours, subtract another $\frac{1}{12}$ :
$\frac{11}{12} - \frac{1}{12} = \frac{10}{12} = \frac{5}{6}$ after reduction.
After 3 hours, subtract another $\frac{1}{12}$ :
$\frac{5}{6} - \frac{1}{12} = \frac{10}{12} - \frac{1}{12} = \frac{9}{12} = \frac{3}{4}$ after reduction.
After 4 hours, subtract another $\frac{1}{12}$ :
$\frac{3}{4} - \frac{1}{12} = \frac{9}{12} - \frac{1}{12} = \frac{8}{12} = \frac{2}{3}$ after reduction.

Therefore, the amount of water that remains in the bottle after 4 hours is $\frac{2}{3}$ .

Final Answer

$\frac{2}{3}$

Key Points to Remember

Essential concepts to master this topic

Rule: Subtract the same fraction repeatedly for each time period
Technique: Convert to common denominators: $\frac{3}{4} - \frac{1}{12} = \frac{9}{12} - \frac{1}{12}$
Check: Total reduction should equal $4 \times \frac{1}{12} = \frac{4}{12} = \frac{1}{3}$ ✓

Common Mistakes

Avoid these frequent errors

Adding fractions instead of subtracting
Don't add $\frac{1}{12}$ each hour = water increases impossibly! The hole causes water to leak out, not fill up. Always subtract the fraction that represents the amount lost each hour.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$\frac{3}{2}-\frac{1}{2}=\text{?}$

FAQ

Everything you need to know about this question

Why can't I just multiply 4 × 1/12 and subtract once?

You absolutely can! Both methods work perfectly. Subtracting $\frac{4}{12} = \frac{1}{3}$ from 1 gives $\frac{2}{3}$ . The step-by-step approach helps you understand what happens each hour.

How do I subtract fractions with different denominators?

Find a common denominator first! For example, $\frac{3}{4} - \frac{1}{12}$ becomes $\frac{9}{12} - \frac{1}{12} = \frac{8}{12}$ , then simplify to $\frac{2}{3}$ .

What does 'full bottle' mean as a fraction?

A full bottle represents the whole amount, which equals 1 or $\frac{12}{12}$ when using twelfths. Think of it as 12 out of 12 parts!

Should I always reduce fractions to lowest terms?

Yes, always simplify! $\frac{8}{12}$ reduces to $\frac{2}{3}$ by dividing both numerator and denominator by their greatest common factor (4).

What if the problem asked about 5 hours instead?

Same process! After 5 hours: $1 - 5 \times \frac{1}{12} = 1 - \frac{5}{12} = \frac{7}{12}$ would remain. The pattern continues for any number of hours.

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