Calculate Remaining Height: 1/5 Daily Progress Over 3 Days

Q: Why do I multiply 1/5 by 3 instead of adding three times?

Multiplication is repeated addition! When you climb the same fraction each day, $ \frac{1}{5} \times 3 $ is much faster than $ \frac{1}{5} + \frac{1}{5} + \frac{1}{5} $.

Q: How do I subtract fractions from 1?

Think of 1 as $ \frac{5}{5} $ when working with fifths! Then subtract: $ \frac{5}{5} - \frac{3}{5} = \frac{2}{5} $. Always use the same denominator.

Q: What if Harry climbed for 5 days instead of 3?

He would climb $ \frac{1}{5} \times 5 = \frac{5}{5} = 1 $ whole mountain! That means he'd reach the peak exactly, with 0 remaining.

Q: Can the remaining amount be larger than what he's already climbed?

Yes! In this problem, Harry climbed $ \frac{3}{5} $ but still needs $ \frac{2}{5} $. Early in long journeys, remaining distance is often larger than progress made.

Q: How do I check my answer is reasonable?

Add your answer to what Harry climbed: $ \frac{3}{5} + \frac{2}{5} = \frac{5}{5} = 1 $. This should equal the whole mountain, which makes sense!

Fraction Subtraction with Multi-Day Progress

Harry likes to climb mountains. Every day, he ascends $\frac{1}{5}$ of the mountain's total height.

How much further must Harry climb to reach the peak after climbing for three days?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 What part will remain for Ilan after 3 days?

00:03 First, let's calculate the part he covered in 3 days

00:06 Multiply the daily progress by the number of days

00:09 This is the part of the mountain that Ilan walks in 3 days

00:12 Now subtract this part from the whole to find the remaining part

00:19 Convert whole to fraction

00:26 Subtract with common denominator

00:31 Calculate the numerator

00:35 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

Harry likes to climb mountains. Every day, he ascends $\frac{1}{5}$ of the mountain's total height.

How much further must Harry climb to reach the peak after climbing for three days?

Step-by-step solution

To solve this problem, we must calculate how much of the mountain Harry has not yet climbed after three days.

Let's break it down step-by-step:

Step 1: Calculate the total amount of mountain climbed in three days.
Harry climbs $\frac{1}{5}$ of the mountain each day. Therefore, in three days, he climbs:
$\frac{1}{5} \times 3 = \frac{3}{5}$
Step 2: Determine how much more Harry needs to climb.
The whole mountain is represented by 1 (or $\frac{5}{5}$ ). To find out how much further Harry must climb, subtract the amount he has already climbed from the whole:
$1 - \frac{3}{5} = \frac{5}{5} - \frac{3}{5} = \frac{2}{5}$

Therefore, the solution to the problem is that Harry must climb an additional $\frac{2}{5}$ of the mountain to reach the peak.

Final Answer

$\frac{2}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: Total progress equals daily rate times number of days
Technique: Subtract from whole: $1 - \frac{3}{5} = \frac{2}{5}$
Check: Progress plus remaining equals whole mountain: $\frac{3}{5} + \frac{2}{5} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Adding days instead of multiplying by daily rate
Don't add 1/5 + 1/5 + 1/5 step by step = confusing and slow! This makes simple problems complicated. Always multiply the daily rate by the number of days: 1/5 × 3 = 3/5.

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 do I multiply 1/5 by 3 instead of adding three times?

Multiplication is repeated addition! When you climb the same fraction each day, $\frac{1}{5} \times 3$ is much faster than $\frac{1}{5} + \frac{1}{5} + \frac{1}{5}$ .

How do I subtract fractions from 1?

Think of 1 as $\frac{5}{5}$ when working with fifths! Then subtract: $\frac{5}{5} - \frac{3}{5} = \frac{2}{5}$ . Always use the same denominator.

What if Harry climbed for 5 days instead of 3?

He would climb $\frac{1}{5} \times 5 = \frac{5}{5} = 1$ whole mountain! That means he'd reach the peak exactly, with 0 remaining.

Can the remaining amount be larger than what he's already climbed?

Yes! In this problem, Harry climbed $\frac{3}{5}$ but still needs $\frac{2}{5}$ . Early in long journeys, remaining distance is often larger than progress made.

How do I check my answer is reasonable?

Add your answer to what Harry climbed: $\frac{3}{5} + \frac{2}{5} = \frac{5}{5} = 1$ . This should equal the whole mountain, which makes sense!

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