Calculate Total Fractions: Adding 5/6 and 1/8 of a Whole

Q: Why can't I just add 5/6 + 1/8 directly?

You can only add fractions when they have the same denominator. Think of it like adding different sized pieces - you need to make them the same size first!

Q: What if the answer is greater than 1?

That's totally normal! $ \frac{23}{24} $ is less than 1, but if Daniela ate more than the whole bag, your answer could be greater than 1 (like $ \frac{25}{24} $).

Adding Fractions with Different Denominators

Daniela bought a large bag of chips

On the first day she ate

$\frac{5}{6}$ of the bag.

On the second day she ate $\frac{1}{8}$ of the bag.

What total part of the bag did she eat?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the total consumed part from the drink

00:05 Connect between the consumed parts according to the given data

00:09 We want to find the smallest common denominator

00:12 Multiply the fractions by 3 and 4 respectively, to find the common denominator

00:15 Remember to multiply both numerator and denominator

00:26 Calculate the multiplications

00:35 Connect under the common denominator

00:41 Calculate the numerator

00:46 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

Daniela bought a large bag of chips

On the first day she ate

$\frac{5}{6}$ of the bag.

On the second day she ate $\frac{1}{8}$ of the bag.

What total part of the bag did she eat?

Step-by-step solution

To solve this problem, we'll add the fractions representing the parts of the bag Daniela ate each day.

Step 1: Identify the fractions.

First day: $\frac{5}{6}$
Second day: $\frac{1}{8}$

Step 2: Find a common denominator for the two fractions. The denominators are 6 and 8. The least common multiple (LCM) of 6 and 8 is 24.

Step 3: Convert each fraction to have the common denominator of 24.

Convert $\frac{5}{6}$ to ?/24: $\frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}$
Convert $\frac{1}{8}$ to ?/24: $\frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24}$

Step 4: Add the converted fractions.

$\frac{20}{24} + \frac{3}{24} = \frac{20 + 3}{24} = \frac{23}{24}$

Step 5: Confirm that this result fits within the options provided. The correct answer matches choice 4.

Therefore, the total part of the bag Daniela ate is $\frac{23}{24}$ .

Final Answer

$\frac{23}{24}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find common denominator before adding fractions with different denominators
Technique: Convert $\frac{5}{6}$ to $\frac{20}{24}$ and $\frac{1}{8}$ to $\frac{3}{24}$
Check: Verify denominators match before adding: $\frac{20}{24} + \frac{3}{24} = \frac{23}{24}$ ✓

Common Mistakes

Avoid these frequent errors

Adding numerators and denominators separately
Don't add $\frac{5}{6} + \frac{1}{8}$ as $\frac{6}{14}$ ! This ignores how fractions work and gives completely wrong answers. Always find a common denominator first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$\frac{3}{9}+\frac{1}{9}=\text{?}$

FAQ

Everything you need to know about this question

How do I find the least common multiple of 6 and 8?

List multiples of each number: 6: 6, 12, 18, 24... and 8: 8, 16, 24... The first number that appears in both lists is 24, so that's your LCM!

Why can't I just add 5/6 + 1/8 directly?

You can only add fractions when they have the same denominator. Think of it like adding different sized pieces - you need to make them the same size first!

What if the answer is greater than 1?

That's totally normal! $\frac{23}{24}$ is less than 1, but if Daniela ate more than the whole bag, your answer could be greater than 1 (like $\frac{25}{24}$ ).

Do I need to simplify 23/24?

Check if 23 and 24 have common factors. Since 23 is prime and doesn't divide 24, $\frac{23}{24}$ is already in simplest form!

How do I multiply fractions to get equivalent fractions?

Multiply both numerator and denominator by the same number. For $\frac{5}{6}$ to get denominator 24: $\frac{5 \times 4}{6 \times 4} = \frac{20}{24}$

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