Fraction Subtraction Problem: Finding Remaining Amount After 5/6 and 1/8 Consumption

Fraction Addition with Common Denominators

Daniela bought a large package of potato chips

On the first day, she ate 56 \frac{5}{6} of the package

On the second day, she ate 18 \frac{1}{8} of the package

On the third day, how much does she have left to eat?

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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 bag
00:04 We want to find the total eaten part and subtract it from the whole
00:07 We'll combine the eaten parts according to the given data
00:10 We want to find the smallest common denominator
00:14 We'll multiply the fractions by 3 and 4 respectively to find the common denominator
00:17 Remember to multiply both numerator and denominator
00:26 Let's calculate the multiplications
00:39 We'll add under the common denominator
00:42 Let's calculate the numerator
00:45 This is the part that was eaten from the bag
00:56 Now we'll subtract this part from the whole to find the remaining part
01:06 We'll convert whole to fraction
01:16 We'll add under the common denominator
01:20 Let's calculate the numerator
01:26 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Daniela bought a large package of potato chips

On the first day, she ate 56 \frac{5}{6} of the package

On the second day, she ate 18 \frac{1}{8} of the package

On the third day, how much does she have left to eat?

2

Step-by-step solution

To solve this problem, we'll proceed with the following steps:

  • Step 1: Calculate the total amount of potato chips eaten over two days.
  • Step 2: Subtract the eaten amount from the whole (1) to find what's left.

Step 1: Addition of Fractions
Combine the fractions of chips eaten on both days:

56+18 \frac{5}{6} + \frac{1}{8}

Find a common denominator for the fractions. The least common multiple of 6 and 8 is 24. Convert each fraction:

56=5×46×4=2024 \frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}

18=1×38×3=324 \frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24}

Add the converted fractions:

2024+324=20+324=2324 \frac{20}{24} + \frac{3}{24} = \frac{20 + 3}{24} = \frac{23}{24}

This means Daniela ate 2324 \frac{23}{24} of the package.

Step 2: Subtract from the whole
The whole package is represented by 1. To find out how much is left, subtract what she ate from 1:

12324=24242324=124 1 - \frac{23}{24} = \frac{24}{24} - \frac{23}{24} = \frac{1}{24}

Therefore, the solution to the problem is that Daniela has 124 \frac{1}{24} of the package left to eat.

3

Final Answer

124 \frac{1}{24}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find common denominator before adding or subtracting fractions
  • Technique: Convert 56 \frac{5}{6} to 2024 \frac{20}{24} and 18 \frac{1}{8} to 324 \frac{3}{24}
  • Check: Verify 2024+324=2324 \frac{20}{24} + \frac{3}{24} = \frac{23}{24} , then 12324=124 1 - \frac{23}{24} = \frac{1}{24}

Common Mistakes

Avoid these frequent errors
  • Adding numerators and denominators separately
    Don't add 56+18 \frac{5}{6} + \frac{1}{8} as 5+16+8=614 \frac{5+1}{6+8} = \frac{6}{14} = wrong answer! This ignores the need for common denominators and gives meaningless results. Always find the LCD first, convert both fractions, 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 LCD of 6 and 8?

+

List the multiples of each number: 6: 6, 12, 18, 24... and 8: 8, 16, 24... The smallest common multiple is 24, so that's your LCD!

Why can't I just subtract each day separately from 1?

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You need to find the total amount eaten first! If you subtract separately, you'd get negative amounts. Always add what was consumed, then subtract from the whole.

What if my answer is bigger than 1?

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Check your work! If someone ate more than the whole package, something went wrong. The remaining amount must be less than 1 (and positive).

Can I convert to decimals instead of using fractions?

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Yes, but be careful with rounding errors! 56=0.8333... \frac{5}{6} = 0.8333... and 18=0.125 \frac{1}{8} = 0.125 . Fractions give exact answers.

How do I know if 1/24 can be simplified further?

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Check if 1 and 24 share any common factors. Since 1 only has itself as a factor, 124 \frac{1}{24} is already in simplest form!

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