Calculate Remaining Fraction: 1/4 + 1/2 of Book Read Over Two Days

Fraction Addition with Common Denominators

Janet reads a book for two days.

On the first day, she reads 14 \frac{1}{4} of the book and on the second day she reads 12 \frac{1}{2} of the book.

How much of the book does she have left to read?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 What part of the book remains to be read?
00:03 We are given the amount of the book that has already been read
00:06 Let's sum up this amount
00:09 Let's multiply the fraction by 2 to find the common denominator
00:12 Make sure to multiply both numerator and denominator
00:17 Let's calculate the multiplications

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Janet reads a book for two days.

On the first day, she reads 14 \frac{1}{4} of the book and on the second day she reads 12 \frac{1}{2} of the book.

How much of the book does she have left to read?

2

Step-by-step solution

To solve this problem, we will follow these steps:

  • Step 1: Calculate the total fraction of the book that Janet reads over the two days.
  • Step 2: Subtract this total from the whole to find the remaining fraction of the book.

Now, let's work through each step:

Step 1: Janet reads 14 \frac{1}{4} of the book on the first day and 12 \frac{1}{2} on the second day. First, we convert these fractions to have the same denominator before adding: 14+12=14+24=34 \frac{1}{4} + \frac{1}{2} = \frac{1}{4} + \frac{2}{4} = \frac{3}{4} This means Janet reads 34 \frac{3}{4} of the book in total.

Step 2: To determine how much of the book remains, we subtract this total from the whole book, which is represented by 1: 134=4434=14 1 - \frac{3}{4} = \frac{4}{4} - \frac{3}{4} = \frac{1}{4} This calculation shows that Janet has 14 \frac{1}{4} of the book left to read.

Therefore, the solution to the problem is 14 \frac{1}{4} .

3

Final Answer

14 \frac{1}{4}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Find common denominator before adding fractions together
  • Technique: Convert 12 \frac{1}{2} to 24 \frac{2}{4} so both fractions have denominator 4
  • Check: Total read plus remaining should equal 1 whole book: 34+14=1 \frac{3}{4} + \frac{1}{4} = 1

Common Mistakes

Avoid these frequent errors
  • Adding fractions without common denominators
    Don't add 14+12=26 \frac{1}{4} + \frac{1}{2} = \frac{2}{6} by adding tops and bottoms separately! This gives completely wrong results because you're adding different-sized pieces. Always convert to the same denominator first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

\( \frac{8}{5}-\frac{4}{5}=\text{?} \)

FAQ

Everything you need to know about this question

Why can't I just add 1/4 + 1/2 = 2/6?

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You can't add fractions by adding numerators and denominators separately! Think of it like pizza slices - you can't add 1 quarter-slice + 1 half-slice by saying "2 slices out of 6." You need pieces of the same size first.

How do I find the common denominator quickly?

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Look for the smallest number that both denominators divide into evenly. For 4 and 2, since 4 is already a multiple of 2, just use 4 as your common denominator!

What does it mean that Janet has 1/4 left?

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It means if you divided the whole book into 4 equal parts, Janet still needs to read 1 of those parts. She's read 3 parts and has 1 part remaining.

How can I check if my fraction addition is correct?

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Add up all the fractions including what's left - they should equal 1 whole book! In this problem: 34 \frac{3}{4} (read) + 14 \frac{1}{4} (remaining) = 44=1 \frac{4}{4} = 1

What if the fractions don't have nice common denominators?

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You can always use the product of both denominators as a common denominator if you can't find a smaller one easily. Then convert both fractions and add normally.

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