create problem involving addition and subtraction of fraction with solutions

### Problem:

Emily is baking a cake and needs to mix different ingredients in fractional amounts. She needs:

- \( \frac{3}{4} \) cup of flour,
- \( \frac{1}{3} \) cup of sugar, and
- \( \frac{2}{5} \) cup of milk.

After mixing the ingredients, she realizes she added an extra \( \frac{1}{6} \) cup of sugar. How much of each ingredient did she use in total, and how much extra sugar did she add beyond the original amount?

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### Solution:

#### Step 1: Total amount of flour
Emily only needs to add flour once, so the total amount of flour used is:

\[
\frac{3}{4} \text{ cup}
\]

#### Step 2: Total amount of sugar
She added \( \frac{1}{3} \) cup of sugar initially and then added an extra \( \frac{1}{6} \) cup. To find the total sugar, we need to add these two fractions.

\[
\frac{1}{3} + \frac{1}{6}
\]

To add these fractions, find the least common denominator (LCD), which is 6.

\[
\frac{1}{3} = \frac{2}{6}
\]

Now, add the fractions:

\[
\frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}
\]

So, the total amount of sugar used is \( \frac{1}{2} \) cup.

#### Step 3: Total amount of milk
Emily only needs to add milk once, so the total amount of milk used is:

\[
\frac{2}{5} \text{ cup}
\]

#### Step 4: Total amount of extra sugar
The extra sugar she added beyond the original amount is:

\[
\frac{1}{6} \text{ cup}
\]

#### Final Answer:
- Total amount of flour: \( \frac{3}{4} \) cup
- Total amount of sugar: \( \frac{1}{2} \) cup
- Total amount of milk: \( \frac{2}{5} \) cup
- Extra sugar added: \( \frac{1}{6} \) cup

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Would you like more details on any step or have any questions?

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Here are 5 related questions for practice:

1. Add \( \frac{3}{7} \) and \( \frac{2}{5} \). 
2. Subtract \( \frac{5}{6} \) from \( \frac{3}{4} \).
3. Emily accidentally adds \( \frac{3}{8} \) cup of milk. What is the total milk now?
4. How much more flour than sugar did Emily originally add?
5. Subtract \( \frac{5}{9} \) from \( \frac{7}{12} \).

**Tip:** When adding or subtracting fractions, always find the least common denominator (LCD) to simplify the process!

Create a problem involving addition and subtraction of fractions with solutions.

Explore how to add and subtract fractions with real-life examples. Learn how Emily solves a baking problem by adding and subtracting fractions of flour, sugar, and milk. This problem covers key concepts such as finding the least common denominator (LCD) and simplifying fractions, suitable for students in Grades 5-7.

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