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!