Here's a word problem involving the addition of fractions, along with its solution:

Word Problem:

John and Alice are baking cookies together. John uses 2/3 of a cup of sugar, and Alice uses 3/4 of a cup of sugar. How much sugar did they use in total?

Solution:

To find out how much sugar they used in total, we need to add the two fractions: 2/3 and 3/4.

Step 1: Find a common denominator

The denominators of the fractions are 3 and 4. The least common denominator (LCD) of 3 and 4 is 12.

Step 2: Rewrite the fractions with the common denominator

• For 2/3, multiply both the numerator and the denominator by 4:
  $\frac{2}{3} \times \frac{4}{4} = \frac{8}{12}$
• For 3/4, multiply both the numerator and the denominator by 3:
  $\frac{3}{4} \times \frac{3}{3} = \frac{9}{12}$

Step 3: Add the fractions

Now that both fractions have the same denominator, you can add them: $\frac{8}{12} + \frac{9}{12} = \frac{17}{12}$

Step 4: Simplify the fraction (if needed)

$\frac{17}{12} \text{ is an improper fraction, which can be written as } 1 \frac{5}{12}.$

So, John and Alice used 1 and 5/12 cups of sugar in total.

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Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. What if John used 1/2 a cup and Alice used 2/5 of a cup?
2. How would the problem change if John used 1 1/4 cups and Alice used 3/8 of a cup?
3. How do you add fractions with different denominators in general?
4. What happens if the result of adding two fractions is a mixed number?
5. How would you subtract fractions with different denominators?

Tip: When adding fractions, always find the least common denominator (LCD) to simplify calculations.