## A Step-By-Step Guide to Solving Fraction Addition and Subtraction Word Problems

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Fraction addition and subtraction problems are prevalent in our daily life, from cooking recipes to splitting bills. To become proficient in solving these word problems, one must master the process of deciphering the problem, identifying the operations needed, and carrying out those operations correctly. This article offers a detailed guide on how to approach fraction addition and subtraction word problems methodically.

### Understanding the Word Problem

To begin, carefully read the word problem to understand the scenario. Identify the fractions involved and whether the problem is asking for the sum (addition) or difference (subtraction). Clues for addition problems often include terms such as "in total," "combined," or "altogether," while subtraction problems may involve words like "less than," "more than," "difference," or "remaining."

### Break Down the Problem

After identifying the operation needed, translate the word problem into a mathematical sentence. For example, in a problem like "Sara ate \( \frac{3}{4} \) of a pizza, and then she ate another \( \frac{1}{2} \) of a pizza. How much pizza has she eaten altogether?" You can translate this into the equation "\( \frac{3}{4} + \frac{1}{2} = ? \)"

### Perform the Addition or Subtraction

With the mathematical equation in hand, proceed to perform the operation. Remember, when adding or subtracting fractions, you need to have a common denominator. In our example, to add \( \frac{3}{4} \) and \( \frac{1}{2} \), you need to convert \( \frac{1}{2} \) to \( \frac{2}{4} \). Then you can add the fractions: \( \frac{3}{4} + \frac{2}{4} = \frac{5}{4} \).

### Interpret the Answer

Once you've found the answer, interpret it in the context of the problem. The answer in our example is \( \frac{5}{4} \), which is equal to \( 1 \frac{1}{4} \). So, Sara has eaten \( 1 \frac{1}{4} \) pizzas.

### Check the Answer

Always check your solution to ensure it makes sense in the context of the problem. In our example, since Sara ate some pizza twice, it's reasonable that she should have eaten more than one pizza.

### Repeated Practice

The key to mastering fraction addition and subtraction word problems is consistent practice. The more problems you solve, the better you'll become at identifying important information and determining the correct operations. Additionally, working with a variety of problems will help you become more comfortable with different problem structures and wording.

Remember, proficiency in mathematics isn't about memorization; it's about understanding concepts and applying them to solve problems. Keep practicing, remain patient with yourself, and embrace the challenge. Your fraction problem-solving skills will only get better with time. Happy problem-solving!

### Exercises

**1)** Billy has \( \frac{3}{4} \) of a pizza and he eats \( \frac{1}{4} \) of it. How much pizza does he have left?

**2)** Sarah had \( \frac{5}{6} \) of a gallon of milk. She used \( \frac{1}{3} \) of a gallon for a recipe. How much milk does she have left?

**3)** If you add \( \frac{2}{5} \) of a bag of sugar to a recipe and then need to add \( \frac{3}{10} \) more, how much sugar have you used in total?

**4)** John runs \( \frac{7}{8} \) of a mile in the morning, and then runs \( \frac{5}{8} \) of a mile in the evening. How many miles does John run in total?

**5)** A cloth is \( \frac{6}{7} \) yard long. If \( \frac{2}{7} \) yard is used to make a handkerchief, how much cloth is left?

**6)** Mary read \( \frac{3}{4} \) of a book on Monday and \( \frac{1}{4} \) of the book on Tuesday. Did she finish reading the book?

**7)** A recipe requires \( \frac{5}{8} \) kg of flour. You already put \( \frac{3}{8} \) kg. How much more flour do you need to add?

**8)** If a pizza is divided into 8 equal slices and John eats 3 slices while Mary eats 2 slices, how much pizza is left?

**9)** A farmer planted \( \frac{7}{8} \) of an acre with corn and \( \frac{5}{8} \) of an acre with beans. How much land did he plant in total?

**10)** Emily did \( \frac{5}{6} \) of her homework in the morning and the remaining \( \frac{1}{6} \) in the evening. Did Emily finish her homework?

** 1) **Billy has \( \frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2} \) of the pizza left.

** 2) **Sarah has \( \frac{5}{6} - \frac{1}{3} = \frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2} \) of a gallon of milk left.

** 3) **You have used \( \frac{2}{5} + \frac{3}{10} = \frac{4}{10} + \frac{3}{10} = \frac{7}{10} \) of a bag of sugar.

** 4) **John runs \( \frac{7}{8} + \frac{5}{8} = \frac{12}{8} = 1\frac{1}{2} \) miles in total.

** 5) **\( \frac{6}{7} - \frac{2}{7} = \frac{4}{7} \) yard of cloth is left.

** 6) **Yes, Mary did finish the book because \( \frac{3}{4} + \frac{1}{4} = 1 \).

** 7) **You need to add \( \frac{5}{8} - \frac{3}{8} = \frac{2}{8} = \frac{1}{4} \) kg of flour.

** 8) **There are \( 8 - 3 - 2 = 3 \) slices of pizza left.

** 9) **The farmer planted \( \frac{7}{8} + \frac{5}{8} = \frac{12}{8} = 1\frac{1}{2} \) acres in total.

** 10) **Yes, Emily did finish her homework because \( \frac{5}{6} + \frac{1}{6} = 1 \).

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