How to solve one-step word problems subtracting fractions (Grade 5)

📚 Understanding One-Step Word Problems with Fraction Subtraction

One-step word problems involving subtraction of fractions present a single, straightforward scenario where you need to find the difference between two fractional quantities. These problems often involve real-world situations where something is being taken away or reduced, and you need to determine what remains. Let's explore this concept further.

📜 History of Fractions

Fractions have been used for thousands of years, dating back to ancient civilizations like the Egyptians and Mesopotamians. Egyptians used fractions extensively in their calculations for land division, construction, and trade. They primarily worked with unit fractions (fractions with a numerator of 1). Over time, different cultures developed various notations and methods for working with fractions, eventually leading to the standardized notation and operations we use today.

📌 Key Principles of Subtracting Fractions

• 🔎 Common Denominator: Before you can subtract fractions, they must have the same denominator. This means the bottom number of each fraction must be the same.
• ➗ Finding the Common Denominator: If the fractions don't have the same denominator, you need to find the least common multiple (LCM) of the denominators. This LCM will be your new common denominator.
• ✏️ Equivalent Fractions: Once you have the common denominator, convert each fraction into an equivalent fraction with the common denominator. Remember, whatever you multiply the denominator by, you must also multiply the numerator by.
• ➖ Subtract the Numerators: After you have equivalent fractions with a common denominator, subtract the numerators (the top numbers) while keeping the denominator the same.
• ➗ Simplify: Finally, simplify the resulting fraction if possible. This means reducing the fraction to its lowest terms by dividing both the numerator and denominator by their greatest common factor (GCF).

📝 Real-World Examples

Let's look at some real-world examples to illustrate how to solve one-step word problems involving subtracting fractions:

1. 🍎 Example 1: Baking a Pie

   Sarah has $\frac{3}{4}$ of a cup of sugar. She uses $\frac{1}{4}$ of a cup for a pie. How much sugar does she have left?

   • ✅ Step 1: Check if the fractions have a common denominator. In this case, both fractions have a denominator of 4.
   • ➖ Step 2: Subtract the numerators: $\frac{3}{4} - \frac{1}{4} = \frac{3-1}{4} = \frac{2}{4}$.
   • ➗ Step 3: Simplify the fraction: $\frac{2}{4}$ can be simplified to $\frac{1}{2}$.
   • 💡 Answer: Sarah has $\frac{1}{2}$ cup of sugar left.

2. 🧵 Example 2: Sewing a Dress

   Emily has $\frac{7}{8}$ of a yard of fabric. She uses $\frac{2}{8}$ of a yard to make a dress. How much fabric does she have left?

   • ✅ Step 1: Check if the fractions have a common denominator. In this case, both fractions have a denominator of 8.
   • ➖ Step 2: Subtract the numerators: $\frac{7}{8} - \frac{2}{8} = \frac{7-2}{8} = \frac{5}{8}$.
   • 💡 Answer: Emily has $\frac{5}{8}$ of a yard of fabric left.

3. 🍕 Example 3: Eating Pizza

   David ate $\frac{2}{5}$ of a pizza, and his friend ate $\frac{1}{5}$ of the same pizza. How much more pizza did David eat than his friend?

   • ✅ Step 1: Check if the fractions have a common denominator. In this case, both fractions have a denominator of 5.
   • ➖ Step 2: Subtract the numerators: $\frac{2}{5} - \frac{1}{5} = \frac{2-1}{5} = \frac{1}{5}$.
   • 💡 Answer: David ate $\frac{1}{5}$ more of the pizza than his friend.

4. 💧 Example 4: Watering Plants

   A watering can is $\frac{5}{6}$ full. You use $\frac{1}{6}$ of the water to water your plants. How full is the watering can now?

   • ✅ Step 1: Check if the fractions have a common denominator. In this case, both fractions have a denominator of 6.
   • ➖ Step 2: Subtract the numerators: $\frac{5}{6} - \frac{1}{6} = \frac{5-1}{6} = \frac{4}{6}$.
   • ➗ Step 3: Simplify the fraction: $\frac{4}{6}$ can be simplified to $\frac{2}{3}$.
   • 💡 Answer: The watering can is now $\frac{2}{3}$ full.

5. 🍫 Example 5: Sharing Chocolate

   Lisa had $\frac{9}{10}$ of a chocolate bar. She gave $\frac{3}{10}$ to her brother. How much of the chocolate bar does Lisa have left?

   • ✅ Step 1: Check if the fractions have a common denominator. In this case, both fractions have a denominator of 10.
   • ➖ Step 2: Subtract the numerators: $\frac{9}{10} - \frac{3}{10} = \frac{9-3}{10} = \frac{6}{10}$.
   • ➗ Step 3: Simplify the fraction: $\frac{6}{10}$ can be simplified to $\frac{3}{5}$.
   • 💡 Answer: Lisa has $\frac{3}{5}$ of the chocolate bar left.

✍️ Practice Quiz

1. Michael has $\frac{2}{3}$ of a bottle of juice. He drinks $\frac{1}{3}$ of the bottle. How much juice is left?

2. A recipe calls for $\frac{5}{8}$ cup of flour. You only want to make half the recipe. How much flour do you need?

3. A construction worker had a piece of wood that was $\frac{7}{10}$ of a meter long. He cut off $\frac{2}{10}$ of a meter. How long is the remaining piece of wood?

💡 Conclusion

Solving one-step word problems involving subtracting fractions becomes much easier when you follow these key principles. Always ensure the fractions have a common denominator, subtract the numerators, and simplify the result. With practice, you'll master these problems and be able to apply these skills in various real-life scenarios.