Step-by-step guide to subtracting mixed numbers with like denominators

📚 Understanding Mixed Numbers

A mixed number is a combination of a whole number and a proper fraction (where the numerator is less than the denominator). For example, $3\frac{1}{4}$ is a mixed number. The '3' is the whole number, and $\frac{1}{4}$ is the fraction.

Subtracting mixed numbers with like denominators involves subtracting the fractional parts and the whole number parts separately. When the fraction you're subtracting is larger than the fraction you're subtracting from, you'll need to borrow from the whole number.

🔢 Key Principles of Subtracting Mixed Numbers

• 🔍 Identify the Whole and Fractional Parts: Separate the whole numbers from the fractions in each mixed number.
• ➖ Subtract the Fractional Parts: Subtract the numerators of the fractions, keeping the denominator the same.
• ➖ Subtract the Whole Numbers: Subtract the whole numbers.
• 🤝 Combine the Results: Write the result as a new mixed number.
• ➕ Borrowing (If Necessary): If the fraction being subtracted is larger, borrow 1 from the whole number, convert it to a fraction with the same denominator, and add it to the existing fraction.
• 🌱 Simplify: Reduce the fraction to its simplest form, if possible.

📝 Step-by-Step Guide

Let's break this down into easy-to-follow steps with an example: $5\frac{3}{7} - 2\frac{1}{7}$

• 🔍 Step 1: Identify the whole and fractional parts. In $5\frac{3}{7}$, 5 is the whole number and $\frac{3}{7}$ is the fraction. In $2\frac{1}{7}$, 2 is the whole number and $\frac{1}{7}$ is the fraction.
• ➖ Step 2: Subtract the fractional parts: $\frac{3}{7} - \frac{1}{7} = \frac{2}{7}$
• ➖ Step 3: Subtract the whole numbers: $5 - 2 = 3$
• 🤝 Step 4: Combine the results: $3\frac{2}{7}$

➕ Subtracting with Borrowing: An Example

Let's look at an example where we need to borrow: $4\frac{1}{5} - 1\frac{3}{5}$

• 🔍 Step 1: Identify the whole and fractional parts.
• 🧮 Step 2: Notice that $\frac{1}{5} - \frac{3}{5}$ would result in a negative fraction. We need to borrow.
• ➕ Step 3: Borrow 1 from the whole number 4, making it 3. Convert the borrowed 1 into $\frac{5}{5}$ and add it to $\frac{1}{5}$: $\frac{1}{5} + \frac{5}{5} = \frac{6}{5}$. So, $4\frac{1}{5}$ becomes $3\frac{6}{5}$.
• ➖ Step 4: Now subtract: $3\frac{6}{5} - 1\frac{3}{5}$
• ➖ Step 5: Subtract the fractional parts: $\frac{6}{5} - \frac{3}{5} = \frac{3}{5}$
• ➖ Step 6: Subtract the whole numbers: $3 - 1 = 2$
• 🤝 Step 7: Combine the results: $2\frac{3}{5}$

💡 Tips and Tricks

• 📝 Always check if the fraction can be simplified after subtracting.
• 🧮 Practice regularly to build confidence.
• ➗ Rewrite mixed numbers as improper fractions if you find it easier to subtract.

➗ Practice Quiz

Solve these subtraction problems:

1. $6\frac{5}{8} - 2\frac{1}{8} = ?$
2. $4\frac{2}{3} - 1\frac{1}{3} = ?$
3. $7\frac{3}{4} - 3\frac{1}{4} = ?$
4. $5\frac{7}{10} - 2\frac{3}{10} = ?$
5. $8\frac{5}{9} - 4\frac{2}{9} = ?$
6. $3\frac{1}{6} - 1\frac{5}{6} = ?$
7. $9\frac{2}{5} - 5\frac{4}{5} = ?$

✅ Answers to Practice Quiz

1. $4\frac{4}{8} = 4\frac{1}{2}$
2. $3\frac{1}{3}$
3. $4\frac{2}{4} = 4\frac{1}{2}$
4. $3\frac{4}{10} = 3\frac{2}{5}$
5. $4\frac{3}{9} = 4\frac{1}{3}$
6. $1\frac{2}{6} = 1\frac{1}{3}$
7. $3\frac{3}{5}$