Easy method to divide fractions by whole numbers for Grade 6

📚 Understanding Fractions and Whole Numbers

Before we dive into dividing fractions by whole numbers, let's quickly review what fractions and whole numbers are.

• 🔢 A fraction represents a part of a whole. It's written as one number over another, like $\frac{1}{2}$ or $\frac{3}{4}$. The top number is the numerator, and the bottom number is the denominator.
• 🍎 A whole number is a number without fractions or decimals, like 1, 2, 3, 10, or 100.

➗ The Key Principle: Multiplying by the Reciprocal

Dividing a fraction by a whole number is the same as multiplying the fraction by the reciprocal of that whole number. The reciprocal of a number is simply 1 divided by that number. This means:

$\frac{a}{b} \div c = \frac{a}{b} \times \frac{1}{c}$

• 🔄 To find the reciprocal of a whole number, write the whole number as a fraction with a denominator of 1 (e.g., 5 becomes $\frac{5}{1}$).
• Flip the fraction! The reciprocal of $\frac{5}{1}$ is $\frac{1}{5}$.
• ✏️ Now, multiply the original fraction by this reciprocal.

💡 Step-by-Step Method with Examples

Let's go through a few examples to make this clear:

Example 1: $\frac{1}{2} \div 3$

• 🔄 Find the reciprocal of 3: 3 becomes $\frac{3}{1}$, and its reciprocal is $\frac{1}{3}$.
• ✖️ Multiply: $\frac{1}{2} \times \frac{1}{3} = \frac{1 \times 1}{2 \times 3} = \frac{1}{6}$
• ✅ So, $\frac{1}{2} \div 3 = \frac{1}{6}$

Example 2: $\frac{2}{5} \div 4$

• 🔄 Find the reciprocal of 4: 4 becomes $\frac{4}{1}$, and its reciprocal is $\frac{1}{4}$.
• ✖️ Multiply: $\frac{2}{5} \times \frac{1}{4} = \frac{2 \times 1}{5 \times 4} = \frac{2}{20}$
• Simplifying the fraction: $\frac{2}{20}$ can be simplified to $\frac{1}{10}$
• ✅ So, $\frac{2}{5} \div 4 = \frac{1}{10}$

✍️ Practice Quiz

Try these practice problems to test your understanding:

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

Answers:

1. $\frac{1}{8}$
2. $\frac{2}{15}$
3. $\frac{1}{8}$
4. $\frac{2}{7}$
5. $\frac{1}{6}$
6. $\frac{1}{9}$
7. $\frac{1}{20}$

📝 Conclusion

Dividing fractions by whole numbers becomes easy once you remember to multiply by the reciprocal. Keep practicing, and you'll master it in no time! 🚀