Solved problems: dividing a fraction by a whole number Grade 5

📚 Dividing Fractions by Whole Numbers: A Comprehensive Guide

Dividing a fraction by a whole number might seem tricky at first, but it's actually quite straightforward! The key is to remember that any whole number can be written as a fraction with a denominator of 1. Once you've done that, dividing fractions becomes a simple matter of multiplying by the reciprocal. Let's break it down.

📜 A Little History

Fractions have been used for thousands of years, dating back to ancient Egypt and Mesopotamia. The need to divide quantities that weren't whole numbers spurred the development of these mathematical tools. Dividing fractions, including by whole numbers, became essential for trade, land measurement, and other practical applications. Over time, standardized methods evolved to make these calculations easier and more consistent.

🔑 Key Principles

• 🔢 Whole Number as a Fraction: Any whole number 'n' can be written as a fraction $\frac{n}{1}$. For example, 5 is the same as $\frac{5}{1}$.
• 🔄 Reciprocal: The reciprocal of a fraction $\frac{a}{b}$ is $\frac{b}{a}$. To find the reciprocal, simply flip the numerator and denominator.
• ➗ Division as Multiplication: Dividing by a fraction is the same as multiplying by its reciprocal. So, $a \div \frac{b}{c} = a \times \frac{c}{b}$.

📝 Steps to Divide a Fraction by a Whole Number

1. ✍️ Write the whole number as a fraction: Put the whole number over 1.
2. 🔄 Find the reciprocal: Find the reciprocal of the whole number (now a fraction).
3. ✖️ Multiply: Multiply the original fraction by the reciprocal you just found.
4. ✅ Simplify: Simplify the resulting fraction if possible.

🌍 Real-World Examples

Example 1: Sharing Pizza

You have $\frac{1}{2}$ of a pizza left and want to share it equally with 3 friends. How much of the original pizza does each friend get?

We need to divide $\frac{1}{2}$ by 3.

1. 3 as a fraction: $\frac{3}{1}$
2. Reciprocal of $\frac{3}{1}$: $\frac{1}{3}$
3. Multiply: $\frac{1}{2} \times \frac{1}{3} = \frac{1 \times 1}{2 \times 3} = \frac{1}{6}$

Each friend gets $\frac{1}{6}$ of the original pizza.

Example 2: Ribbon Cutting

You have $\frac{2}{3}$ of a meter of ribbon and need to cut it into 4 equal pieces. How long will each piece be?

We need to divide $\frac{2}{3}$ by 4.

1. 4 as a fraction: $\frac{4}{1}$
2. Reciprocal of $\frac{4}{1}$: $\frac{1}{4}$
3. Multiply: $\frac{2}{3} \times \frac{1}{4} = \frac{2 \times 1}{3 \times 4} = \frac{2}{12}$
4. Simplify: $\frac{2}{12} = \frac{1}{6}$

Each piece of ribbon will be $\frac{1}{6}$ of a meter long.

✍️ Practice Quiz

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

✅ Answer Key

1. $\frac{1}{8}$
2. $\frac{1}{5}$
3. $\frac{1}{8}$
4. $\frac{1}{14}$
5. $\frac{2}{9}$
6. $\frac{1}{10}$
7. $\frac{1}{15}$

💡 Conclusion

Dividing fractions by whole numbers is a fundamental skill in mathematics. By understanding the principles of reciprocals and multiplication, you can easily solve these types of problems. Remember to practice regularly to build your confidence and accuracy! Keep exploring the world of fractions – they're everywhere!