Understanding Division of Fractions

Oct 13, 2025 by recoveryshake.com 6 views

Division of Fractions: Simplifying Complex Operations

When dealing with fractions, division can be a bit tricky, especially when the fractions are complex. In this article, we will explore two division problems involving fractions and simplify them to their simplest form.

Understanding Division of Fractions

Division of fractions is the inverse operation of multiplication. When we divide one fraction by another, we are essentially asking how many times the second fraction fits into the first fraction. To divide fractions, we need to follow a specific procedure.

Step 1: Invert the Second Fraction

The first step in dividing fractions is to invert the second fraction. This means we flip the numerator and denominator of the second fraction. For example, if we have $\frac{a}{b} \div \frac{c}{d}$ , we will invert the second fraction to get $\frac{c}{d} \rightarrow \frac{d}{c}$ .

Step 2: Multiply the Fractions

Once we have inverted the second fraction, we can multiply the two fractions together. This is done by multiplying the numerators and denominators separately. For example, if we have $\frac{a}{b} \div \frac{c}{d}$ , we will multiply the fractions to get $\frac{a \cdot d}{b \cdot c}$ .

Simplifying the Result

After multiplying the fractions, we need to simplify the result to its simplest form. This involves canceling out any common factors between the numerator and denominator.

a) $\frac{3}{11} \div \frac{3}{11}$

Let's apply the steps we learned to the first problem.

Step 1: Invert the Second Fraction

The second fraction is $\frac{3}{11}$ . We will invert it to get $\frac{11}{3}$ .

Step 2: Multiply the Fractions

Now we will multiply the two fractions together. We have $\frac{3}{11} \cdot \frac{11}{3}$ .

Step 3: Simplify the Result

After multiplying the fractions, we get $\frac{3 \cdot 11}{11 \cdot 3}$ . We can cancel out the common factors between the numerator and denominator to get $\frac{1}{1}$ .

The Final Answer

The final answer to the first problem is $\boxed{1}$ .

b) $\frac{9}{10} \div \frac{3}{5}$

Let's apply the steps we learned to the second problem.

Step 1: Invert the Second Fraction

The second fraction is $\frac{3}{5}$ . We will invert it to get $\frac{5}{3}$ .

Step 2: Multiply the Fractions

Now we will multiply the two fractions together. We have $\frac{9}{10} \cdot \frac{5}{3}$ .

Step 3: Simplify the Result

After multiplying the fractions, we get $\frac{9 \cdot 5}{10 \cdot 3}$ . We can simplify the result to get $\frac{45}{30}$ .

Step 4: Cancel Out Common Factors

We can cancel out the common factors between the numerator and denominator to get $\frac{3}{2}$ .

The Final Answer

The final answer to the second problem is $\boxed{\frac{3}{2}}$ .

Conclusion

In this article, we learned how to divide fractions and simplify the results to their simplest form. We applied the steps we learned to two division problems involving fractions and obtained the final answers. Division of fractions is an essential operation in mathematics, and understanding how to simplify complex operations is crucial for solving problems in various fields.