70+ Dividing Fractions by Fractions Word Problems |5th Grade - Free Printable

To find out how many halves are in eight-sixths, we need to divide the fraction $\frac{8}{6}$ by the fraction $\frac{1}{2}$.

Step 1: Set up the division problem.
$$ \frac{8}{6} \div \frac{1}{2} $$

Step 2: Change division to multiplication.
To divide by a fraction, you multiply by its reciprocal. This means you keep the first fraction the same, change the division sign to multiplication, and flip the second fraction upside down.
* Keep $\frac{8}{6}$
* Change $\div$ to $\times$
* Flip $\frac{1}{2}$ to become $\frac{2}{1}$

Now the equation is:
$$ \frac{8}{6} \times \frac{2}{1} $$

Step 3: Simplify the fractions (optional but helpful).
We can simplify $\frac{8}{6}$ before multiplying. Both 8 and 6 can be divided by 2.
* $8 \div 2 = 4$
* $6 \div 2 = 3$

So, $\frac{8}{6}$ becomes $\frac{4}{3}$. The equation is now:
$$ \frac{4}{3} \times \frac{2}{1} $$

*(Note: The image simplifies differently by cross-canceling the 6 and the 2, which also works perfectly fine. Let's stick to the standard multiplication to verify.)*

Step 4: Multiply the numerators and denominators.
* Multiply the top numbers (numerators): $4 \times 2 = 8$
* Multiply the bottom numbers (denominators): $3 \times 1 = 3$

Step 5: Write the final fraction.
The result is $\frac{8}{3}$.

Let's double-check using the method shown in the image exactly:
1. $\frac{8}{6} \times \frac{2}{1}$
2. Simplify: Divide 6 and 2 by their common factor, 2. The 6 becomes 3, and the 2 becomes 1.
3. Equation becomes: $\frac{8}{3} \times \frac{1}{1}$
4. Multiply: $8 \times 1 = 8$ and $3 \times 1 = 3$.
5. Result: $\frac{8}{3}$

Both methods give the same result.

Final Answer:
\frac{8}{3}