Using Fraction Bars to Divide Fractions with unlike Denominators

Divide: 3/5 ÷ 1/3
The fraction bars show 1 whole, 3 thirds, 5 fifths, and 15 fifteenths.
Think: How many _ are in 3/5?
Find the dividend.

The fraction of a group left over is 4 fifteenths / _ fifteenths .
3/5 ÷ 1/3 = _ 4/5

1 answer

To divide the fractions \( \frac{3}{5} \) by \( \frac{1}{3} \), you can follow these steps:

  1. Understand the Problem: You need to figure out how many \( \frac{1}{3} \) portions are in \( \frac{3}{5} \).

  2. Changing to Multiplication: Remember that dividing by a fraction is the same as multiplying by its reciprocal. So, \[ \frac{3}{5} \div \frac{1}{3} = \frac{3}{5} \times \frac{3}{1} = \frac{3 \times 3}{5 \times 1} = \frac{9}{5} \]

  3. Convert to Mixed Number: The fraction \( \frac{9}{5} \) can be converted to a mixed number: \[ \frac{9}{5} = 1 \frac{4}{5} \text{ (since 5 goes into 9 once, leaving a remainder of 4)} \]

  4. Final Statement: Therefore, \[ \frac{3}{5} \div \frac{1}{3} = 1 \frac{4}{5} \]

Now to fill in the blanks in your statements:

  • The dividend is \( \frac{3}{5} \).
  • The fraction of a group left over is \( 4 \) fifteenths out of \( 5 \) fifteenths.
  • Finally, \( \frac{3}{5} \div \frac{1}{3} = 1 \frac{4}{5} \).

So the final answer is: \[ 3/5 \div 1/3 = 1 \frac{4}{5} \]