4th Grade Equivalent Fractions Worksheet Solutions (PDF)

Strip A: 1 of 3 parts is shaded, \(\frac{1}{3}\). Strip B: 2 of 6 parts are shaded, \(\frac{2}{6}\).

The shaded parts are the same length.

Answer: \(\frac{1}{3} = \frac{2}{6}\), yes.

\(2 \times 3 = 6\), so multiply the numerator by 3 too: \(1 \times 3 = 3\).

Answer: \(\frac{3}{6}\).

\(3 \times 4 = 12\), so \(2 \times 4 = 8\).

Answer: \(\frac{2}{3} = \frac{8}{12}\).

\(4 \times 2 = 8\), so \(3 \times 2 = 6\).

Answer: \(\frac{3}{4} = \frac{6}{8}\).

\(5 \times 2 = 10\), so \(1 \times 2 = 2\).

Answer: \(\frac{1}{5} = \frac{2}{10}\).

The denominator went from 6 to 3, so divide by 2. \(4 \div 2 = 2\).

Answer: \(\frac{4}{6} = \frac{2}{3}\).

The numerator went from 6 to 3, so divide by 2. \(8 \div 2 = 4\).

Answer: \(\frac{6}{8} = \frac{3}{4}\).

The dashed line shows the dots are at the same point. The bottom line has 8 parts, and the dot is at the 6th mark.

Check: \(3 \times 2 = 6\) and \(4 \times 2 = 8\).

Answer: \(\frac{6}{8}\).

\(5 \times 2 = 10\), so \(\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}\).

\(5 \times 20 = 100\), so \(\frac{2}{5} = \frac{2 \times 20}{5 \times 20} = \frac{40}{100}\).

Answer: \(\frac{4}{10}\) and \(\frac{40}{100}\).

\(10 \times 10 = 100\), so multiply the numerator by 10: \(3 \times 10 = 30\).

Answer: \(\frac{30}{100}\).

\(6 \times 2 = 12\) and \(5 \times 2 = 10\).

Answer: Yes, \(\frac{5}{6} = \frac{10}{12}\).

The numerator was multiplied by \(3 \times 2 = 6\), which is 2. The denominator would be \(8 \times 2 = 16\), not 12.

Also \(\frac{6}{12}\) is equal to \(\frac{1}{2}\), and \(\frac{3}{8}\) is less than \(\frac{1}{2}\).

Answer: No. The same number did not multiply both parts.

Divide the numerator and denominator by 3: \(9 \div 3 = 3\) and \(12 \div 3 = 4\).

Answer: \(\frac{3}{4}\).

\(12 \div 4 = 3\), so divide the numerator by 4: \(8 \div 4 = 2\).

Answer: \(\frac{2}{3}\).

\(4 \times 2 = 8\) and \(2 \times 2 = 4\), so \(\frac{2}{4}\) = \(\frac{4}{8}\).

Answer: Yes, they ate the same amount (one half).

\(4 \times 3 = 12\), so \(3 \times 3 = 9\).

Answer: \(\frac{9}{12}\).

3 dimes is \(\frac{3}{10}\) of a dollar.

\(\frac{3}{10} = \frac{3 \times 10}{10 \times 10} = \frac{30}{100}\), and 30 cents is 30 out of 100 cents.

Answer: \(\frac{3}{10}\) = \(\frac{30}{100}\) of a dollar.

Change thirds to sixths: \(\frac{2}{3} = \frac{4}{6}\).

\(\frac{4}{6}\) is four sixths, so he needs 4 scoops.

Answer: 4 scoops.

Start with \(\frac{2}{3}\). Multiply the top and bottom by 2 to get \(\frac{4}{6}\), by 3 to get \(\frac{6}{9}\), and by 4 to get \(\frac{8}{12}\).

Answer: Yes. Each fraction comes from multiplying 2 and 3 by the same number.

\(\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}\).

\(\frac{3}{5} = \frac{3 \times 20}{5 \times 20} = \frac{60}{100}\).

Answer: \(\frac{6}{10}\) and \(\frac{60}{100}\); 60 squares.