4th Grade Equivalent Fractions Test Solutions and Scoring (PDF)

A: \(\frac{2}{3}\). B: \(\frac{8}{12}\).

\(3 \times 4 = 12\) and \(2 \times 4 = 8\), so they are equal.

\(\frac{2}{3} = \frac{8}{12}\)

Scoring: 1 point for both fractions; 1 point for a correct explanation or equation.

(a) \(5 \times 2 = 10\), so \(3 \times 2 = 6\). (b) \(6 \times 2 = 12\), so \(5 \times 2 = 10\).

(a) 6 (b) 10

Scoring: 1 point for each correct number.

(a) \(10 \times 10 = 100\), so \(7 \times 10 = 70\). (b) \(5 \times 20 = 100\), so \(4 \times 20 = 80\).

(a) 70 (b) 80

Scoring: 1 point for each correct number.

\(3 \times 2 = 6\) and \(4 \times 2 = 8\): yes. \(3 \times 3 = 9\) and \(4 \times 3 = 12\): yes. \(\frac{8}{12}\) = \(\frac{2}{3}\): no. \(\frac{5}{6}\): no.

\(\frac{6}{8}\) and \(\frac{9}{12}\)

Scoring: 2 points for both and no extras; 1 point if one is missing or one extra is listed.

To make an equivalent fraction, both parts must be multiplied (or divided) by the same number. Adding 1 changes the amount.

\(3 \times 4 = 12\) and \(2 \times 4 = 8\), so \(\frac{2}{3}\) = \(\frac{8}{12}\).

Adding does not keep the value; \(\frac{8}{12}\)

Scoring: 1 point for the explanation; 1 point for \(\frac{8}{12}\).

(a) The bottom line is cut into eighths, and the dot is at the 4th mark: \(\frac{4}{8}\).

(b) \(\frac{2}{4} = \frac{4}{8}\).

(c) \(\frac{2}{4}\) is one half, and \(\frac{1}{2} = \frac{5}{10}\).

(a) \(\frac{4}{8}\) (b) \(\frac{2}{4}\) = \(\frac{4}{8}\) (c) \(\frac{5}{10}\)

Scoring: 1 point for each part. Accept any correct equation in (b).

(a) \(3 \times 10 = 30\), so \(\frac{30}{100}\).

(b) \(100 \div 25 = 4\) and \(25 \div 25 = 1\), so \(\frac{1}{4}\).

(c) \(8 \div 2 = 4\) and \(6 \div 2 = 3\), so \(\frac{3}{4}\).

(a) \(\frac{30}{100}\) (b) \(\frac{1}{4}\) (c) \(\frac{3}{4}\)

Scoring: 1 point for each part.

(a) \(6 \times 2 = 12\) and \(2 \times 2 = 4\), so \(\frac{2}{6}\) = \(\frac{4}{12}\). They ate the same amount.

(b) \(3 \times 2 = 6\) and \(1 \times 2 = 2\), so \(\frac{1}{3}\) = \(\frac{2}{6}\). Yes.

(a) yes (b) yes

Scoring: (a) 1 point for yes, 1 point for the multiplication reason; (b) 1 point.

Multiply the numerator and denominator by 2: \(\frac{5 \times 2}{8 \times 2} = \frac{10}{16}\). Any correct multiple works, such as \(\frac{15}{24}\).

\(\frac{10}{16}\)

Scoring: 1 point for any correct equivalent fraction.