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

4th Grade math test solutions: Comparing Fractions – Maths PDF

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This compare fractions test answers for 4th Grade covers comparing fractions (Common Core 4.NF.A.2), with a free PDF to print.

Use this answer key and scoring guide to grade the comparing fractions test. Each solution shows the common denominator or reasoning, and the scoring notes explain partial credit out of 20 points.

Grade 4 · Common Core State Standards: 4.NF.A.2

Compare fractions test answers: worked solutions

Question 1 – Same part [2 pts]

(a) Same denominator, 5 is more than 3. (b) Same numerator, sixths are smaller than fourths.

(a) \(\frac{5}{8} > \frac{3}{8}\) (b) \(\frac{2}{6} < \frac{2}{4}\)

Scoring: 1 point for each correct symbol.

Question 2 – Different denominators [2 pts]

(a) \(\frac{3}{4} = \frac{9}{12}\) and \(\frac{2}{3} = \frac{8}{12}\). (b) \(\frac{4}{8} = \frac{1}{2}\).

(a) \(\frac{3}{4} > \frac{2}{3}\) (b) \(\frac{1}{2} = \frac{4}{8}\)

Scoring: 1 point for each correct symbol.

Question 3 – Compare to one half [2 pts]

(a) Half of 10 is 5, and 4 is less than 5. (b) Half of 6 is 3, and 5 is more than 3.

(a) \(\frac{4}{10} < \frac{1}{2}\) (b) \(\frac{5}{6} > \frac{1}{2}\)

Scoring: 1 point for each correct symbol.

Question 4 – Strips [2 pts]

\(\frac{3}{5} = \frac{6}{10}\), and 6 tenths is less than 7 tenths.

In tenths, 6 is less than 7.

\(\frac{3}{5} < \frac{7}{10}\)

Scoring: 1 point for writing \(\frac{3}{5}\) as \(\frac{6}{10}\); 1 point for the correct comparison.

Question 5 – Order the fractions [2 pts]

Use sixths: \(\frac{5}{6}\), \(\frac{2}{6}\), \(\frac{3}{6}\), \(\frac{4}{6}\). Order the numerators: 2, 3, 4, 5.

\(\frac{1}{3}, \frac{1}{2}, \frac{2}{3}, \frac{5}{6}\)

Scoring: 2 points for the correct order; 1 point if only two fractions are swapped.

Question 6 – Points on a number line [3 pts]

(a) A is at 3 eighths. (b) B is at 6 eighths (the same as \(\frac{3}{4}\)). (c) 3 eighths is less than 6 eighths.

Labeled points.

(a) \(\frac{3}{8}\) (b) \(\frac{6}{8}\) (c) \(\frac{3}{8} < \frac{6}{8}\)

Scoring: 1 point for each part.

Question 7 – Ethan's claim [2 pts]

The numerators are the same. Thirds are smaller pieces than halves, so \(\frac{1}{3}\) is less than \(\frac{1}{2}\).

Ethan is not correct. \(\frac{1}{3} < \frac{1}{2}\)

Scoring: 1 point for saying he is not correct; 1 point for a reason about the size of the pieces.

Question 8 – Race results [3 pts]

Use twelfths: \(\frac{5}{6}\) = \(\frac{10}{12}\), \(\frac{3}{4}\) = \(\frac{9}{12}\), \(\frac{2}{3}\) = \(\frac{8}{12}\).

(a) Maya (b) \(\frac{2}{3} < \frac{3}{4} < \frac{5}{6}\)

Scoring: (a) 1 point; (b) 2 points for the correct order, 1 point for one pair in the wrong order.

Question 9 – Water bottles [2 pts]

Use 24: \(\frac{3}{8} = \frac{9}{24}\) and \(\frac{5}{12} = \frac{10}{24}\).

Bottle B has more water, because \(\frac{5}{12} > \frac{3}{8}\)

Scoring: 1 point for common denominator work; 1 point for the correct bottle.

Total score

Total

20 points

Key facts behind this compare fractions test answers

Key facts

Compare fractions only when they are parts of the same whole.
Same denominator: compare numerators. Same numerator: compare denominators and the smaller denominator is greater.
A common denominator turns a hard comparison into a numerator comparison, such as 8/12 < 9/12.
Benchmark 1/2: a fraction is less than 1/2 when its numerator is less than half the denominator.
Record a comparison with >, < or = and check it on a number line.

How to use this compare fractions test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

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