4th Grade Comparing Fractions Test Answer Key and Scoring Guide (PDF)

Q: Why does the key use sixths for question 5?

Sixths work because the denominators 2, 3, and 6 all divide evenly into 6. That turns one half into three sixths, one third into two sixths, and two thirds into four sixths. Then the numerators 2, 3, 4, and 5 are easy to order.

Q: What if I used a different method than the key?

Any correct method earns credit. The key picks one method to show the steps, but benchmarks, strips, and common denominators all work. Check that your final answer matches and that your work shows your reasoning in a clear way.

Q: How do I explain why one third is less than one half?

Say that the whole is split into more parts for thirds than for halves, so each third is smaller. You can also draw two strips of the same length and shade one half on one and one third on the other. The half is clearly longer.

$4th grade comparing fractions test answer key – Maths PDF$

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This 4th grade comparing fractions test answer key covers comparing fractions (Common Core 4.NF.A.2), with a free PDF to print.

Key takeaway: This answer key helps fourth grade students see how each point on the fraction comparison test was earned.

Topic: Comparing Fractions (4th grade)
Content: Worked solutions and a scoring guide for 9 questions
Standards: 4.NF.A.2
Answers: Every step shown, with the method to review
Format: Free printable PDF, US Letter, black and white

This answer key helps fourth grade students see how each point on the fraction comparison test was earned. Also, it gives full solutions to all nine questions, with the method named for each one and the reasoning written out in a full sentence.

The key shows a common denominator for questions 2, 5, and 8, a benchmark for question 3, and a number line reading for question 6. Then, explanations for questions 7 and 9 model what a complete written answer looks like. Add up your points out of 20, then spend 15 minutes redoing every question that lost credit with a different method.

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

4th grade comparing fractions test answer key: worked solutions

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.

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) $\frac{1}{2} = \frac{4}{8}$

Also, Scoring: 1 point for each correct symbol.

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.

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.

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 and after

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.

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.

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.

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 4th grade comparing fractions test answer key

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.

Common mistakes with this 4th grade comparing fractions test answer key

Students count an explanation as correct because the answer was right. Instead, the key shows what a full reason looks like, and a bare yes or no does not earn full credit.
Students copy the common denominator but not the final comparison. Also, the last line should name which fraction is greater, not just give new numerators.
Students trust the picture in question 4 without checking. Instead, count the equal parts on each strip before comparing.
Students ignore partial credit in question 8. Naming the farthest runner is worth a point, and the ordering is worth two.

How to learn from your test

Group missed questions into symbols, ordering, and explanations. Practice the group with the most lost points first. Repeat this habit on every problem for the best results.
Compare your explanation with the key sentence by sentence. Notice whether you named a method and gave a reason.
Teachers can have students write a corrected explanation on a sticky note, which keeps the lesson short and focused.

Download the 4th grade comparing fractions test answer key as a PDF with the button below and keep it with your notes.

4th grade comparing fractions test answer key: frequently asked questions

Why does the key use sixths for question 5?

Sixths work because the denominators 2, 3, and 6 all divide evenly into 6. That turns one half into three sixths, one third into two sixths, and two thirds into four sixths. Then the numerators 2, 3, 4, and 5 are easy to order.

What if I used a different method than the key?

Any correct method earns credit. The key picks one method to show the steps, but benchmarks, strips, and common denominators all work. Check that your final answer matches and that your work shows your reasoning in a clear way.

How do I explain why one third is less than one half?

Say that the whole is split into more parts for thirds than for halves, so each third is smaller. You can also draw two strips of the same length and shade one half on one and one third on the other. The half is clearly longer.

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