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Quizzes > Mathematics

Rational Number Practice Problems: Test Fractions, Decimals, and Integers

Quick quiz with rational number practice questions. Instant results.

Editorial: Review CompletedCreated By: Abby NoviaUpdated Aug 23, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration promoting a free rational number quiz on a coral background

This quiz helps you practice rational numbers by comparing, ordering, and working with fractions, decimals, and integers. Get instant results, see mistakes, and build speed. For more focused practice, try the adding and subtracting fractions quiz or the decimal quiz; for a wider refresh, check the basic math quiz.

Simplify the fraction 4/8.
1/2
2/4
4/16
3/4
To simplify 4/8, divide both the numerator and denominator by their greatest common divisor, which is 4. Dividing 4 by 4 gives 1, and 8 by 4 gives 2, so the fraction reduces to 1/2. Simplifying fractions helps make them easier to work with in calculations and comparisons. .
Which of the following is a rational number?
?2
?
3/5
e
A rational number can be expressed as a fraction of two integers. 3/5 fits this definition because both 3 and 5 are integers. Numbers like ?2, ?, and e are irrational because they cannot be written as exact fractions. .
Convert the decimal 0.25 to a fraction in simplest form.
1/4
25/100
2/8
1/5
0.25 means 25 hundredths, which is 25/100. Simplify by dividing numerator and denominator by 25, resulting in 1/4. This creates the simplest form of the fraction. .
What is 2/3 + 1/4?
11/12
3/7
5/7
8/12
To add 2/3 and 1/4, first find a common denominator of 12. Convert 2/3 to 8/12 and 1/4 to 3/12, then add to get 11/12. Always simplify if possible. .
Calculate 7/8 ? 1/3.
13/24
6/11
5/24
7/11
Find a common denominator of 24: 7/8 is 21/24 and 1/3 is 8/24. Subtracting gives (21 ? 8)/24 = 13/24. This fraction is already in simplest form. .
What is (?3/5) × (10/9)?
?2/3
?30/45
?3/5
2/3
Multiply numerators and denominators: (?3 × 10)/(5 × 9) = ?30/45. Simplify by dividing by 15 to get ?2/3. Keep track of the negative sign. .
Evaluate (5/6) ÷ (10/15).
5/4
1/2
3/4
15/60
Division by a fraction is the same as multiplying by its reciprocal: (5/6) × (15/10) = 75/60, which simplifies to 5/4. Simplify by dividing numerator and denominator by 15. .
Which rational number lies between 3/7 and 1/2 on the number line?
4/9
2/5
3/8
5/10
Convert to decimals: 3/7 ? 0.4286, 1/2 = 0.5. 4/9 ? 0.4444, which lies between them. The others are either below or equal to one of the endpoints. .
Express ?1.75 as a fraction in simplest form.
?7/4
?1 3/4
?14/8
?35/20
?1.75 equals ?1 3/4, which as an improper fraction is ?(1×4+3)/4 = ?7/4. Simplify if needed, though ?7/4 is already in simplest form. .
Compute (2/3) ÷ (4/9) ? (1/2).
1
1/3
2/3
3/2
First divide: (2/3) × (9/4) = 18/12 = 3/2. Then subtract 1/2: 3/2 ? 1/2 = (3?1)/2 = 2/2 = 1. Follow order of operations carefully. .
Convert the repeating decimal 0.??? (0.272727…) to a fraction in simplest form.
3/11
27/99
2/11
25/90
Let x = 0.272727… then 100x = 27.272727… Subtracting gives 99x = 27, so x = 27/99 = 3/11 after dividing numerator and denominator by 9. This is the fraction form of the repeating decimal. .
0
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Study Outcomes

  1. Identify Rational Numbers -

    Recognize and list numbers that can be expressed as a ratio of integers, including fractions, integers, and terminating or repeating decimals.

  2. Simplify Fractions -

    Reduce complex fractions to their simplest form and generate equivalent fractions to strengthen understanding of rational numbers practice.

  3. Classify Number Types -

    Differentiate between rational and irrational numbers and determine whether expressions such as 9/3 qualify as rational numbers.

  4. Solve Rational Number Problems -

    Apply addition, subtraction, multiplication, and division to solve a variety of rational numbers problems with confidence.

  5. Analyze Quiz Performance -

    Review results to pinpoint strengths and weaknesses, helping you focus future rational numbers practice on targeted areas.

Cheat Sheet

  1. Definition and Closure Properties -

    According to MIT OpenCourseWare, any number expressible as p/q with q≠0 is rational, and they are closed under addition, subtraction, multiplication, and division (except by zero). For rational numbers practice, note that "is 9/3 a rational number?" is trivially yes, since 9/3 simplifies to 3.

  2. Equivalent Fractions and Simplification -

    Per Khan Academy, simplify by dividing numerator and denominator by their GCF to create equivalent fractions, like turning 8/12 into 2/3. A handy mnemonic is "Divide and Conquer" to remember GCF simplifies problems on rational numbers quickly.

  3. Converting Between Improper Fractions and Mixed Numbers -

    As outlined by the National Council of Teachers of Mathematics, convert by dividing numerator by denominator to get a whole number plus a remainder (e.g., 11/4 = 2 3/4). This conversion is essential in rational numbers practice when working with mixed-number problems.

  4. Comparing and Ordering -

    Use cross-multiplication - multiply diagonals and compare products - to order fractions without converting to decimals (e.g., compare 3/5 vs. 4/7 by checking 3×7 and 4×5). This strategy, recommended by Stanford University math resources, streamlines many rational numbers problems.

  5. Operations: Addition, Subtraction, Multiplication, Division -

    For addition/subtraction, find the least common denominator to combine fractions; for division, "invert and multiply" using reciprocals as taught in Cambridge University's math guide. Consistent practice with rational number practice problems boosts fluency in each operation.

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