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Quizzes > Mathematics > Basic Math & Arithmetic

Master Rational Number Practice Problems - Take the Quiz!

Ready to tackle problems on rational numbers? Dive into our practice quiz now!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration promoting a free rational number quiz on a coral background

This rational number practice quiz helps you work with fractions, decimals, integers, negatives, and mixed numbers, including comparing, ordering, and operations. Use it to check weak spots before a test and build speed and accuracy as you aim for 100%.

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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