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Quizzes > Mathematics > Basic Math & Arithmetic

Rational Numbers Quiz: Test Your Fraction Skills!

Think 'is 7/6 a rational number'? Dive In and Prove It!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art fraction shapes six over seven and seven over six question marks on dark blue background for rational numbers quiz

This quiz helps you decide if 6/7 is a rational number and practice sorting other fractions with clear, quick questions. You'll see cases like 7/6 and explore how 1/8 fits , getting instant feedback so you can spot gaps before a test.

Is 6/7 a rational number?
No, because the numerator and denominator are prime numbers.
No, because denominators must be powers of 10.
Yes, because its decimal form terminates.
Yes, because it can be expressed as a ratio of two integers.
A rational number is any number that can be expressed as the quotient of two integers with a nonzero denominator. The fraction 6/7 clearly has integer numerator 6 and integer denominator 7. Therefore, 6/7 is a rational number. .
Which of the following best defines a rational number?
A number that cannot be expressed as a ratio of two integers.
A number with only prime factors in the denominator.
A number expressed as the quotient of two integers where the denominator is not zero.
A number with a non-terminating, non-repeating decimal expansion.
A rational number is defined as any number that can be written as m/n where m and n are integers and n ? 0. This definition covers both terminating and repeating decimals. It excludes numbers that cannot be expressed as such a ratio. .
Is 7/6 a rational number?
No, because only proper fractions can be rational.
Yes, because 7/6 is the quotient of two integers.
No, because the numerator is larger than the denominator.
Yes, because its decimal form terminates.
Any fraction of two integers with a non-zero denominator is rational, regardless of whether it is proper or improper. Here 7 and 6 are integers and 6 ? 0. Hence 7/6 is rational. .
Which of these decimal representations indicates a rational number?
1.4142135...
0.(142857)
3.1415926...
0.1234567...
A decimal that eventually repeats or terminates represents a rational number. The notation 0.(142857) means that 142857 repeats indefinitely. This pattern arises from the fraction 1/7 and other rational numbers. .
Which fraction is equivalent to 6/7?
5/6
12/15
18/21
36/49
Multiplying numerator and denominator of 6/7 by 3 gives 18/21, which is equivalent to 6/7. The other options do not simplify to 6/7. .
What is the repeating decimal expansion of 6/7?
0.(857142)
0.(142857)
0.8(57142)
0.857142
Dividing 6 by 7 yields a repeating cycle of six digits: 857142. This cycle repeats indefinitely, so we write 0.(857142). .
Which of the following decimals corresponds to the fraction 7/6?
1.16
1.1(6)
1.07
1.(16)
The fraction 7/6 equals 1.1666..., which is written as 1.1(6) to indicate that the digit 6 repeats. The other notations either imply a different repeating pattern or a terminating decimal. .
Which property describes the result of adding two rational numbers?
Always rational
Always irrational
Only rational if denominators are equal
May be irrational
The set of rational numbers is closed under addition, meaning the sum of any two rational numbers is always rational. This follows from writing each as a fraction and combining them over a common denominator. .
Which of the following numbers is irrational?
?49
?2
0.(9)
4/5
?2 cannot be expressed as a ratio of two integers and has a non-repeating, non-terminating decimal expansion. ?49 = 7 and 0.(9) = 1 are both rational, as is 4/5. .
Which statement about the decimal expansions of rational numbers is true?
They either terminate or eventually repeat.
They always repeat.
They always terminate.
They never repeat.
A key property of rational numbers is that their decimal expansions either terminate after a finite number of digits or enter an infinite repeating cycle. They cannot produce a nonrepeating, nonterminating pattern. .
Which set represents all rational numbers?
{ decimals that never repeat }
{ square roots of integers }
{ m/n | m, n ? Z, n ? 0 }
{ m/n | m, n ? N }
The standard definition of Q, the rationals, is all ratios m/n where m and n are integers and n ? 0. Requiring n in N or focusing on nonrepeating decimals excludes valid rationals. .
Which continued fraction represents the rational number 6/7?
[0;1,6]
[1;6]
[0;6,1]
[1;0,7]
A finite simple continued fraction represents a rational number. Converting 6/7 yields [0;1,6], meaning 0 + 1/(1 + 1/6). Other patterns correspond to different values. .
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Study Outcomes

  1. Determine Rationality of Specific Fractions -

    Use the definition of rational numbers to decide if 6/7 or 7/6 qualify as rational numbers.

  2. Apply Rational Number Definitions -

    Apply the concept of a rational number to identify other examples of rational numbers, including fractions, integers, and terminating or repeating decimals.

  3. Compare Rational Numbers -

    Compare pairs of rational numbers to determine which is larger or smaller and explain their relative values.

  4. Simplify Rational Expressions -

    Simplify fractional expressions to their simplest form to reinforce understanding of numerator-denominator relationships.

  5. Solve Practice Quiz Questions -

    Complete interactive quiz questions and receive instant feedback to test and deepen comprehension of rational numbers.

  6. Analyze Common Pitfalls -

    Identify and correct common mistakes when working with rational numbers to build accuracy and confidence.

Cheat Sheet

  1. Formal Definition and 6/7 Example -

    A rational number is any value that can be written as a fraction a/b where a and b are integers and b≠0. Asking "is 6/7 a rational number" is straightforward: since both 6 and 7 are integers and 7≠0, 6/7 qualifies. Sources like Khan Academy and MathWorld confirm this fundamental definition.

  2. Reciprocal Insight with 7/6 -

    Understanding reciprocals helps you see that if 6/7 is rational, its reciprocal 7/6 is also rational because integer ratios flip but stay valid. Asking "is 7/6 a rational number" has the same logic - 7 and 6 are integers and 6≠0. University-level texts (e.g., MIT OpenCourseWare) reinforce that reciprocals of nonzero rationals remain rational.

  3. Decimal Representations -

    Every rational number has a decimal form that either terminates or repeats. For example, 6/7 = 0.857142857142… with the block "857142" repeating indefinitely, illustrating a repeating decimal. Britannica and educational journals on number theory discuss this pattern as a hallmark of rationality.

  4. Comparing Rational Numbers -

    To compare fractions like 6/7 and 7/6, use cross-multiplication: 6×6 vs 7×7 tells you which is larger without converting to decimals. This simple "cross-multiply and compare" trick lets you order or compare rational numbers quickly. Check math resources from MathIsFun or official curricula for step-by-step examples.

  5. Practice with Quizzes and Mnemonics -

    Boost retention by tackling a rational numbers practice quiz that covers "is 6/7 a rational number," "is 7/6 a rational number," and other examples of rational numbers. Use the mnemonic "Keep Denominator, Multiply Numerator" to remind yourself to check integer conditions. Official educational sites like UNESCO's math portal and classroom worksheets offer curated exercises to reinforce these concepts.

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