Mathematics Questions and Answers – Properties of Rational Numbers

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Properties of Rational Numbers”.

1. Which of the following type of numbers are closed under only multiplication?
a) Rational Numbers
b) Integers
c) Whole Numbers
d) Natural Numbers
View Answer

Answer: c
Explanation:

Numbers Closed Under
Addition Subtraction Multiplication Division
a) Rational Numbers Yes Yes No
b) Integers Yes No
c) Whole Numbers Yes
d) Natural Numbers No
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2. By using the properties of rational numbers solve the following equation (8 + 0) + (6 * 3).
a) 26
b) 24
c) 28
d) 0
View Answer

Answer: a
Explanation: By using the properties of rational numbers like addition and multiplication, we can solve the equation and get to the correct answer.
(8+0) + (6 * 3)
= (8) + (18)
= 26.

3. Solve: \((\frac{15}{6}) * (\frac{2}{3})\).
a) \(\frac{3}{5}\)
b) \(\frac{2}{5}\)
c) \(\frac{5}{3}\)
d) \(\frac{5}{2}\)
View Answer

Answer: c
Explanation: Using the property of multiplication, we can solve the question.
\((\frac{15}{6}) * (\frac{2}{3})\)
= \((\frac{5}{2}) * (\frac{2}{3})\)
= 5/3.
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4. Which number should be subtracted from \(\frac{16}{15}\) to get \((\frac{-16}{15})\)?
a) \(\frac{31}{15}\)
b) \(\frac{32}{15}\)
c) \(\frac{-32}{15}\)
d) 0
View Answer

Answer: b
Explanation: Using the properties of addition and subtraction we can solve this problem.
\(\frac{16}{15} – x = \frac{-16}{15}\)
Therefore \(\frac{16}{15} + \frac{16}{15}\) = x
Therefore x = \(\frac{32}{15}\)
Option \(\frac{-32}{15}\) cannot be the correct answer, as the question itself asks to subtract the number in order to obtain \(\frac{-16}{15}\).

5. Simplify: \(\frac{11}{2} + \frac{11}{4} – \frac{11}{8} + \frac{11}{16}\).
a) \(\frac{44}{2}\)
b) \(\frac{44}{4}\)
c) \(\frac{44}{16}\)
d) \(\frac{121}{16}\)
View Answer

Answer: d
Explanation: In order to simplify the given equation we have to equate the denominators.
We will do this by taking the least common multiple.
Therefore \(\frac{11}{2} + \frac{11}{4} – \frac{11}{8} + \frac{11}{16} = \frac{88}{16} + \frac{44}{16} – \frac{22}{16} + \frac{11}{16}\)
= \(\frac{121}{16}\).
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6. Which of the following rational number is in the standard form?
a) \(\frac{16}{21}\)
b) \(\frac{16}{24}\)
c) \(\frac{21}{15}\)
d) \(\frac{-21}{56}\)
View Answer

Answer: a
Explanation: A rational number is said to be in it’s standard form when the numbers cannot be further reduced.
Here, we can see that the options other than the option \(\frac{16}{21}\) can be reduced.
When \(\frac{16}{24}\) is reduced, we get \(\frac{2}{3}\)… Standard Form.
When \(\frac{21}{15}\) is reduced, we get \(\frac{7}{5}\)… Standard Form.
When \(\frac{-21}{56}\) is reduced, we get \(\frac{-3}{8}\)… Standard Form.

7. Fill in the blanks \(\frac{-15}{32}\) / ____ = \(\frac{12}{32}\).
a) \(\frac{39}{128}\)
b) \(\frac{128}{39}\)
c) \(\frac{128}{-39)}\)
d) \(\frac{-5}{4}\)
View Answer

Answer: d
Explanation: Using the properties of addition and subtraction we can solve this problem.
\(\frac{-15}{32} / x = \frac{12}{32}\)
Therefore x = \(\frac{-15}{32} / \frac{12}{32}\)
Therefore x = \(\frac{-15}{32} * \frac{32}{12}\)
Therefore x = \(\frac{-15}{12}\)
Therefore x = \(\frac{-5}{4}\).
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8. What is the multiplicative inverse of \(\frac{15}{135}\)?
a) \(\frac{15}{135}\)
b) \(\frac{-15}{135}\)
c) 1
d) 9
View Answer

Answer: d
Explanation: \(\frac{15}{135}\) * x = 1
Therefore \(\frac{1}{9}\) * x = 1
Therefore x = 9
Multiplicative inverse of a particular number, is the number which gives 1 on multiplication with the number. There is one and only one multiplicative inverse for all numbers.

9. Which of the following lies between 2 and 3?
a) \(\frac{5}{2}\)
b) \(\frac{6}{2}\)
c) \(\frac{6}{3}\)
d) \(\frac{12}{3}\)
View Answer

Answer: a
Explanation: The correct answer to the question is \(\frac{5}{2}\), since it is the only number that lies between 2 and 3. While the others don’t lie in the given range.
Options \(\frac{6}{2}\) and \(\frac{6}{3}\) are not correct because the question states “between” and not “equal to”.
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10. What is the reciprocal of \(\frac{1}{-x}\)?
a) x
b) -x
c) \(\frac{1}{x}\)
d) \(\frac{1}{-x}\)
View Answer

Answer: b
Explanation: The number obtained by dividing a number by 1 is its reciprocal. All the numbers have one and only one reciprocal number.

Sanfoundry Global Education & Learning Series – Mathematics – Class 8.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter