# 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

Explanation:

Numbers Closed Under
a) Rational Numbers Yes Yes No
b) Integers Yes No
c) Whole Numbers Yes
d) Natural Numbers No

2. By using the properties of rational numbers solve the following equation (8 + 0) + (6 * 3).
a) 26
b) 24
c) 28
d) 0

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) $$\frac{5}{2}$$

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.

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

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) $$\frac{121}{16}$$

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 $$\frac{11}{2} + \frac{11}{4} – \frac{11}{8} + \frac{11}{16} = \frac{88}{16} + \frac{44}{16} – \frac{22}{16} + \frac{11}{16}$$
= $$\frac{121}{16}$$.

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) $$\frac{-21}{56}$$

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) $$\frac{-5}{4}$$

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 = $$\frac{-5}{4}$$.

8. What is the multiplicative inverse of $$\frac{15}{135}$$?
a) $$\frac{15}{135}$$
b) $$\frac{-15}{135}$$
c) 1
d) 9

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) $$\frac{12}{3}$$

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”.

10. What is the reciprocal of $$\frac{1}{-x}$$?
a) x
b) -x
c) $$\frac{1}{x}$$
d) $$\frac{1}{-x}$$ 