# Mathematics Questions and Answers – Rational Numbers Between Two Rational Numbers

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This set of Mathematics Quiz for Class 8 focuses on “Rational Numbers Between Two Rational Numbers”.

1. Which number lies between the numbers $$\frac{1}{4}$$ and $$\frac{1}{6}$$?
a) $$\frac{1}{5}$$
b) $$\frac{1}{6}$$
c) $$\frac{1}{3}$$
d) $$\frac{1}{2}$$

Explanation: The given fractional numbers represents $$\frac{1}{4}$$ = 0.25 and $$\frac{1}{6}$$ = 0.17
Our options are $$\frac{1}{5}$$ = 0.20
$$\frac{1}{6}$$ = 0.17
$$\frac{1}{3}$$ = 0.33
$$\frac{1}{2}$$ = 0.50
The only option between 0.17 and 0.25 is $$\frac{1}{5}$$ i.e. 0.20.

2. The rational number which is not lying between 6 and 7 is ________
a) $$\frac{36}{7}$$
b) $$\frac{45}{7}$$
c) $$\frac{46}{7}$$
d) $$\frac{13}{2}$$

Explanation: The only number which is not between 6 and 7 is $$\frac{36}{7}$$
$$\frac{36}{7}$$ = 5.14
$$\frac{45}{7}$$ = 6.42
$$\frac{46}{7}$$ = 6.57
$$\frac{13}{2}$$ = 6.5.

3. Between any consecutive two integers, there are always infinite integers.
a) True
b) False

Explanation: The set of integers is […., -1, 0, 1, ….] there cannot be any integers between two integers.
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4. The maximum number of integers between two consecutive natural numbers is ________
a) zero
b) 2
c) 3
d) infinite

Explanation: There can be an infinite number of rational numbers between any two consecutive natural numbers. But there cannot be any integers between two consecutive natural numbers.

5. Which on the following number lies between $$\frac{3}{10}$$ and $$\frac{3}{10000}$$.
a) $$\frac{3}{1000}$$
b) $$\frac{3}{10000}$$
c) $$\frac{3}{100000}$$
d) $$\frac{3}{1000000}$$

Explanation: The given fractional numbers represents $$\frac{3}{10}$$ = 0.3 and $$\frac{3}{10000}$$ = 0.00003
Our options are in fractions, converting it into decimal form we get,
$$\frac{3}{1000}$$ = 0.0003
$$\frac{3}{10000}$$ = 0.00003
$$\frac{3}{100000}$$ = 0.000003
$$\frac{3}{1000000}$$ = 0.0000003.
The only option between 0.3 and 0.00003 is $$\frac{3}{1000}$$ i.e. 0.0003.

6. $$\frac{32}{9}$$ lies between which pair?
a) $$\frac{6}{5}$$ and $$\frac{7}{2}$$
b) $$\frac{3}{2}$$ and $$\frac{5}{2}$$
c) $$\frac{7}{2}$$ and $$\frac{10}{2}$$
d) $$\frac{7}{2}$$ and $$\frac{6}{5}$$

Explanation: When we place the 4 given pairs and the number on the number line we observe that the number $$\frac{32}{9}$$ lies between the pair $$\frac{7}{2}$$ and $$\frac{10}{2}$$, while other options fail to capture the given number between them. Hence the correct pair is $$\frac{7}{2}$$ and $$\frac{10}{2}$$.

7. Which of the following is the greatest number among the given rational numbers?
a) $$\frac{139}{26}$$
b) $$\frac{72}{21}$$
c) $$\frac{99}{36}$$
d) $$\frac{101}{20}$$

Explanation: The numbers when placed on the number line, the number which is placed farthest from 0 is the greatest. Here the numbers are, $$\frac{139}{26}$$ = 5.34
$$\frac{72}{21}$$ = 3.42
$$\frac{99}{36}$$ = 2.75
$$\frac{101}{20}$$ = 5.05
So, we conclude that the greatest number is $$\frac{139}{26}$$ and hence would be placed farthest from 0.

8. [….., -1, 0, 1, …….] the given set shows which type of numbers?
a) Rational numbers
b) Integers
c) Natural numbers
d) Whole numbers

Explanation: The given set is of integers.
The sets of other numbers are,
Whole number -> [0, 1, 2, 3, 4, ……]
Natural number -> [1, 2, 3, 4, …….]
Rational number -> [……, 0, ……..] This set consists of all numbers on the number line.

9. Pick the smallest number of the following.
a) –$$\frac{139}{26}$$
b) –$$\frac{72}{21}$$
c) –$$\frac{99}{36}$$
d) –$$\frac{101}{20}$$

Explanation: The numbers when placed on the number line, the number which is placed nearest from 0 is the smallest. Here the numbers are, –$$\frac{139}{26}$$ = -5.34
–$$\frac{72}{21}$$ = -3.42
–$$\frac{99}{36}$$ = -2.75
–$$\frac{101}{20}$$ = -5.05
So, we conclude that the smallest number is –$$\frac{139}{26}$$ and hence would be placed smallest from 0. Thing to remember: When the numbers are placed on the left side of the number line, the number farthest from the center is the smallest number. This is due to the negative sign.

10. Pick the option which has the ordered pair of BIG and SMALL number.
a) $$\frac{6}{3}$$ and $$\frac{7}{3}$$
b) $$\frac{12}{11}$$ and $$\frac{11}{12}$$
c) $$\frac{13}{22}$$ and $$\frac{33}{11}$$
d) $$\frac{12}{4}$$ and $$\frac{13}{5}$$

Explanation: Here we have to find the ordered pair of numbers and the order should be big following by small. This condition is only satisfied by one pair of numbers which is $$\frac{12}{4}$$ and $$\frac{13}{5}$$.

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

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