8TH RATIONAL NUMBERS 1

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Exercise 1.1 – Solutions

1. −19/5 lies between the integers ______ and ______.

Answer: −4 and −3

Convert the fraction into decimal form:

−19 ÷ 5 = −3.8

The number −3.8 is greater than −4 and less than −3.

Therefore, −19/5 lies between −4 and −3.

2. The decimal form of the rational number 15/−4 is ______.

Answer: −3.75

Divide 15 by −4:

15 ÷ (−4) = −3.75

Since a positive number divided by a negative number gives a negative answer, the decimal form is −3.75.

3. The rational numbers −8/3 and 8/3 are equidistant from ______.

Answer: 0

Two numbers are equidistant from zero if they are opposites of each other.

Here:
−8/3 and 8/3 have the same distance from 0 on the number line.

Therefore, they are equidistant from 0.

4. The next rational number in the sequence −15/24, 20/−32, −25/40 is ______.

Answer: −30/48

Simplify each fraction:

−15/24 = −5/8
20/−32 = −5/8
−25/40 = −5/8

All fractions are equivalent to −5/8.

Continuing the pattern:
−30/48 = −5/8

Therefore, the next rational number is −30/48.

5. The standard form of 58/−78 is ______.

Answer: −29/39

The HCF of 58 and 78 is 2.

Divide numerator and denominator by 2:

58/−78 = (58 ÷ 2)/(−78 ÷ 2)
= 29/−39
= −29/39

Hence, the standard form is −29/39.

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Rational Numbers MCQ Quiz

1. Which rational number definitely lies between −3/4 and −2/5 ?

−1/10 −13/20 −9/10 2/5

✅ Correct Answer: −13/20

Convert the fractions into equivalent fractions with denominator 20:

−3/4 = −15/20
−2/5 = −8/20

Any rational number between −15/20 and −8/20 will work.
−13/20 lies perfectly between them.

2. A student says that −14/20 is NOT between −3/4 and −2/5. What is the correct statement?

The student is correct −14/20 equals −2/5 −14/20 lies between them −14/20 is greater than 0

✅ Correct Answer: −14/20 lies between them

We know:

−15/20 < −14/20 < −8/20

Hence −14/20 lies between −3/4 and −2/5.

3. Which method is most useful for quickly finding rational numbers between two fractions having different denominators?

Add the numerators only Find the LCM of denominators Multiply only denominators Ignore signs

✅ Correct Answer: Find the LCM of denominators

Fractions with different denominators are easier to compare after converting them into equivalent fractions with a common denominator.

The LCM helps us create equal denominators quickly.

4. Which of the following fractions is closest to −3/4 ?

−16/20 −15/20 −9/20 −5/20

✅ Correct Answer: −15/20

Multiply numerator and denominator of −3/4 by 5:

−3/4 = −15/20

Therefore, −15/20 is exactly equal to −3/4.

5. Which statement about rational numbers between two given rational numbers is TRUE?

Only one rational number exists No rational number exists Exactly ten rational numbers exist Infinitely many rational numbers exist

✅ Correct Answer: Infinitely many rational numbers exist

Between any two rational numbers, we can always create more rational numbers by converting them into equivalent fractions with larger denominators.

Therefore infinitely many rational numbers exist between any two rational numbers.

True or False – Rational Numbers

1. 0 is the smallest rational number.

Answer: FALSE

Rational numbers include negative numbers also.

Examples:
−1, −2, −100, −1/2 etc.

Since there are infinitely many rational numbers smaller than 0, it is NOT the smallest rational number.

2. −4/5 lies to the left of −3/4.

Answer: TRUE

Convert into decimal form:

−4/5 = −0.8
−3/4 = −0.75

Since −0.8 is smaller than −0.75, it lies to the left on the number line.

3. −19/5 is greater than 15/−4.

Answer: FALSE

Simplify both numbers:

−19/5 = −3.8
15/−4 = −3.75

Since −3.8 is less than −3.75,
−19/5 is NOT greater than 15/−4.

4. The average of two rational numbers lies between them.

Answer: TRUE

The average of two rational numbers a and b is:

(a + b) / 2

This value always lies between the two numbers.

Example:
Average of 2 and 6 is:
(2 + 6)/2 = 4

And 4 lies between 2 and 6.

5. There are an unlimited number of rational numbers between 10 and 11.

Answer: TRUE

Between any two rational numbers, infinitely many rational numbers exist.

Between 10 and 11 we can write:
10.1, 10.01, 10.001, 10.5, 10.75 and many more.

Therefore, there are unlimited rational numbers between 10 and 11.