RATIONAL NUMBERS BETWEEN TWO RATIONAL NUMBERS WORKSHEET

Problem 1 :

Find out a rational numbers lying between 1/4 and 1/3.

Solution

Problem 2 :

Find out a rational numbers lying between 2 and 3.

Solution

Problem 3 :

Find out a rational numbers lying between -1/3 and 1/2.

Solution

Problem 4 :

Find out two rational numbers lying between -3 and -2.

Solution

Problem 5 :

Find out six rational numbers lying between -4/8 and 3/8.

Solution

Problem 6 :

Find out ten rational numbers lying between -4/13 and 7/13.

Solution

Problem 7 :

Find out three rational numbers lying between 4 and 5.

Solution

Problem 8 :

Find out three rational numbers lying between 2/3 and 3/4.

Solution

Problem 1 :

Find three rational numbers between 2/3 and 3/4.

Solution

Problem 2 :

Find ten rational numbers between -2/5 and 1/2

Solution

Problem 3 :

Find five rational numbers between 2/3 and 4/5

Solution

Problem 4 :

Find five rational numbers between -3/2 and 5/3

Solution

Problem 5 :

Find five rational numbers between 1/4 and 1/2

Solution

Problem 6 :

Find each weighted average.

a. The coordinate 2 has a weight of 1, and the coordinate 8 has a weight of 2.

b. The coordinate 3 has a weight of 1, the coordinate 5 has a weight of 3, and the coordinate 9 has a weight of 2.

Solution

Problem 7 :

Identify the segment bisector of XY. Then find the length of XY.

Solution

Problem 8 :

Identify the segment bisector of XY. Then find the length of XY.

Solution

Problem 9 :

identify the segment bisector of line segment JK. Then find length of JM.

Solution

Problem 10 :

identify the segment bisector of line segment JK. Then find length of JM.

Solution

Classify each number as RATIONAL (Q) or IRRATIONAL (I)

Problem 1 :

√47

Solution

Problem 2 :

11/9

Solution

Problem 3 :

19/4

Solution

Problem 4 :

√96

Solution

Problem 5 :

19/14

Solution

Problem 6 :

15/4

Solution

Problem 7 :

√84

Solution

Problem 8 :

-9

Solution

Problem 9 :

√72

Solution

Problem 10 :

0

Solution

Problem 11 :

8/9

Solution

Problem 12 :

Which statement is not always true?

1) The product of two irrational numbers is irrational.

2) The product of two rational numbers is rational.

3) The sum of two rational numbers is rational. 

4) The sum of a rational number and an irrational number is irrational

Solution

Problem 13 :

Determine if the product of 3√2 and 8 √18 is rational or irrational ? Explain your answer.

Solution

Problem 14 :

Which of the following numbers is irrational?

a) 0.252525…     b) 0.875       c) 0.3754152…     d) -0.121212…

Solution

Problem 15 :

The product of any two irrational numbers is:

a) always an irrational number           b) always a rational number

c) always an integer             d) sometimes rational, sometimes irrational

Solution

Problem 16 :

Between two rational numbers:

a) there is no rational number          b) there is exactly one rational number

c) there are infinitely many rational numbers

d) there are only rational numbers and no irrational numbers

Solution

Problem 17 :

If a = -2 , b = -1, then find 𝑎^−𝑏 − 𝑏^𝑎.

Solution

Problem 18 :

Find the three rational numbers between:

(i) -1 and -2

(ii) 0.1 and 0.11

Solution

Tell whether each expression is rational or irrational.

Problem 1 :

-√64

Solution

Problem 2 :

√1600

Solution

Problem 3 :

±√160

Solution

Problem 4 :

√144

Solution

Problem 5 :

√125

Solution

Problem 6 :

-√340

Solution

Problem 7 :

√1.96

Solution

Problem 8 :

-√0.09

Solution

Problem 9 :

Which statement is not always true?

1) The sum of two rational numbers is rational.

2) The product of two irrational numbers is rational.

3) The sum of a rational number and an irrational number is irrational.

4) The product of a nonzero rational number and an irrational number is irrational

Solution

Problem 10 :

(-2 - √3) (-2 + √3) when simplifies is 

a) Positive and irrational       b) Positive and rational

c) Negative and irrational      d) negative and rational

Solution

Problem 11 :

Given that following expressions.

I  -5/8 + 3/5      II. 1/2 + √2      III. √5 √5     IV. 3√49

Which expression(s) result in an irrational number?

1) II, only      2) III, only      3) I, III, IV       4) II, III, IV

Solution

Problem 12 :

A teacher wrote the following set of numbers on the board:

a = √20, b = 2.5 and c = √225

explain why a + b is irrational, but b + c is rational

Solution