Number System and Rational Numbers: Practice Quizzes and Learning Resources

Question 1

Find the absolute value of -2.5.

Accepted Answer

2.5

Answer

-2.5

Question 2

Given the inequalities 2x > 5 and 5 > 3, can we use the transitive property to directly compare 2x and 3?

Accepted Answer

Yes, 2x > 3.

Answer

Yes, but only if x is positive.

Answer

No, the transitive property cannot be applied here.

Answer

No, because 2x includes a variable while 3 is a constant.

Question 3

Simplify the fraction 24/36 by finding the greatest common factor.

Accepted Answer

2/3

Answer

4/6

Answer

6/9

Answer

8/12

Question 4

What is the process of rationalizing the denominator?

Provide an example to demonstrate your explanation.

Accepted Answer

Rationalizing the denominator means converting a fraction with a radical in the denominator into an equivalent fraction with a rational denominator.

Answer

Rationalizing the denominator involves making the denominator a whole number.

Answer

Rationalizing the denominator is a technique for finding the common denominator of two fractions.

Answer

Rationalizing the denominator is not a valid mathematical operation.

Question 5

Which fraction is equivalent to 2/5 and has a denominator of 20?

Accepted Answer

8/20

Answer

4/10

Answer

12/30

Answer

16/40

Question 6

What are rational exponents? Provide an example to illustrate your explanation.

Accepted Answer

Rational exponents are exponents that can be expressed as fractions, allowing us to represent roots and fractional powers of numbers.

Answer

Rational exponents can only be applied to positive numbers.

Answer

Rational exponents have no connection to the properties of exponents.

Answer

Rational exponents are exponents that are always irrational numbers.

Question 7

Find the product of the rational numbers negative two-thirds and one-fifth.

Accepted Answer

-2/15

Answer

2/15

Answer

-1/15

Question 8

Order the following rational numbers from least to greatest. Explain your reasoning: -2/3, 0, 1/4, -0.5, 0.6

Accepted Answer

-2/3, -0.5, 0, 1/4, 0.6

Answer

-0.5, -2/3, 0, 1/4, 0.6

Answer

1/4, -2/3, -0.5, 0, 0.6

Answer

0.6, -0.5, 1/4, -2/3, 0

Question 9

Given rational numbers a/b and c/d, demonstrate that their sum, a/b + c/d, is also a rational number.

Accepted Answer

The sum of any two rational numbers is always a rational number.

Answer

The sum of any two rational numbers is always an integer.

Answer

The sum of any two rational numbers is always a decimal.

Answer

The sum of any two rational numbers is always 0.

Question 10

What feature differentiates a terminating decimal from a non-terminating decimal?

Accepted Answer

Limited digits after the decimal point

Answer

Recurring digits

Answer

Value exceeding 1

Answer

Fraction in the denominator

Question 11

Simplify the expression: 3/4 + 2/3

Accepted Answer

7/12

Answer

5/7

Answer

5/12

Answer

11/12

Question 12

Solve the equation: x - 1/2 = 3/4

Accepted Answer

x = 5/4

Answer

x = 1/2

Answer

x = 1

Answer

x = 3/4

Question 13

Which of the following is true about the inequality x < 0?

Accepted Answer

The solution set is all negative numbers.

Answer

The solution set is all positive numbers.

Answer

The solution set is all numbers.

Answer

The solution set is the empty set.

Question 14

Order these rational numbers from least to greatest: -1/2, 0.5, -0.25, 3/4

Accepted Answer

-0.25, -1/2, 0.5, 3/4

Answer

3/4, 0.5, -1/2, -0.25

Answer

-1/2, -0.25, 3/4, 0.5

Answer

0.5, 3/4, -1/2, -0.25

Question 15

Explain why 0 is classified as a rational number.

Accepted Answer

0 is a rational number because it can be expressed as a fraction of two integers, specifically 0/1.

Answer

0 is an irrational number because its decimal representation is non-terminating and non-repeating.

Question 16

A rectangular garden has an area of 3/4 of a square meter. If the width of the garden is 1/2 of a meter, what is the length of the garden in meters?

Accepted Answer

1 1/4

Answer

1/4

Answer

1 1/2

Question 17

Which of the following is NOT a major historical advancement in the development of rational numbers?

Accepted Answer

René Descartes' coordinate geometry

Answer

Cuneiform tablets from ancient Babylonia

Answer

Euclid's Elements

Question 18

What is the least common multiple of 12 and 18?

Accepted Answer

36

Answer

6

Answer

12

Answer

18

Question 19

What does it mean to rationalize the denominator of a radical expression? Provide an example to illustrate your explanation.

Accepted Answer

Making the denominator a rational number by multiplying and dividing by an appropriate radical expression.

Answer

Removing the radical from the denominator.

Answer

Simplifying the expression by combining like terms.

Answer

Making the numerator a rational number.

Question 20

Let's explore two rational numbers, a/b and c/d. Explain why their sum, a/b + c/d, is also a rational number.

Accepted Answer

The sum of two rational numbers is always a rational number.

Answer

The sum of two rational numbers is always an irrational number.

Question 21

Order the following rational numbers from least to greatest: -1/2, 0, 1/3, 3/4

Accepted Answer

-1/2, 0, 1/3, 3/4

Answer

0, -1/2, 1/3, 3/4

Answer

1/3, -1/2, 0, 3/4

Answer

3/4, 1/3, 0, -1/2

Question 22

Find the greatest common factor (GCF) of 24 and 36.

Accepted Answer

6

Answer

2

Answer

3

Answer

12

Question 23

Which of the following is equivalent to the fraction 5/8?

Accepted Answer

0.625

Answer

0.5

Answer

0.75

Answer

0.875

Question 24

Solve the inequality: 2x + 3 > 7

Accepted Answer

x > 2

Answer

x > 3

Answer

x < 2

Answer

x < 3

Question 25

Ordering Rational Numbers:

Which of the following is the correct order of these rational numbers from least to greatest?

-2/3, 0.5, -0.25, 3/4

Accepted Answer

-0.25, -2/3, 3/4, 0.5

Answer

-2/3, -0.25, 0.5, 3/4

Answer

0.5, -0.25, -2/3, 3/4

Answer

3/4, -2/3, -0.25, 0.5

Question 26

Which of the following rational numbers is the greatest?

Accepted Answer

1/2

Answer

-3/5

Answer

0

Answer

-0.6

Question 27

Convert the decimal 0.75 to a fraction.

Accepted Answer

3/4

Answer

1/4

Answer

3/8

Answer

1/8

Question 28

Find the least common multiple (LCM) of 6 and 8.

Accepted Answer

24

Answer

12

Answer

48

Answer

96

Question 29

Which of the following is **not** a property of real numbers?

Accepted Answer

They are not closed under division

Answer

They are closed under addition

Answer

They are dense

Answer

They are ordered

Question 30

Solve for **x**: x + 3/4 = 5/6

Accepted Answer

7/12

Answer

3/4

Answer

1/4

Answer

1/2

Question 31

Which of the following is the **greatest** number?

Accepted Answer

0.75

Answer

3/5

Answer

0.65

Answer

2/3

Question 32

Which of the following is the **least common multiple** of 6 and 8?

Accepted Answer

24

Answer

16

Answer

32

Answer

12

Question 33

Which of the following is a **rational number**?

Accepted Answer

-3/4

Answer

√2

Answer

e

Answer

π

Question 34

Which of the following is an **irrational number**?

Accepted Answer

√5

Answer

-7

Answer

0.25

Answer

1/2

Question 35

Which of the following is a **mixed number**?

Accepted Answer

2 1/2

Answer

0.75

Answer

-3/4

Answer

√10

Question 36

Which of the following is a **decimal number**?

Accepted Answer

0.625

Answer

1/4

Answer

2 1/2

Answer

√3

Question 37

Which of the following is not a rational number?

Accepted Answer

√2

Answer

-3

Answer

-0.5

Answer

2/5

Question 38

Which of the following is equivalent to -0.75?

Accepted Answer

-3/4

Answer

3/4

Answer

4/3

Answer

7/4

Question 39

Solve for x: 2x - 5 = 11

Accepted Answer

8

Answer

3

Answer

-3

Answer

5.5

Question 40

**Which rational number lies between -1 and 0?**

Accepted Answer

-1/2

Answer

1

Answer

0

Answer

-2

Question 41

**Solve the inequality 3x - 4 < 10.**

Accepted Answer

x < 5

Answer

x > 5

Answer

x > 4

Answer

x < 4

Question 42

Which of the following is NOT a rational number?

Accepted Answer

√2

Answer

3/4

Answer

0.125

Answer

-5/7

Question 43

Find the product of 1/2 and -4/5

Accepted Answer

-2/5

Answer

4/5

Answer

-4/5

Answer

2/5

Question 44

Which property of rational numbers allows us to represent them as fractions?

Accepted Answer

They can be expressed as the quotient of two integers.

Answer

They cannot be ordered.

Answer

Their decimal expansions are always finite.

Answer

They are always positive.

Question 45

Which of the following numbers is NOT a rational number?

Accepted Answer

√2

Answer

0.75

Answer

1.5

Answer

-3/4

Question 46

Convert the fraction 3/8 to its decimal equivalent.

Accepted Answer

0.375

Answer

0.625

Answer

0.333...

Answer

0.4

Question 47

Which of the following numbers is the largest?

Accepted Answer

2.5

Answer

-2.5

Answer

1.5

Answer

0.5

Question 48

Find the sum of -3/4 and 1/2.

Accepted Answer

-1/4

Answer

1/4

Answer

-1/2

Answer

1/2

Question 49

What is the product of -2/3 and 9/4?

Accepted Answer

-3/2

Answer

3/2

Answer

-6/7

Answer

6/7

Question 50

Solve the equation 2x + 3 = 7.

Accepted Answer

2

Answer

3

Answer

4

Answer

1

Question 51

Solve the inequality: 3x - 5 > 1

Accepted Answer

x > 2

Answer

x ≥ 2

Answer

x ≤ 2

Answer

x < 2

Question 52

A recipe calls for 1/2 cup of flour. You want to make 3/4 of the recipe. How much flour do you need?

Accepted Answer

3/8 cup

Answer

1/2 cup

Answer

3/4 cup

Answer

1/4 cup

Question 53

Find the absolute value of -5/2.

Accepted Answer

5/2

Answer

-5/2

Answer

-2/5

Answer

2/5

Question 54

Which of the following represents the set of all integers?

Accepted Answer

... , -3, -2, -1, 0, 1, 2, 3, ...

Answer

-1, 0, 1, 2, ...

Answer

1, 2, 3, ...

Answer

0, 1, 2, 3, ...

Question 55

Which of the following is NOT a rational number?

Accepted Answer

√2

Answer

-3/4

Answer

π

Answer

0.5

Question 56

Simplify the expression: -2/7 - 1/3

Accepted Answer

-19/21

Answer

-11/21

Answer

-3/7

Question 57

Which of the following is equivalent to 3/4?

Accepted Answer

0.75

Answer

0.25

Answer

1.25

Answer

0.5

Question 58

Find the least common multiple of 6 and 12.

Accepted Answer

12

Answer

6

Answer

24

Answer

2

Question 59

Solve the equation: x + 2/3 = 1/2

Accepted Answer

1/6

Answer

-1/3

Answer

1/3

Answer

-1/6

Question 60

Which of the following is true about the inequality 2x - 5 > 1?

Accepted Answer

x > 3

Answer

x < 3

Answer

x < -3

Answer

x > -3

Question 61

Which of the following is NOT a property of rational numbers?

Accepted Answer

Closure under multiplication

Answer

Closure under addition

Answer

Commutative property of addition

Answer

Closure under subtraction

Question 62

Convert the mixed number 2 3/4 to an improper fraction.

Accepted Answer

11/4

Answer

5/4

Answer

7/4

Answer

3/4

Question 63

Which of the following is the greatest common factor of 12 and 18?

Accepted Answer

6

Answer

3

Answer

2

Answer

9

Question 64

Solve the inequality: -3(x - 1) ≤ 9

Accepted Answer

x ≤ -2

Answer

x ≥ -2

Answer

x ≤ 2

Answer

x ≥ 2