Number System and Rational Numbers: Online Quizzes and Practice Tests

Question 1

How does the commutative property of addition work with rational numbers? Give an example to show your understanding.

Accepted Answer

The commutative property means that you can change the order of the numbers you add without changing the answer. For rational numbers, this means that a + b = b + a, no matter what the values of a and b are.

Answer

The commutative property does not apply to rational numbers.

Answer

The commutative property only works for rational numbers if the denominators of the fractions are the same.

Answer

The commutative property does not work for rational numbers if the numbers are negative.

Question 2

Which property of absolute value is shown in the equation: |-2 * 3| = | -2 | * | 3 | ?

Accepted Answer

The absolute value of a product is equal to the product of the absolute values.

Answer

The absolute value of a negative number is positive.

Answer

The absolute value of a sum is equal to the sum of the absolute values.

Question 3

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

Accepted Answer

11/4

Answer

5/4

Answer

6/4

Answer

8/4

Question 4

Which of the following is equivalent to -1/2?

Accepted Answer

-0.5

Answer

0.5

Answer

1/2

Answer

-2

Question 5

Which of the following is the least common multiple (LCM) of 6 and 8?

Accepted Answer

24

Answer

12

Answer

48

Answer

36

Question 6

What is the smallest positive number that is divisible by both 12 and 18?

Accepted Answer

54

Answer

6

Answer

36

Answer

72

Question 7

Which statement about the number -0.5 is correct?

Accepted Answer

It is a rational number.

Answer

It is an irrational number.

Answer

It is a positive number.

Answer

It is a zero.

Question 8

Find the solution to the inequality x - 1/4 > 1/2.

Accepted Answer

x > 3/4

Answer

x < 3/4

Answer

x > 1/4

Answer

x < 1/4

Question 9

Solve for x: 3x - 5 = 10

Accepted Answer

5

Answer

-5

Answer

15

Answer

-15

Question 10

Order the following numbers from least to greatest: -2, 0.5, 1/2, 2/3

Accepted Answer

-2, 0.5, 1/2, 2/3

Answer

0.5, -2, 1/2, 2/3

Answer

2/3, 0.5, 1/2, -2

Answer

1/2, 2/3, -2, 0.5

Question 11

Which of these numbers is rational?

Accepted Answer

1/3

Answer

√2

Answer

π

Answer

e

Question 12

Solve the inequality: x + 5 is greater than 12

Accepted Answer

x > 7

Answer

x < 7

Answer

x > -7

Answer

x < -7

Question 13

Solve for x: 2x - 5 equals 11

Accepted Answer

x = 8

Answer

x = 3

Answer

x = 16

Answer

x = 22

Question 14

Select the number that is not a rational number:

Accepted Answer

π

Answer

0.5

Answer

-3/4

Answer

√2

Question 15

Evaluate the expression: | -5/6 |

Accepted Answer

5/6

Answer

-5/6

Answer

1/6

Answer

-1/6

Question 16

Which fraction is equivalent to 6/10?

Accepted Answer

2/5

Answer

3/5

Answer

1/2

Answer

3/4

Question 17

Find the least common multiple (LCM) of 4 and 6:

Accepted Answer

12

Answer

2

Answer

4

Answer

24

Question 18

Which of the following expressions represents a mixed number?

Accepted Answer

1 and 1/2

Answer

3/4

Answer

0.5

Answer

-2/3

Question 19

Solve the equation: x - 2/5 = 1/10

Accepted Answer

x = 3/10

Answer

x = 1/2

Answer

x = 4/10

Answer

x = 5/10

Question 20

Which of the following rational numbers is the greatest?

Accepted Answer

0.9

Answer

0.5

Answer

0.75

Answer

0.8

Question 21

Convert the fraction 5/8 to a decimal.

Accepted Answer

0.625

Answer

0.5

Answer

0.6

Answer

0.75

Question 22

Simplify the algebraic expression: 3x + 2y - x + 5y

Accepted Answer

2x + 7y

Answer

4x + 3y

Answer

2x - 3y

Answer

4x - 7y

Question 23

Which of the following inequalities is true?

Accepted Answer

3 > -2

Answer

-3 < 2

Answer

3 < -2

Answer

-3 > 2

Question 24

Compare the rational numbers -3/5 and -1/2. Which statement is true? Provide a brief explanation.

Accepted Answer

-3/5 is less than -1/2

Answer

-3/5 is greater than -1/2

Answer

-3/5 is equal to -1/2

Answer

I need help comparing rational numbers.

Question 25

Which of the following best describes the rational number -3/4?

Accepted Answer

Negative

Answer

Positive

Answer

Neither positive nor negative

Question 26

Which statement is NOT true about rational numbers?

Accepted Answer

Rational numbers are always positive.

Answer

Rational numbers can be written as a fraction.

Answer

The sum of two rational numbers is always rational.

Answer

There's always another rational number between any two.

Question 27

Simplify the expression: 2x + 3x - 5

Accepted Answer

5x - 5

Answer

5x + 5

Answer

x - 5

Answer

x + 5

Question 28

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

Accepted Answer

24

Answer

12

Answer

18

Answer

30

Question 29

Identify the rational number from the following options:

Accepted Answer

0.12345...

Answer

√2

Answer

π

Answer

e

Question 30

Find the least common multiple (LCM) of 6 and 12.

Accepted Answer

12

Answer

2

Answer

3

Answer

6

Question 31

Solve for x in the equation: x + 5 = -3

Accepted Answer

x = -2

Answer

x = -8

Answer

x = 2

Answer

x = 8

Question 32

Which of the following is considered a rational number?

Accepted Answer

3/4

Answer

π

Answer

√2

Answer

e

Question 33

Compare the rational numbers -1/2 and -3/4. Choose the correct inequality.

Accepted Answer

-1/2 < -3/4

Answer

-1/2 > -3/4

Answer

-1/2 = -3/4

Answer

Cannot be determined

Question 34

Express the repeating decimal 0.666... as a fraction.

Accepted Answer

2/3

Answer

3/5

Answer

1/2

Answer

4/9

Question 35

What are equivalent fractions? Provide three examples to demonstrate the concept.

Accepted Answer

Equivalent fractions are fractions that have the same value, even though their numerators and denominators may be different.

Answer

Equivalent fractions must have the same numerator and denominator.

Answer

Equivalent fractions are fractions that can be simplified to the same lowest terms.

Question 36

Which of the following best describes the least common multiple (LCM) of two numbers?

Accepted Answer

The smallest number that is divisible by both numbers evenly.

Answer

The greatest common factor (GCF) of the two numbers.

Answer

The sum of the two numbers divided by two.

Answer

The product of the two numbers.

Question 37

You are doubling a recipe that calls for 2/3 cup of flour and 1/4 cup of sugar. How much flour and sugar will you need?

Accepted Answer

1 1/3 cups of flour, 1/2 cup of sugar

Answer

2/6 cups of flour, 1/8 cups of sugar

Answer

1 cup of flour, 1/4 cup of sugar

Answer

4/3 cups of flour, 2/4 cups of sugar

Question 38

Which of the following rational numbers is the greatest?

Accepted Answer

3/4

Answer

-1/2

Answer

-3/4

Answer

1/4

Question 39

Which of the following is a type of rational number?

Accepted Answer

Decimal

Answer

Natural number

Answer

Irrational number

Answer

Complex number

Question 40

Which of the following is the correct order of rational numbers from least to greatest: -3, -1/2, 0, 1/4, and 2?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 41

Which of the following is equivalent to the fraction 1/3?

Accepted Answer

0.33

Answer

0.25

Answer

0.5

Question 42

Identify the rational number among the following options: √2, π, 0.125

Accepted Answer

0.125

Answer

π

Answer

√2

Question 43

Write the correct inequality to represent the statement: The number x is greater than or equal to -3.

Accepted Answer

x ≥ -3

Answer

x > -3

Answer

x ≤ -3

Question 44

Find the absolute value of the rational number -2/3.

Accepted Answer

2/3

Answer

-1/3

Answer

-2/3

Answer

1/3

Question 45

Which of the following is a rational number?

Accepted Answer

-3/7

Answer

e

Answer

π

Answer

√2

Question 46

Order the following rational numbers from least to greatest: 1/2, -1/4, 0, 3/8

Accepted Answer

-1/4, 0, 1/2, 3/8

Answer

3/8, 1/2, 0, -1/4

Answer

1/2, 3/8, 0, -1/4

Answer

-1/4, 0, 3/8, 1/2

Question 47

Find the greatest common factor (GCF) of 12 and 18.

Accepted Answer

6

Answer

12

Answer

9

Answer

3

Question 48

Solve the inequality: x - 2 > 5

Accepted Answer

x > 7

Answer

x < 7

Answer

x < -7

Answer

x > -7

Question 49

Which of the following is a real-world application of rational numbers?

Accepted Answer

Calculating the average speed of a car

Answer

Measuring the area of a circle

Answer

Finding the circumference of a sphere

Answer

Determining the volume of a cube

Question 50

Simplify the algebraic expression: 2(x + 3) - 5

Accepted Answer

2x + 1

Answer

x + 1

Answer

x - 1

Answer

2x - 1

Question 51

Determine the least common multiple (LCM) of 4 and 6.

Accepted Answer

12

Answer

9

Answer

3

Answer

2

Question 52

Which of the following numbers is a rational number?

Accepted Answer

0.25

Answer

e

Answer

√2

Answer

π

Question 53

Identify the smallest negative number among the following:

Accepted Answer

-10

Answer

-2

Answer

-5

Answer

-1

Question 54

Find the opposite of the rational number 3/4.

Accepted Answer

-3/4

Answer

1/4

Answer

2/4

Question 55

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

Accepted Answer

They do not form a group under multiplication.

Answer

They have a unique additive identity.

Answer

They are closed under addition.

Answer

They are ordered.

Question 56

Select the decimal representation equivalent to -3/4?

Accepted Answer

-0.75

Answer

-3.4

Answer

0.34

Question 57

Find the greatest common factor (GCF) of 12 and 18?

Accepted Answer

6

Answer

3

Answer

2

Answer

12

Question 58

Determine the least common multiple (LCM) of 6 and 8?

Accepted Answer

24

Answer

32

Answer

12

Answer

16

Question 59

Simplify the expression 2/3 x 3/4:

Accepted Answer

1/2

Answer

1/3

Answer

6/7

Answer

3/4

Question 60

Simplify the expression 3/4 ÷ 1/2:

Accepted Answer

3/2

Answer

1/2

Answer

4/3

Answer

2/3

Question 61

Which of the following is equivalent to -3/4?

Accepted Answer

-0.75

Answer

-1.25

Answer

0.75

Answer

-1/4

Question 62

Identify the mixed number from the following?

Accepted Answer

2 1/3

Answer

0.5

Answer

-2

Answer

-3/4

Question 63

Which of the following is a repeating decimal?

Accepted Answer

0.333...

Answer

0.7

Answer

-0.5

Answer

0.25

Question 64

Which of the following numbers is NOT considered a rational number due to the presence of an imaginary unit?

Accepted Answer

√-9

Answer

0.125

Answer

5/6

Answer

¼