Properties of Real Numbers

Real Numbers Review

by Aqil Mohammed

Identifying Rational and Irrational Numbers

Multiple Choice

Is the number rational or irrational?

• Rational - 
• Irrational

Multiple Choice

Is the number rational or irrational?

• Rational
• Irrational

Multiple Choice

Is the number rational or irrational?

• Rational
• Irrational

Multiple Choice

Is the number rational or irrational?

• Rational
• Irrational

Multiple Choice

Select the ONLY number that is RATIONAL 

• π
• π/4
• √2
• √49

Multiple Choice

Select the ONLY number that is IRRATIONAL

• π / π
• 0.1234567...
• 3√4
• -0.74747474...

Converting fractions to decimals

Multiple Choice

Read ⁷/₁₀ aloud. What decimal is read the same way and is equivalent?

• 0.7

• 0.07

• 0.007

• 7

Multiple Choice

What is 3/4 as a decimal?

• 0.34

• 0.75

• 1.25

• 1.33

Multiple Choice

What is 7/8 as a decimal?

• 0.875

• 0.78

• 0.125

• 0.111111111111111111111111111111

Multiple Choice

Convert $$\frac{3}{5}$$  to a decimal

• 0.6

• 0.3

• 0.35

• 0.06

​Converting improper fractions to mixed numbers

Multiple Choice

Write the improper fraction as a mixed number.

⁵/₄ =

• 1¹/₃

• 1¹/₄

• 3¹/₃

• 3¹/₄

Multiple Choice

Write the improper fraction as a mixed number.

¹⁰/₃

• 3¹/₃

• 2³/₂

• ³/₁₀

• 3²/₃

Multiple Choice

Write the improper fraction as a mixed number.

21/5

• 5 1/5

• 4 2/5

• 4 1/5

• 5 4/5

Converting mixed numbers to improper fractions​

Multiple Choice

Convert this mixed number to an improper fraction.

• $$\frac{24}{5}$$

• $$\frac{10}{5}$$
  

• $$\frac{30}{5}$$
  

• $$\frac{34}{5}$$

Multiple Choice

Convert this mixed number to an improper fraction.

• $$\frac{1}{15}$$

• $$\frac{15}{15}$$
  

• $$\frac{16}{15}$$
  

• $$\frac{2}{15}$$

Multiple Choice

$$Write\ \ 6\frac{1}{3}\ as\ an\ improper\ fraction.$$  

• $$\frac{3}{13}$$  

• $$\frac{18}{3}$$  
  

• $$\frac{19}{3}$$  
  

• $$\frac{12}{3}$$  

Converting decimals to fractions​

Multiple Choice

What is the equivalent fraction?

• 1/2

• 0/2

• 2/100

• 1/5

Multiple Choice

What is the equivalent fraction?

• 3/2

• 3/20

• 5/33

• 1/5

Multiple Choice

What is the equivalent fraction?

• 62/10

• 31/5

• 31/50

• $$\frac{12}{3}$$  

Multiple Choice

What is the equivalent fraction?

• 13/10

• 1/3

• 1_3/10

• 3/10

Converting repeating decimals to fractions​

Multiple Choice

• 1/2
• 1/10
• 1/100
• 1/9

Multiple Choice

• 3/10
• 1/3
• 1/9
• 30/99

Multiple Choice

• 7/50
• 14/9
• 7/45
• 14/99

​Powers and Exponents

Evaluate Numerical and Algebraic Expressions​

Multiple Select

What number represents the base?

• 3

• 5

• 15

• 125

Multiple Choice

What number is the exponent?

• 3

• 5

• 15

• 125

Multiple Choice

What is the value of the power?

• 3

• 5

• 15

• 125

Multiple Choice

What is the numerical expression as a power?

$$9\cdot9\cdot9\cdot9$$  

• $$9^4$$  

• $$4^9$$  

• $$94$$  

• $$49$$  

Multiple Choice

Identify the correct expanded form and value for the power.

$$\left(-1\right)^5$$  

• $$\left(-1\right)\left(-1\right)\left(-1\right)\left(-1\right)\left(-1\right)\ =\ 1$$  

• $$\left(-1\right)\left(-1\right)\left(-1\right)\left(-1\right)\left(-1\right)=-1$$  

• $$\left(5\right)\left(-1\right)\ =-5$$  

• $$\left(-1\right)\left(5\right)=-5$$  

Multiple Choice

Identify the statement with the correct symbol.  

• $$\left(-2\right)^2<-2^2$$  

• $$\left(-2\right)^2>-2^2$$  

• $$\left(-2\right)^2=-2^2$$  

Multiple Choice

Identify the statement with the correct symbol.

• $$3^2<\left(-3\right)^2$$

• $$3^2>\left(-3\right)^2$$

• $$3^2=\left(-3\right)^2$$

Multiple Choice

Identify the statement with the correct symbol.

• $$5^2<2^5$$

• $$5^2>2^5$$

• $$5^2=2^5$$

Multiple Choice

The volume of a cube can be calculated using the formula v = lwh. Write the volume of the cube as a power.

• $$5^3$$

• $$3^5$$

• $$5^2$$

• $$125$$

Multiple Choice

What is the correct way to express  $$x\cdot x\cdot x$$  ?

• 3x

• $$x^3$$  

• 3

• x + 3

Multiple Choice

What is the correct way to express  $$y\cdot y\cdot y\cdot y\cdot y$$  ?

• 5y

• $$y^5$$  

• 5

• y + 5

​Multiply and Divide Monomials

Multiple Choice

n²⋅n⁴⋅n⁵

• n¹¹
• n⁴⁰
• n¹³
• n²²

Multiple Choice

Evaluate the expression using the quotient rule.

• x¹³
• x⁵
• x³⁶
• x^-5

Multiple Choice

• 10x⁹
• 24x¹⁴
• 24x⁹
• 10x¹⁴

Multiple Choice

Simplify:

• x⁶
• x⁵
• x¹⁴
• x²

Multiple Choice

2n⁴ * 5n⁴

• 7n⁴
• 10n¹⁶
• 10n⁸
• none of the above

Multiple Choice

Simplify the expression.

• 1/y⁵
• 1/y²
• y²
• y⁵

Multiple Choice

• 8x⁴
• 8x⁸
• 6x⁴
• 6x⁸

Multiple Choice

• 2a²b⁶
• 1/(2a²b⁶)
• b⁶/2a²
• 2b⁶/a²

Powers of Monomials

Multiple Choice

$$\left(x^4\right)^2$$  

• $$x^8$$  

• $$x^6$$  

Multiple Choice

$$\left(y^3\right)^4$$  

• $$y^7$$  

• $$y^{12}$$  

Multiple Choice

$$\left(-2x^2\right)^3$$  

• $$-2x^5$$  

• $$-6x^6$$  

• $$-8x^5$$  

• $$-8x^6$$  

Multiple Choice

$$\left(-5y^4\right)^2$$  

• $$25y^6$$  

• $$-25y^8$$  

• $$25y^8$$  

• $$-5y^8$$  

Multiple Choice

$$\left(a^3\right)^2\left(b^4\right)^3$$  

• $$a^5b^7$$  

• $$a^6b^{12}$$