Rational Numbers, Exponents, and Polynomials

Equivalent Rational Numbers

Are 0.5 and 1/2 equivalent? Yes, they are equivalent because 0.5 = 1/2.

Fraction to Decimal Conversion

Write the fraction 3/4 as a decimal. 3/4 = 0.75.

Negative Exponents

Simplify: 2^(-3) = 1/(2^3) = 1/8.

Negative Exponents Simplification

Simplify: (5/3)^(-2) = 1/(5/3)^2 = 1/(25/9) = 9/25.

Scientific Notation

Write 450,000 in scientific notation. 450,000 = 4.5 × 10^5.

Standard Form Conversion

Convert 5.6 × 10^3 to standard form. 5.6 × 10^3 = 5600.

Multiplication in Scientific Notation

Multiply: (2 × 10^4) × (3 × 10^2) = 6 × 10^6.

Division in Scientific Notation

Divide: (6 × 10^5) / (2 × 10^3) = 3 × 10^2 = 300.

Prime Factorization of 60

Find the prime factorization of 60. 60 = 2^2 × 3 × 5.

Prime Factorization of 84

Find the prime factorization of 84. 84 = 2^2 × 3 × 7.

Greatest Common Factor (GCF)

Find the GCF of 24 and 36. GCF = 2^2 × 3 = 12.

GCF of 18 and 45

Find the GCF of 18 and 45. GCF = 3^2 = 9.

Least Common Multiple (LCM)

Find the LCM of 4 and 6. LCM = 2^2 × 3 = 12.

LCM of 8 and 12

Find the LCM of 8 and 12. LCM = 2^3 × 3 = 24.

Add and Subtract Fractions

3/4 + 1/2 = 5/4 = 1 1/4.

Subtract Mixed Numbers

2 1/3 - 1 2/3 = 2/3.

Multiply Fractions

3/5 × 4/7 = 12/35.

Divide Mixed Numbers

2 1/4 ÷ 3/8 = 9/4.

Order of Operations

Simplify: 3 + 4 × (6 - 2) = 19.

Square Root of 81

Find the square root of 81. √81 = 9.

Perfect Square Check

Is 64 a perfect square? Yes, √64 = 8.

Rational vs. Irrational

Is 7 rational or irrational? 7 is irrational.

Properties of Real Numbers

Is the set of real numbers closed under addition? Yes, because adding two real numbers always results in a real number.

Commutative Property Example

Example: 3 × 5 = 5 × 3.

Commutative Property

3×5=5×3

Equation for the sum of x and 7 equals 12

x+7=12

Simplified expression of 3x+5−2x

x+5

Solution for x+7=15

x=15−7=8

Solution for x−5=10

x=10+5=15

Solution for 2x+5=15

x=5

Solution for x−4=12

x=12+4=16

Solution for 2(3x+5)=26

x=8

Solution for 3(x+4)−5=22

x=5

Solution for 2x+3=5x−6

x=3

Solution for 4x−3=2x+7

x=5

Solution for x²+3=7

x=8

Solution for 3x/4=9

x=12

Solution for 0.5x+2.5=7

x=9

Solution for 1.2x=6.6

x=5.5

Convert 0.3̅ to a fraction

0.3̅=1/3

Convert 0.6̅ to a fraction

0.6̅=2/3

Graph x>3 on a number line

Draw an open circle at 3 and shade to the right.

Graph x≤−2 on a number line

Draw a closed circle at -2 and shade to the left.

Solution for x+4≥10

x≥6

Solution for x−3<5

x<8

Solution for 3x≥12

x≥4

Solution for x/5≤2

x≤10

Degree of 3x⁴+2x³+5x

Degree = 4

Degree of x²+4x+7

Degree = 2

Total cost for 5 items at $3 each and a fixed fee of $10

Total cost = 5×3+10=25

Area of a rectangle with length 2x+5 and width x+3

Area = (2x+5)(x+3)=2x²+11x+15

Add (3x²+4x)+(5x²−2x)

8x²+2x

Subtract (6x²+5x)−(3x²+4x)

3x²+x

Multiply (2x+3)×(x−4)

2x²−5x−12

Find the GCF of 6x² and 9x

GCF = 3x

Factor 6x²+9x

3x(2x+3)