Selcat

Selcat 2/21

Jessi Horn

Order of Operations

PEMDAS

• Please (Parentesis)

• Excuse (Exponents)

• My (Multiply)

• Dear (Divide)

• Aunt (Add)

• Sally (Subtract)

• MD & AS from left to right!

Open Ended

7 + (6 × 5² + 3)

Open Ended

12 / 6 × 3 / 2

Open Ended

3 + 6 ÷ 3 × 2

Open Ended

5 × 3 - 12 ÷ 4 + 8

Open Ended

30 - (5 × 2³ - 15)

Open Ended

(3 + 2)² - 5 × 3 + 2³

Open Ended

(15 ÷ 3 + 4) - (3² - 7 × 2)

Open Ended

(4² - 6 + 5) / (3² + 8 - 7 × 2)

Open Ended

(7 - √9) × (4² - 3 + 1)

Open Ended

 $\frac{2^4+\left(16-3\cdot4\right)}{\left(6+3^2\right)\div\left(7-4\right)}$  

Reciprocal

• To get the reciprocal of a number, we divide 1 by the number.

• The reciprocal is also called the "Multiplicative Inverse"

• Example: the reciprocal of 2 is ½ (a half)

• The reciprocal of 4 is ¹/₄

• The reciprocal of ¹/₄ is 4 (back to 4 again)

• Example: the reciprocal of ³/₄ is ⁴/₃

• Every number has a reciprocal except 0

Multiplying a Number by Its Reciprocal

• 2 × (¹/₂) =

• 10 × (¹/₁₀) =

• 
  

• 
  

• 
  

• 
  

Open Ended

What is the reciprocal of 1/7 ?

Open Ended

Which is the reciprocal of 2/3?

Open Ended

What is the reciprocal of 50 ?

Conversions

• You should always use metric units in your work

The metric system

• T (tera-trillion) 1,000,000,000,000

• G (giga-billion) 1,000,000,000

• M (mega-million) 1,000,000

• k (kilo-thousand) 1,000

• h (hecto-hundred) 100

• da (deka-ten) 10

• unit1  

The metric system continued

• unit 1

• d (deci-tenth) 0.1

• c (centi-hundredth) 0.01

• m (milli-thousandth) 0.001 µ

• (micro-millionth) 0.000 001

• n (nano-billionth) 0.000 000 001

• p (pico-trillionth) 0.000 000 000 001

Open Ended

The prefix 'kilo' means

Open Ended

The prefix 'milli' means

Open Ended

The prefix 'deci' means

Open Ended

The prefix 'centi' means

Imperial to Metric

• 1 inch [in] = 2.54 cm

• 1 foot [ft] = 12 in = 0.3048 m

• 1 yard [yd] = 3 ft = 0.9144 m

• 1 mile = 1760 yd = 1.6093 km

• If you know 1in = 2.54cm, you can find the rest

Open Ended

What is 5,000 yards in kilometers?

Open Ended

What is 40 ft in meters?

Open Ended

36.52 mg = ________ g

Open Ended

15m = _________dm

Open Ended

27.32mm= _________ m

Open Ended

_____________mph = 14.5 kmph

Open Ended

2ft = _____ m

Exponents

• The exponent of a number says how many times to use the number in a multiplication.

• 8² could be called "8 to the power 2" or "8 to the second power", or simply "8 squared"

• In 8² the "2" says to use 8 twice in a multiplication,

  so 8² = 8 × 8 = 64

• 2^4 is the same as 2⁴

Open Ended

What is the value of 6³ ?

Open Ended

What is the value of 3⁴ ?

Open Ended

What is the value of (-3)⁵?

Open Ended

What is the value of 5² + 6² ?

Laws of exponets

Laws Explained

Open Ended

5^-3

Open Ended

What is the value of 2^-4?

Open Ended

What is the value of 5^-2?

Open Ended

What is the value of (-2)^-5?

Open Ended

What is the value of (-10)⁰?

Open Ended

x⁴x³

Open Ended

What is the value of 2² - 2^-2 ?

The law that x^m/xⁿ = x^m-n 

•  how many times do we end up multiplying "x"? Answer: "m" times, then reduce that by "n" times (because we are dividing), for a total of "m-n" times.

• Example: x⁴/x² = (xxxx) / (xx) = xx = x²

• So, x⁴/x² = x^(4-2) = x²

Open Ended

 $\frac{x^5}{x^6}$  

Open Ended

 $\frac{x^6}{x^5}$   

The law that (x^m)ⁿ = x^mn

• So (x³)⁴ = x^3×4 = x¹²

Open Ended

Which of the following is equivalent to (x^½)⁶

The law that (x/y)ⁿ = xⁿ/yⁿ

• Example: (x/y)³ =x³/y³

Open Ended

x⁰ × (x²)³ ÷ (x² × x^½)

Open Ended

 $\frac{\left(3ab\right)^2}{2b^{-2}}\cdot\frac{4b^{-1}a^4}{b^2}$  

Open Ended

 $\sqrt{169}$  

Open Ended

 $\sqrt{225}$  

Open Ended

 $\sqrt{200}$  

Evaluating Expressions (or Formulas)

• To evaluate an 3xpression is to:

  Replace (substitute) its variable with a given number or expression.

  
  

• evaluate   2x+4 for x=5

• Just replace the variable "x" with "5":

  2×5 + 4 = 14

  
  

Open Ended

-7a+b² use a=-6 and b=1

Open Ended

 $y-\left(\frac{x}{2}\right)^2\ \ use\ x=-10\ and\ y=5$  

Open Ended

If x = 5 + √3, what is the value of x² − 10x + 25?

Solving equations

• There is no "one perfect way" to solve all equations.

• our goal is to end up with x = something

• we want to move everything except "x" (or whatever name the variable has) over so that it is alone on one side of the equal sign.

Example: Solve 3x−6 = 9

• Start with: 3x−6 = 9

• Add 6 to both sides: 3x = 9+6

• Divide by 3: x = (9+6)/3

• Now we have x = something,

  and a short calculation reveals that x = 5

Open Ended

 $\sqrt{\frac{x}{2}}=3$  

Open Ended

5x + 2 = -8

Open Ended

3y - 7 = 26

Open Ended

 $\frac{1}{4}x-3=4$  

Open Ended

 $\frac{2}{3}x+5=-7$  

Open Ended

 $\sqrt{2x+9}-5=0$  

Open Ended

 $x^2-9=0$  

Open Ended

 $\left(x-3\right)^2=16$  

Open Ended

x²-7=9