Reasoning Principles

Question 1

Define Coefficient

Answer 1

A number attached in front of a variable 6x

Question 2

Define and exemplify Absolute Value

Answer 2

A Numbers distance from zero, value is always positive no matter if negative or positive
- defined by strait brackets

|-7|= 7

Question 3

show where numerator and denominator is on fraction

Answer 3

x = Numerator
Y = Denominator

Question 4

Show the parts of Long Division from Fractions and Equations

Answer 4

The long Division bracket:

Numerator goes inside it while denominator goes to the left of it

Dividend is also the first term in equation to divide, so it goes inside

Divisor goes to the left and is also the secondary terms

Question 5

Show a method of Converting Fraction to Decimal if Division is complicated

Answer 5

• Start by turning the denominator to the lowest common multiple LCM of 10 ^2
• then you just use the multiplier to get to the LCM and do the same to numerator
• then you take the amount of zeros in denominator and add decimal points to numerator. Done

Ex

5/8 LCM of 8 and 10 is 1000 by 125

625/1000 converts to .625

Question 6

Define Communitive, Associative, and Distributive Property

Answer 6

Communitive means adding and multiplying can be rearranged to get same answer

Associative means even with multiple terms add/mult can be rearranged and be same

Distributive property for multiplication means when a coefficient or term is in front of parentheses then you can multiple all those terms individually then add up sum for the answer, do only if its easier
- this can help simply equation if you do this backwards, its pretty advanced and you need to know the structure of equations well

Question 7

Define Prime and Composite Numbers

Answer 7

Prime numbers only have factors of itself and 1, most are odd except 2
Ex 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29

Composite numbers is all other non prime

Question 8

What is Greatest Common Factor GCF and Least Common Multiple LCM

Answer 8

GCF Is the greatest factor two or more numbers share, you look to the left and find the highest shared numbers

LCM is when you look to you right of a set of numbers multiples and find the first one that is in common

Question 9

How do you Add and sub Fraction

Answer 9

With LCM for the Denominator if not the same, covert denominator and then simply add or subtract converted numerators, simply after

Question 10

Multiply and Divide Fraction

Answer 10

Simply multiply across the terms of fractions to a new fraction, simply

Division you want to flip the divisor, but it doesnt really matter, then multiply across

Question 11

Simply Fractions

Answer 11

Use your head or use GCF, once you find it then divide both numerator and denominator by GCF

Question 12

Explain Exponent Rules

Answer 12

Power of itself, multiplied

If its 1, then it is the base
If its 0, then its 1

If Expo is outside parentheses, then you must raise both coefficient and base to the power, then simply for new real equation

(2x)^2 = (2^2)(x^2)=4x^2

Negative exponents also are just flipped as a fraction (Reciprocal) 1/x^2=x^-2

Question 13

Explain Exponent in Operations

Answer 13

Add/Sub - Can only operate if the variable and expo are the same, add/sub the coefficient, keep the variable/expo the same / 3x^2+x^2=4x^2

Mult - Can multiply if the base is the same, you add the expo, keep the base same, if coefficients present you multiply that / 2x^2*x^3=2x^5

Div - same as muli but opposite, subtract expo, divide coefficients ⭐️ if negative expo remember you turn to a fraction flipped

Power to power- if expo is being raised to another expo, then you multiply the expo, keep base same, coefficient is also raised to power if present

Question 14

Define Radicals

Answer 14

Radicals are signify the square root of the value under it, its like a check sign with long division bracket

Square root is the opposite of squaring something, your discovering the base that allows to multiply itself to get to the value we seek.
- whole numbered square roots are called a perfect square
-square roots are always positive

Square root of fractions, you need to find square root individually of numerator and denominator

Simplifying radicals is a thing, you must find a factor of term that’s a perfect square, then have the x multiple still a radical and the perfect square solved right next to it.

Question 15

Exemplify operations with radicals

Answer 15

Add/sub - you can add or sub terms only if the base of radicals are the same, keep base same and add/sub coefficients

Mult/div - you can do regardless of any value, just mult/div base and coefficients separately

Question 16

Define and exemplify Factorials

Answer 16

Factorials is a number with a ! Next to it. It means to multiply the factorial with every whole number next to it to zero 5! = 5x4x3x2x1 = 120

Sometimes you will see a factorial of a fraction, just list out all the factors and cancel out the common ones, then just multiply what you have left and that’s your answer