Question

This may be useful for some users. Might be worth taking a look at this if you have similar questions. Thanks to @mathslover for taking the time to get the LaTeX for me! This is what the topics cover:
1.)Order or Operations and Whole Numbers
2.) Problem Solving
3.)Simplifying Fractions-GCF and Factors Method
4.) Multiplying Fractions
5.) Dividing Fractions
I just had to make some changes and again thanks to @mathslover for helping me with the LaTeX!!!

Answer 1

\(\color{brown}{\textbf{Order of Operations}}\)
1.) P – Parentheses- Evaluate what is inside
2.) E- Exponents- Evaluate any exponents
3.) MD- Multiply and Divide- Perform multiplication and division from left to right
4.) AS- Add and Subtract- Perform addition and subtraction from left to right

Examples:
\(~~4+[6 \times 3]~~~~~~~~~~~~ \color{blue}{ 3(4-2)^2 +5} ~~~~~~~~~~~~ \color{red}{3 \times {(18+4)}^2 – 4 \times {(5-3)}^2 } \)
\(~~4 + 18 ~~~~~~~~~~~~~~~~~~~ \color{blue}{ 3{(2)}^2 +5 } ~~~~~~~~~~ ~~~~~~~~ \color{red}{ 3 \times {(22)}^2 – 4 \times {(2)}^2} \)
\(~~22~~~~~~~~~~~~~~~~~~~~~~~~~ \color{blue}{3(4) +5} ~~~~~~~~~~~~~~~~~~~~~ \color{red}{ 3 \times (484) – 4 \times (4) }\)
\(~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \color{blue}{12 + 5} ~~~~~~~~~~~~~~~~~~~~~~~ \color{red}{1452-16} \)
\(~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \color{blue}{17}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \color{red}{1436} \)


\(\color{brown}{\textbf{Problem Solving}}\)
\(\text{1.) Understand the problem}\\
\text{2.) Create a plan}\\
\text{3.) Find the answer}\\
\text{4.) Check the answer} \)

\(\color{brown}{\textbf{Keywords:}}\)
Addition: Sum, increase by, plus, added to, total, more than
Subtraction: Difference, decreased by, how many more, minus, take away, less than,
Multiplication: product, times, twice(multiply by 2), of triple(multiply by 3)
Division: quotient, per, divided by, divided into

\(\color{brown}{\textbf{Examples:}}\)
Twice(multiply) the sum of \(7 \)and \(4\) = \(2(7+4) = 2(11) = 22\)
The difference of \(9 \) and \(3\) divided by \(3\) = \(9-3/3 = 6/3 = 2\)
Three times the product of \(2\) and \(4\) = \(3(2\times4) = 3(8) = 24\)

\(\color{brown}{\textbf{Area of a Rectangle:}}\)
The area of a figure is the measure of the surface inside the figure. The area of a rectangle is found by multiplying its length by its width.

\(\textbf{Example:}\) The phone company charges $20 for installation and $25 a month for basic service. How much money will Monique pay for one year of service with installation?

\(\color{brown}{\textbf{Understand the problem: }}\)We need to find the cost for one year of service. We are given a monthly fee and a one-time installation fee. We know there are 12 months in a year.

\(\color{brown}{\textbf{Create a plan:}}\) We need to add the installation fee to charge for 12 months of service.

Find the answer: \(25\times12 = 300\) Next we add. \(300 + 20 = 320\)
So, Monique will pay \(\$320\) for one year of service with installation.

\(\color{brown}{\textbf{Simplifying Fractions- GCF and Factors Method}}\)
\(\textbf{Equivalent Fractions}\)- Are Fractions that represent the same value
\(\text{Simplest Form-}\) If there is no common factor other than one, that divides exactly into the numerator and the denominator.

\(\textbf{Using the GCF Method:}\)
\(\text{1.) Find the GCF of the numerator and denominator}\\
\text{2.) Divide the numerator and the denominator by the GCF}\\ \)

\(\textbf{NOTE:}\) Dividing the numerator and the denominator by the same non-zero does not change the value of a fraction. Doing this, gives us an equivalent Fraction.
Example: \(4/8\) Divided by \(4/4\) (same thing as 1) = \(1/2\)

\(\textbf{Factors Method:}\)
\(\text{1.) Find any factor that is common to both the numerator and denominator}\\
\text{2.) Divide the numerator and denominator by the common factor}\\
\text{3.) Repeat this process until there are no common factors except for 1}\\ \text{that divide exactly into both the numerator and the denominator}\)

Example: \(20/32 / 2/2 = 10/16 / 2/2 = 5/8\)

\(\color{brown}{\textbf{Multiplying Fractions:}}\)
\(\text{1.) Multiply the numerators to get the numerator of the product}\\
\text{2.) Multiply the denominator to get the denominator of the product}\\
\text{3.) Simplify}\)
Example: \(4/7 \times 2/5 = 12/35\)

\(\color{brown}{\textbf{Multiplying Fractions- Simplifying First}}\)
1.) Write the problem as on fraction. Do NOT multiply yet.
2.) Divide by common factors in the numerator and denominator
3.) Multiply the remaining factors in the numerator and denominator
Example: \(7/10 \times 5/8 = 7z85/10*8 = 7*1/ 2*8 = 7/16\)

\(\color{brown}{\textbf{Application:}}\)
Elizabeth bought a sandwich and ate half of it. She gave her brother one-half of what was left. How much of the sandwich did her brother get?
~ We need to find out how much her brother got.
~ Find \(1/2 \times 1/2 \)= \(1 \times 1/(2 \times 2) = 1/4\)
Her brother received \(1/4\) of the sandwich.

\(\color{brown}{\textbf{Dividing Fractions}}\)
Reciprocal- two numbers are reciprocals of each other if their product is 1.
To find the reciprocal, flip the fraction.
\(3/4\) - \(4/3\)
\(5\) = \(5/1\) = \(1/5\)
NOTE: The number \(0\) does not have a reciprocal. \(0 = 0/1 = 1/0 = \text{Undefined.}\)
\(\text{Rule: Dividing by a fraction is the same as multiplying by its reciprocal.}\)
\(\textbf{Procedure:}\)
\(\text{1.) Invert the second Fractions- that is, take its reciprocal}\\
\text{2.) Multiply this reciprocal by the first fraction.Rewrite the problem using one fraction}\\
\text{3.) Divide by common factors in the numerator and denominator}\\
\text{4.) Multiply the remaining factors and simplify}\)
Example: \(\cfrac{3/5}{1/2} = 2/1 \times 3/5 = 6/5\)

Caution: Do not divide by common factors before you invert and multiply!
Example: \(3/7 / 3/8 = 8/3 \times 3/7 = 8/7 \)


\(\color{brown}{\textbf{Writing Fractions with an LCD}}\)
\(\textbf{Finding the LCM (Least Common Multiple) }\)
1.) If one number divides exactly into the other, the LCM is simply the larger of the two numbers.
Example: LCM of 4 and 8 is 8
2.) If the numbers have no common factor other than 1, the LCM is the product of the two numbers. Example: LCM of 5 and 7 is 35
3.) If the two numbers have a common factor other than 1, you need to choose a method for finding the LCM. Example: The LCM of 4 and 6 is 12
List Method
GCF Method
Prime Factor
LCM(Least Common Multiple)
LCD(Least Common Denominator)
\(\color{brown}{\textbf{LCM vs. LCD}}\)
\(\bf{LCM}\) stands for least common multiple. Use the LCM with most numbers. \(\bf{LCD}\) stands for least common denominator. Use the LCD with fractions. Least Common Denominator(LCD) is the least common multiple(LCM) of the denominators.
\(\textbf{NOTE:}\) The Exact same process is used to find both the LCD and the LCM since finding the LCD is the same as finding the LCM of the denominators.
Equivalent Fractions- Fractions are equivalent if they represent the same value. What other fractions also represent 1/6?
~ To write an equivalent fraction multiply the numerator and denominator of the original fraction by the same non-zero number. This is the same as multiplying the original fraction by 1, which does not change the fractions value. Example: \(1/6 * 2/2 = 2/12\)


1.) Find the LCD
2.) Find the number that you need to multiply the denominator to get the LCD. This number will be different for each fraction.
3.) Rewrite each fraction as an equivalent fraction whose denominator is the LCD. For each fraction, multiply the numerator and denominator by the number found in step 2.

Example: Rewrite \(1/6\) and \(7/9\) using the LCD as the denominator.
LCD is \(18\)
\(1/6 \times 3/3 = 3/18 \) \(7/9 \times 2/2 = 14/18\)



\(\color{brown}{\textbf{Adding and Subtracting like Fractions}}\)
\(1/8, ~ 3/8, ~ 7/8\) are like fractions because they have a common denominator.
Adding like Fractions:
1.) Add the numerators
2.) Keep the denominator
3.) Simplify if possible.
Example: \(6/7 – 2/7 = 4/7\)



\(\color{brown}{\textbf{Adding and Subtracting unlike Fractions}}\)
To add or subtract unlike fractions, first we must rewrite the fractions with a common denominator. Usually we use the LCD or least common Denominator.
CAUTION: Be sure you have a common denominator when adding or subtracting fractions.
1.) Find the least common denominator
2.) Rewrite the fractions with the least common denominator
3.) Add or subtract the numerators
4.) Keep the denominator
5.) Simplify if possible
Example:
Add ¾ + 1/6 LCD = 12
¾ * 3/3 = 9/12
1/6 * 2/2 = 2/12
9/12 + 2/12 = 11/12

\(\color{brown}{\textbf{Changing a mixed number to an Improper Fraction}}\)
Mixed number is the sum of a whole number and a fraction.
Improper fraction is a numerator that is greater than, or equal to the denominator
An improper Fraction represent at least on whole unit
1.) Multiply the denominator by the whole number
2.) Add the numerator to this product
3.) Write this value over the original denominator

Answer 2

Good work @YanaSidlinskiy !

Answer 3

Thanks, Mathslover:)

Answer 4

@YanaSidlinskiy

Simply marvelous work, Very detailed explanation. Keep up the amazing work and have a wonderful day.

- The OpenStudy Librarian, Joshua

Answer 5

Thanks, Librarian. It is definitely useful for some users! Working on my second part of the tutorial! So, just bear with me and wait on my next tutorial:)

Answer 6

@YanaSidlinskiy that was great :)

Answer 7

You're Most Welcome!

Answer 8

:D

Answer 9

Splendid work @YanaSidlinskiy

Answer 10

Thanks, @xapproachesinfinity
That word though, splendid. It's fantastic!

Answer 11

\(\huge\color{green}{{\rm PEMDAS}~\rm !! :)}\) AUNTii!!!!

Answer 12

@YanaSidlinskiy good work neat and clean :);P

Answer 13

Good Job :)

Answer 14

Thanks @Nnesha and @TheSmarOne

Answer 15

\(\color{blue}{\text{Originally Posted by}}\) @YanaSidlinskiy
Thanks @Nnesha and @TheSmarOne
\(\color{blue}{\text{End of Quote}}\)
@TheSmartOne ***

Answer 16

Lol, sorry, sorry! @TheSmartOne I think I'll become like @e.mccormick
Missing out every letter.

Answer 17

Not every letter. If it was every letter, then all I would be saying is, "\(\qquad\)" all the time.

Answer 18

Oops, Meant "every other letter". Lol.

Answer 19

H_w _s _t _v_r_ o_h_r _e_t_r?

Answer 20

Lol, I know you know what I mean. O my. :P I'll have to take the time and screenshot some stuffs and show you, lol.

Answer 21

Hehe. Well, I wrote as instead of was when I did my first reply, so it is not like I do not know what you mean... =P

Answer 22

Ya, ya. I think I should be more specific more often. hha!

Answer 23

Something like right here:

Answer 24

Find any of my "oyu" mistakes?

Answer 25

Hhaaha! Not yet, lol. But you do know where I got that from, right?

Answer 26

#TutorialPostSpammed

Answer 27

^figured.

Answer 28

OP Spam!

Answer 29

Lol.