Question

Math Help for users. This may be useful for some users. This is what the topics cover. Disregard the cut off words. They are 'fractions'.
Refresh your screen if you see the black diamonds. Might worth a look here=)
1.)Order or Operations and Whole Numbers
2.) Problem Solving
3.)Simplifying Fractions-GCF and Factors Method
4.) Multiplying Fractions
5.) Dividing Fractions

Answer 1

\(\huge\color{RED}{Order~of~Operations}\)
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
Problem Solving
1.) Understand the problem
2.) Create a plan
3.) Find the answer
4.) Check the answer

Keywords:

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

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*4) = 3(8) = 24

Are 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.

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?

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.

Create a plan: We need to add the installation fee to charge for 12 months of service.

Find the answer: 25*12 = 300 Next we add. 300 + 20 = 320.
So, Monique will pay $320 for one year of service with installation.


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

Using the GCF Method:
1.) Find the GCF of the numerator and denominator
2.) Divide the numerator and the denominator by the GCF
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)= ½

Factors Method:
1.) Find any factor that is common to both the numerator and denominator
2.) Divide the numerator and denominator by the common factor
3.) Repeat this process until there are no common factors except for 1 that divide exactly into both the numerator and the denominator
Example: 20/32 / 2/2 = 10/16 / 2/2 = 5/8

\(\huge\color{red}{Multiplying~Fractions}\)
Multiplying Fractions:
1.) Multiply the numerators to get the numerator of the product
2.) Multiply the denominator to get the denominator of the product
3.) Simplify
Example: 4/7 * 2/5 = 12/35

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 * 5/8 = 7z85/10*8 = 7*1/ 2*8 = 7/16

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 ½ * ½ = 1*1/2*2 = ¼
Her brother received ¼ of the sandwich.


\(\huge\color{red}{Dividing~Fractions}\)
Reciprocal- two numbers are reciprocals of each other if their product is 1.
To find the reciprocal, flip the fraction.
¾  4/3
5 = 5/1 = 1/5
NOTE: The number 0 does not have a reciprocal. 0 = 0/1 = 1/0 = Undefined.
Rule: Dividing by a fraction is the same as multiplying by its reciprocal.
Procedure:
1.) Invert the second Fractions- that is, take its reciprocal
2.) Multiply this reciprocal by the first fraction. Rewrite the problem using one fraction
3.) Divide by common factors in the numerator and denominator
4.) Multiply the remaining factors and simplify
Example: 3/5 / ½ -- 2/1 * 3/5 = 6/5

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


\(\huge\color{red}{Writing~Fractions~with~an~LCD}\)
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)
LCM vs. LCD
LCM stands for least common multiple. Use the LCM with most numbers. LCD stands for least common denominator. Use the LCS with fractions. Least Common Denominator(LCD) is the least common multiple(LCM) of the denominators.
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 * 3/3 = 3/18 7/9 * 2/2 = 14/18


\(\huge\color{red}{Adding~and~Subtracting~like~Fractions}\)
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



\(\huge\color{red}{Adding~and~Subtracting~unlike~Fractions}\)
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

\(\normalsize\color{red}{Changing~a~mixed~number~to~an~Improper~Fraction}\)
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

I may add some stuff here and there...

Answer 2

Nice :) I came to know about the difference between LCD and LCM. Thanks to you!

Answer 3

:) You're Welcome! It was just something I had to post.