Pre-Algebra : Operations and Properties
Study concepts, example questions & explanations for Pre-Algebra
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Example Questions
Example Question #53 : Addition And Subtraction
Write solution as an improper fraction.
When adding or subtracting fractions, you must find the common denominator. This is best done by finding the least common multiple of the denominators, in this case 5 and 3. What is the lowest number that is divisible by both 5 and 3? Often, the easiest solution is to multiply the denominators together. This works most often with single digit numbers. Anything larger and you will have to find the least common multiple another way.
The LCM of 5 and 3 is 15 (5 x 3). Now you know that both fractions must have 15 on the bottom. Now, to convert 4/5 to ?/15, you must recognize how many times 5 goes into 15 (3), and multiply the numerator by that number. Therefore:
Do the same with the other side.
Now that the denominators match, all that's left is to add the numerators together.
This solution is already an improper fraction (the numerator is larger than the denominator), therefore you may leave the fraction as is.
Example Question #1 : Multiplication And Division
Express in degrees: 
Since 
Example Question #3 : How To Use The Order Of Operations In Pre Algebra
Suppose you know the values of 
In which order would you carry out the four operations in the expression?
Divide, multiply, subtract, add
Multiply, subtract, add, divide
Add, subtract, multiply, divide
Subtract, add, multiply, divide
Multiply, add, subtract, divide
Multiply, subtract, add, divide
A fraction bar in an expression acts as both a division symbol and a grouping symbol, so we evaluate the numerator first. Within the numerator, there is a multplication, a subtraction, and an addition, so, by order of operations, we multiply first. Addition and subtraction are carried out right to left; the subtraction is left of the addition, so we subtract next, then add. Finally, we divide the numerator by the denominator.
In summary: Multiply, subtract, add, divide
Example Question #2 : Multiplication And Division
Simplify the following as far as possible:
If we use the foil method we get the following:
First:
Inner:
Outer:
Last:
If that is simplified we're left wiht
Example Question #3 : Multiplication And Division
Simplify:
The whole operation is squared, so to better understand how to solve it it can be rewritten as:
Using order of operations we get the following:
First:
Inner:
Outer:
Last:
When this is simplified we have
Example Question #181 : Operations
Simplify:
The equation can be rewritten as 
First the foil method should be used, leaving us with:
Then the 2 can be distributed to each of the factors inside the parentheses. Leaving the solution:
Example Question #5 : Multiplication And Division
Which expression simplifies to
First:
Inner:
Outer:
Last:
Example Question #6 : Multiplication And Division
What expression simplifies to
When simplified using the FOIL method 
First:
Inner:
Outer:
Last:
When the 2 is distributed and the expression simplified we are left with
Example Question #2 : Multiplication And Division
A salesman for a car dealership earns 12% commission on all sales. What will be his commission for a week if he sells three cars that week - a $55,000 SUV on Tuesday, a $28,000 car on Thursday, and a $42,000 van on Friday?
The total sale price of the cars he sells will be
12% of $125,000 is
which is the salesman's commission.
Example Question #2 : Multiplication And Division
Read the following problem but do not solve it.
Acording to Mr. Smith's will, when he dies, each of his six children is to be left a parcel of land 510 acres in area. If these six parcels make up all of the farm, then how large is Mr. Smith's farm now?
Which of the following expressions must be evaluated in order to answer this question?
There are six parcels of equal size; the total size is therefore the product of the common size (510 acres) and the number of parcels (6). This is
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