Pre-Algebra Final Review (December)

Place Value

• In our number system, the position a number is in determines its value. If a 5 is in a hundreds place, it would be 500; if that five would be in a millions place, then it would be 5,000,000.

• We can use Place Value to write numbers in expanded form. To write a number in expanded form, we must add each digit's value. We may also use exponents. For example:
• 213 in expanded form without exponents would be 200 + 10 + 3.

• We can write numbers in words by writing them how we would read them, but using letters instead of numbers. We must place the comma the same way we do in digit numbers.



• To find the perimeter of a figure, we must sum up the lengths of all it sides.



• To round, we must always look at the digit to the right of the number we want to round. If it is larger than 4, the rounded number goes up, if it's less than 5, it stays the same. All the digits after the rounded number always change to zero.

• When we estimate we get an approximate result to our problem very quickly. We must round all numbers and add them; we will end up with a very basic sum.

• Exponents are a shorter way to express repeated multiplications.

• The Order of Operations (PEMDAS) is an order that must be followed to solve operations that involve addition, subtraction, multiplication, division and exponents.

• An average is a single value that summarizes the significance of a set of unequal values. The mean (average value), the median (middle number), and the mode (most repeated number) are all types of averages.

• The area of an object is the amount of surface it has, each different figure has a different formula to find are, some are:
• square = sides squared (S2)
• rectangle = length times width (lw)
• parallelogram = base times height (bh)
• triangle = base times height times half (bh x 1/2)

• The volume is the measure of the space enclosed by a solid.

• The surface area is the total area of all surfaces of an object.

• The absolute value of a number is its distance from zero on the number line, it doesn't matter if it's positive or negative. Opposite numbers are numbers that are the same distance from zero, but in opposite directions (positive and negative).



• To add negative and positive numbers, we must subtract them and place the sign of the larger value. We can use a number line to make this process easier. To subtract negatives, it is recommended we change it to the sum of the opposite.

 



• To multiply and divide negative numbers, we must multiply normally and apply the use of several rules:
• equal signs = positive answer
• different signs = negative answer

• We can use the distributive property to assist us with simplifying algebraic expressions; we can multiply and divide unlike terms, but we can't subtract or add them.

• Proper fractions represent an amount that is smaller to one, while improper fractions represent an amount that is larger than one. Improper fractions can be turned into mixed numbers. 

•  We can reduce fractions to simplest form, or lowest terms, this means there is no common factors between the numerator (above number) and the denominator (below number).

• To multiply fractions, we multiply the numerators and multiply the denominators. To divide them we must multiply the fraction by the reciprocal.

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• To add and subtract fractions, we must find an LCD (Least Common Denominator) and make sure the two denominators are equal.



• We can also change a mixed number to an improper fraction by multiplying the denominator by the whole number and adding it to the numerator.

• We can add, subtract, multiply, and divide mixed numbers like fractions, but we have to consider certain rules.

• Complex fractions are fractions within fractions, you must simplify them to obtain the lowest term fraction.

NOTE: This is an interactive review, if you only read the text you won't be learning everything.

RECOMMENDATION: Read each bullet, if you fully understand that subject, skip the video. If you have problems with a certain subject, watch the video. Remember you must be on a computer to see the videos, as they cannot be seen through tablets or phones.