TERMS YOU SHOULD BE FAMILIAR WITH:
Numerator: the number on top (which tells how many parts you have)
Denominator: the number on the bottom (which tells how many parts are in
the whole)
In the example below 3 (numerator) out of 4 (denominator) parts are shaded dark.
This is represented by the fraction 
.
Proper fraction: the top number (numerator) is less
than the bottom number (denominator).
Examples:
Improper fraction: the algebra -homework-2/square-root-in-the-numerator.html">numerator is equal to or is
larger than the denominator.
Examples:
Mixed number: a whole number is written next to a
proper fraction.
Examples:
Common Denominator : is a number that can be divided
evenly by all of the denominators in the problem.
Examples: Find the common denominator of
and
and 
The common denominator for these fractions is 12. It also
happens to be the least common denominator.
Sum : The result when two numbers are added.
Difference : The result when two numbers are subtracted.
Product: The result when two numbers are multiplied.
Quotient: The result when two numbers are divided.
** FRACTIONS **
REDUCING FRACTIONS TO LOWEST TERMS:
STEP 1: Find a number that goes evenly into the numerator and the denominator of
the fraction.
STEP 2: Check to see whether another number goes evenly into both the numerator
and denominator. Stop when there are
no more numbers that can go into the fraction.
Example:
(8 will go in evenly to both
numbers)
(2 will go in evenly
to both numbers)
CHANGING MIXED NUMBERS TO IMPROPER FRACTIONS:
STEP 1: Multiply the denominator by the whole number.
STEP 2: Add the result to the numerator.
STEP 3: Place the total over the denominator.
Example:
ADDING AND SUBTRACTING FRACTIONS :
In order to add or subtract fractions, the denominators must be equal (have a
common denominator.)
Example:
Example:
(you must
find a common denominator)
MULTIPLYING FRACTIONS:
Step 1. Multiply the numerators across.
Step 2. Multiply the denominators across. (note: they do not need to be equal)
Step 3. Make sure the product is in its lowest terms.
Example:
reduce to lowest terms
MULTIPLYING WITH MIXED NUMBERS:
Step 1: Change every mixed number to an improper fraction.
Step 2: Multiply numerators across, then denominators across.
Step 3: Change the improper fraction to a mixed number in lowest terms.
Example:
DIVIDING FRACTIONS:
Step 1: The fraction that is to the right of the division sign will need to be
turned upside down by writing the numerator in
the denominator position and the denominator in the numerator position.
Step 2: Follow the rules for multiplying.
Example:
reduce to lowest terms
=
** DECIMALS **
TERMS:
Decimal number : Any number that includes place value to the right of a
decimal point.
Decimal point: A dot or point that separates the decimal value from the
integral value of a number.
ADDITION AND SUBTRACTION OF DECIMALS:
Step 1: You must line up the decimal points in the problem. (Note: when the
decimal points are lined up, the digits are
automatically lined up in the correct place value.)
Step 2: Add or subtract.
Example:
MULTIPLYING DECIMALS:
Step 1: Write the problem and multiply as you would a whole number
multiplication problem.
Step 2: The product (answer) has the same number of decimal places after the
decimal point as the total number of decimal
places in the two numbers being multiplied.
Example: 1.89 x 5.03 = (note: there are 4 numbers to the right of the decimal
point)
(place decimal point 4
spaces from the right)
DIVIDING A DECIMAL BY A WHOLE NUMBER:
Step 1: Place the decimal point above its position in the problem.
Step 2: Divide the same way as you divide whole numbers.
Example: divide 2.701 by 73
DIVIDING A DECIMAL BY A DECIMAL NUMBER:
Step 1: Move the decimal point of the divisor ( one nts/expanding-brackets-algebra.html">outside the bracket ) as far right
as you can go. Then move the decimal point
in the dividend (inside the bracket) the same number of places as the divisor.
Step 2: Place the decimal point directly above its position in the problem. Then
divide the same way as you would divide
whole numbers.
In the example below the decimal point is moved 2 places to the right in both
the divisor and the dividend.
Example: 4.374 .03 =
Comparing Decimals:
Step 1: To compare decimals, write the decimal numbers with the same number of
decimal places.
Step 2: Compare to see which is larger.
Example: Which is greater: 0.9 or 0.91?
0.90
0.91
0.91 is greater than 0.90
** PERCENTS **
PERCENT: “PER” means “out of” or “divided by” and “CENT” means 100 (i.e. 100
cents in a dollar), therefore,
PERCENT mean “out of 100” or “divided by 100.”
Percent is another way of writing fractions with a denominator of 100.
Percent refers to a value compared to a whole expressed as 100, rather than
compared to a whole expressed as 1.
Percents are always expressed with a percent sign: %. 100% represents the whole
amount, any value less than 100 is less
than the whole, and any value greater than 100 is more than the whole.
Percents are used to describe a part of something. Percents are used to figure
out sales or the amount of interest someone
will pay on a loan. When converting a percent to its fraction form, it will
always have a denominator of 100.
CHANGING DECIMALS TO PERCENTS OR PERCENTS TO DECIMALS:
The important key is where to move the decimal point. If changing from decimal
to a percent, you would need to move the
decimal point two places to the right and add the percent sign.
Example:
0.35 = 35%
0.8 = 80%
To change from percent to decimal, you need to move the
decimal point two places to the left and drop the percent sign.
Example:
30% = .3
0.9% = .009
CONVERTING FRACTION TO PERCENT:
Divide the bottom number of the fraction (denominator) into the top number
(numerator) and move the decimal point two
places to the right.
Example
- or -
Multiply the fraction by 100%
Example:
CONVERTING PERCENT TO FRACTION:
Write the percent as a fraction with 100 as the denominator. Then reduce the
fraction to lowest terms.
Example:
