Fractions, Decimals, Percents
DecimalPercent
*Move the decimal point 2 places to the right
(multiply by 100)
PercentDecimal
*Move the decimal point 2 places to the left
(divide by 100)
FractionDecimal
* Numerator  Denominator
Decimal → Fraction
Say the decimal the right way, write the fraction and simplify if
needed.
Percent → Fraction
Percent means “out of 100” – Put the percent over 100 and simplify.
FractionPercent
*Change the denominator to 100
OR
* Numerator ÷ Denominator X 100
Decimals
Rounding Decimals
1. Find the digit in the place you are rounding to.
2. Look at the number to its right. If this number is less than 5, keep
the digit the same. If this number is 5 or greater, round the digit up.
Comparing Decimals
 Begin by comparing the whole numbers (to the left of
the decimal point)
 Compare the digits – place by place – starting with the
tenths place
3. Keep all numbers to the left of your place the same.
4. All numbers to the right become 0.
Adding and Subtracting
Be sure to line up the decimal point.
Multiplying Decimals
Dividing Decimals
To multiply decimal numbers:

If you are not dividing by a whole number, move
decimal point to right to make it a whole number and
move decimal point under the division sign the same
number of places.

Put decimal point directly above decimal point in the
dividend.

Divide as usual. Keep dividing until the answer
terminates or repeats.
**Multiply the numbers just as if they were whole numbers.


Line up the numbers on the right - do not line up the decimal
points.
Place the decimal point in the answer by starting at the right and
moving a number of places equal to the total of decimal places
in both numbers multiplied
Fractions
Mixed  Improper
Denominator  Whole Number + Numerator = new numerator,
keep denominator
Improper  Mixed
denominator “goes into” Numerator = whole number
Remainder = new numerator – keep denominator
Dividing
1) Make improper fractions.
Simplify Fractions
Multiplying
2) Flip the second fraction and multiply.
3) Simplify answer. Fix improper fractions.
Divide numerator and denominator by same thing until you can’t
divide any more
4) Make improper fractions.
Comparing Fractions
5) Multiply across the numerator and across the
denominator.
Use a “cross multiplying” method
6) Simplify answer. Fix improper fractions.
Adding / Subtracting
Borrowing – Subtraction only
1) Change both fractions to ones with a common
denominator
1) Change both fractions to ones with a common
denominator
2) Add or subtract whole numbers, add or subtract fractions.
2) IF you have to borrow, borrow one from the whole
number, add the denominator to the numerator.
3) Simplify answer. Fix improper fractions.
3) Subtract whole numbers, add or subtract fractions.
4) Simplify answer. Fix improper fractions.
Rounding Fractions and Mixed Numbers to the nearest whole number.
Compare the fraction to . If it is bigger than , round up. If it is smaller than , round down.
Hint: Multiply the numerator by 2. If this number is bigger than the denominator, round up. If it is smaller than the denominator
round down!
factors – numbers that are multiplied – alternately – numbers that
divide another number evenly
Multiples – “counting by” numbers – numbers gotten by
multiplying one number by other numbers
Example: 60: 1, 2 , 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Example: 2 – 2, 4, 6, 8, 10, 12, …
GCF
LCM



find all factors of both numbers
then select the ones that are common to both, and
then choose the greatest (biggest).
Example: What are the common factors of 15 and 30?
The factors of 15 are 1, 3, 5, and 15
The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30
15 is the GCF.
List the multiples of the numbers until you get a match.
Example: Find the least common multiple for 6 and
8
Multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, ...
Multiples of 6 are: 6, 12, 18, 24, 30, 36, ...
probability – the chance that something is going to happen
mean – (average) the sum of the data divided by how many
pieces of data there are
Probability =
# of ways that an event can occur
# of possible outcomes
median – the middle number when a set of numbers are
arranged in order – if there are two middle numbers, add them
together and divide by 2
What is the probability of choosing a vowel from the
alphabet? 5 vowels out of 26 letters – probability 5/26
prime number – a number with exactly 2 factors – one and itself
composite number – numbers with 3 or more factors
** 0 and 1 are neither prime nor composite
mode – the number(s) that appears most in a set of data
Prime Factorization – use factor trees
Proportions – one way to solve is to cross-multiply and divide
(2)(6) ÷ 3 = 4
A ratio is a comparison of two numbers or measurements. The
numbers or measurements being compared are called the
terms of the ratio.
A rate is a special ratio in which the two terms are in different
units. When rates are expressed as a quantity of 1, such as 2
feet per second or 5 miles per hour, they are called unit rates.