Mixed Number to Improper Fraction - ANSWER Multiply the denominator by the whole
number, add to the numerator. Keep the denominator the same.
least common denominator - ANSWER The least common multiple of the denominators
of two or more fractions. To determine the LCD of the fractions, list the multiples of the
denominators and find the smallest number that is common to the lists.
equivalent fractions - ANSWER Two fractions a/b and c/d are equivalent if ad=bc
Adding/subtracting fractions with same denominator - ANSWER a/b + c/b = (a+c)/b or
a/b +c/b = (a-c)/b
Distributive property of division over addition - ANSWER (a+c)/b = a/b + c/b
Adding/subtracting fractions with different denominators - ANSWER a/b + c/d = (ad +
bc)/bd ... a/b - c/d = (ad - bc)/bd
Subtracting a fraction from a whole number - ANSWER A - b/c = (c x A - b)/c
Multiplying fractions - ANSWER a/b x c/d = ac/bd
Dividing fractions - ANSWER Multiply by the reciprocal: a/b x c/d = a/b x d/c = ad/bc
Two methods for simplifying fractions - ANSWER Cross cancel and top-and-bottom cancel
1
,1 over a fraction - ANSWER 1/a/b = b/a
How to simplify a complex fraction: Method 1 - ANSWER Multiply both the numerator of
the complex fraction and the denominator of the complex fraction by the LCD
How to simplify a complex fraction: Method 2 - ANSWER Write the numerator of the
complex fraction as a single fraction, do the same to the denominator, then divide
How to simplify a complex fraction: Method 3 - ANSWER After doing method 2,
(a/b)/(c/d) = ad/bc
Bowtie method of comparing fractions - ANSWER
Best way to compare size of multiple fractions - ANSWER Find the least common
denominator and then compare the numerators
2 other ways to compare fractions - ANSWER 1. Use a reference point
2. Use a common numerator (larger denominator = smaller fraction)
Given a fraction, multiplying or dividing both the numerator and the denominator by the
same nonzero constant... - ANSWER will not change the value of the fraction. Ex: 1/2 x
5/5 = 5/10
Given a fraction, adding or subtracting from the numerator and denominator the same
nonzero constant... - ANSWER will change the value of the fraction
If a fraction is between 0 and 1, adding a positive constant to top and bottom will...
2
,Subtracting from the top and bottom of this fraction a positive constant will... - ANSWER
Make the fraction larger
Make the fraction smaller (as long as it's still + )
If a fraction is greater than 1, adding a positive constant to top and bottom will...
Subtracting from the top and bottom of this fraction a positive constant will... - ANSWER
Make the fraction smaller
Make the fraction larger (as long as it's still +)
How to add or subtract decimals - ANSWER vertically line up the decimal points of the
numbers and then add/subtract
How to multiply decimals - ANSWER Does not require aligning the decimal points.
arrange with right justification, multiply like normal and then count the total number of
decimal places to the right of the decimal in the numbers. Then move the decimal point of
the product to the left the same number of spaces
Shortcut for multiplying decimals - ANSWER Count the total number of decimal places
from the two numbers being multiplied. That will be the number of decimal places in the
answer (unless the answer ends in 0)
How to divide decimals - ANSWER 1. Move the decimal point of the divisor to the right
until it becomes a whole number
2. Move the decimal point of the dividend to the right the same number of places
3. Divide the numbers by long division. For the quotient, keep the decimal in the same place
as the new dividend
How to compare the size of decimals - ANSWER Compare them place by place, left to
right. The larger decimal will have the larger number at the first place of difference
Percent means - ANSWER divide by 100
3
, x% = - ANSWER x/100
How to convert a fraction to percent - ANSWER Multiply by 100 and add %
How to convert a decimal or integer to percent - ANSWER Move decimal point two places
to the right and add %
Convert percent to decimal - ANSWER Move the decimal two places to the left and drop
the %
Convert a fraction to a decimal - ANSWER Divide numerator by denominator using long
division
Converting Terminating Decimals to Fractions - ANSWER If one decimal place: write the
number (as if the decimal point were not there) over 10
If two decimal places: write the number (without decimal) over 100
If three decimal places: write the number (without decimal) over 1000
1/6 = - ANSWER .167 or 16.7%
1/7 = - ANSWER .143 or 14.3%
1/8 = - ANSWER .125 or 12.5%
1/9 = - ANSWER .111 or 11.1%
Decimal equivalents of Base 6 fractions - ANSWER .167
4
number, add to the numerator. Keep the denominator the same.
least common denominator - ANSWER The least common multiple of the denominators
of two or more fractions. To determine the LCD of the fractions, list the multiples of the
denominators and find the smallest number that is common to the lists.
equivalent fractions - ANSWER Two fractions a/b and c/d are equivalent if ad=bc
Adding/subtracting fractions with same denominator - ANSWER a/b + c/b = (a+c)/b or
a/b +c/b = (a-c)/b
Distributive property of division over addition - ANSWER (a+c)/b = a/b + c/b
Adding/subtracting fractions with different denominators - ANSWER a/b + c/d = (ad +
bc)/bd ... a/b - c/d = (ad - bc)/bd
Subtracting a fraction from a whole number - ANSWER A - b/c = (c x A - b)/c
Multiplying fractions - ANSWER a/b x c/d = ac/bd
Dividing fractions - ANSWER Multiply by the reciprocal: a/b x c/d = a/b x d/c = ad/bc
Two methods for simplifying fractions - ANSWER Cross cancel and top-and-bottom cancel
1
,1 over a fraction - ANSWER 1/a/b = b/a
How to simplify a complex fraction: Method 1 - ANSWER Multiply both the numerator of
the complex fraction and the denominator of the complex fraction by the LCD
How to simplify a complex fraction: Method 2 - ANSWER Write the numerator of the
complex fraction as a single fraction, do the same to the denominator, then divide
How to simplify a complex fraction: Method 3 - ANSWER After doing method 2,
(a/b)/(c/d) = ad/bc
Bowtie method of comparing fractions - ANSWER
Best way to compare size of multiple fractions - ANSWER Find the least common
denominator and then compare the numerators
2 other ways to compare fractions - ANSWER 1. Use a reference point
2. Use a common numerator (larger denominator = smaller fraction)
Given a fraction, multiplying or dividing both the numerator and the denominator by the
same nonzero constant... - ANSWER will not change the value of the fraction. Ex: 1/2 x
5/5 = 5/10
Given a fraction, adding or subtracting from the numerator and denominator the same
nonzero constant... - ANSWER will change the value of the fraction
If a fraction is between 0 and 1, adding a positive constant to top and bottom will...
2
,Subtracting from the top and bottom of this fraction a positive constant will... - ANSWER
Make the fraction larger
Make the fraction smaller (as long as it's still + )
If a fraction is greater than 1, adding a positive constant to top and bottom will...
Subtracting from the top and bottom of this fraction a positive constant will... - ANSWER
Make the fraction smaller
Make the fraction larger (as long as it's still +)
How to add or subtract decimals - ANSWER vertically line up the decimal points of the
numbers and then add/subtract
How to multiply decimals - ANSWER Does not require aligning the decimal points.
arrange with right justification, multiply like normal and then count the total number of
decimal places to the right of the decimal in the numbers. Then move the decimal point of
the product to the left the same number of spaces
Shortcut for multiplying decimals - ANSWER Count the total number of decimal places
from the two numbers being multiplied. That will be the number of decimal places in the
answer (unless the answer ends in 0)
How to divide decimals - ANSWER 1. Move the decimal point of the divisor to the right
until it becomes a whole number
2. Move the decimal point of the dividend to the right the same number of places
3. Divide the numbers by long division. For the quotient, keep the decimal in the same place
as the new dividend
How to compare the size of decimals - ANSWER Compare them place by place, left to
right. The larger decimal will have the larger number at the first place of difference
Percent means - ANSWER divide by 100
3
, x% = - ANSWER x/100
How to convert a fraction to percent - ANSWER Multiply by 100 and add %
How to convert a decimal or integer to percent - ANSWER Move decimal point two places
to the right and add %
Convert percent to decimal - ANSWER Move the decimal two places to the left and drop
the %
Convert a fraction to a decimal - ANSWER Divide numerator by denominator using long
division
Converting Terminating Decimals to Fractions - ANSWER If one decimal place: write the
number (as if the decimal point were not there) over 10
If two decimal places: write the number (without decimal) over 100
If three decimal places: write the number (without decimal) over 1000
1/6 = - ANSWER .167 or 16.7%
1/7 = - ANSWER .143 or 14.3%
1/8 = - ANSWER .125 or 12.5%
1/9 = - ANSWER .111 or 11.1%
Decimal equivalents of Base 6 fractions - ANSWER .167
4
