Download Operations of Rational Numbers Notes

Operations of Rational Numbers Notes
Rational number: a number that can be written as a ratio; whole number, fractions, repeating or terminating decimals
Adding
Subtracting
Multiplying
Dividing
Signed Numbers
*Think of the sign as a direction on a number
line
+ = right
- = left
pos + pos = pos pos + neg = depends on larger
neg + neg = neg neg + pos = number
Fractions
*Get like denominators and
rename the fractions
*Re-write the subtraction problem as addition of
the opposite number
ex: -1.2 – 3.8 = -1.2 + (-3.8)
-2 – (-5) = -2 + 5 “double negative”
pos – neg = pos + pos = pos
neg – pos = neg + neg = neg
pos – pos = pos + neg = depends on larger
neg – neg = neg + pos =
number
*If the signs are the same, the product is positive
*If the signs are different, the product is negative
*(-1) times a number equals the opposite of that
number
pos x pos = pos
pos x neg = neg
neg x neg = pos
neg x pos = neg
*Same as multiplying since division is the same
as multiplying by the reciprocal
pos
pos
 pos
 neg
pos
neg
neg
neg
 pos
 neg
neg
pos
*Get like denominators and
rename the fractions
Decimals
*Line up the decimals
*Mixed numbers are okay
*Line up the decimals
*Mixed numbers are okay, but
you may have to borrow from
a whole number
*Cross simplify then multiply
across the numerators and
denominators
*convert to improper fractions
first
*Multiply by the reciprocal;
“switch and flip” = switch the
sign from division to
multiplication and then flip the
second fraction
*convert to improper fractions
first
*Don’t line up the decimals,
count the number of decimal
places “held” after finished
multiplying
*Convert the divisor (the
number you’re dividing by)
into a whole number by moving
the same number of decimal
places in each number
(equivalent to multiplying both
numbers by a power of ten)


Absolute value = = the distance from zero; always positive because it is a distance; complete the operations inside the absolute
 and then make the final result
 positive
value signs
