Improper fractions Flashcards
proper fractions
numerators < denominator
improper fractions
numerators > denominator
mixed numbers
whole numbers followed by a proper fraction e.g. (2 1/3)
converting improper fraction to mixed numbers
improper-7/2 –> (mixed)-(3 1/2)
convert mixed numbers to improper fraction
mixed (6 2/3)– improper (20/3)
least common denominator
common multiple of all the denominators
adding/subtracitng with unlike denominator
express fractions with same denominator by identifying the least common denominator
improper fractions to mixed numbers
eg 9/2= 4+1/2=4 1/2
proper fraction to mixed numbers
eg 2/3= not possible
complex fractions
size comparison of fractions-common denominator
larger the numerator, the larger the fraction, keeping the denominator constant
size comparison of fractions- common numerator
larger the denominator, the smaller the fraction
size fractions- adding a positive constant to num and deno
I) 0<a/b<1, and k-positive non zero constant, then (a+k)/(b+k)~1, then a/b<(a+k)/(b+k)
II) a/b>1 and k-positive non zero constant, then (a+k)/(b+k)~1, then a/b>(a+k)/(b+k)
size fractions- subtracting a positive constant to num and deno
I) 0<a/b<1, and k-positive non-zero constant, then
(a-k)/(b-k) = farther from 1, then a/b>(a-k)/(b-k)
II) a/b>1 and k-positive non-zero constant, then
(a-k)/(b-k) is farther than 1, then a/b<(a-k)/(b-k)
size comparison-decimals
compare numbers place by place, starting from tenths
converting decimal to per cent
multiply decimal by 100 or move the decimel to two places toward right
converting per cent to decimal
drop the percent sign & move the decimal to two places in the left
base fraction
it has numerator equal to 1 and every other fraction with the same denominator will be a multiple of this base fraction
base fraction
when solution involves complex multiplication of decimals, convert them into their respective fractions
principle square root
non negative square root value of the number
square and square root of nu b/w o and 1
if 0<x<1, then x2<x<sqrt(x)
square
when the number b/w o to 1 is squared, its value decreases in comparison to the original number
square value of larger numbers
determine the square of unique unit digits of the original number and find the unit digit and thus unit digit of final square value will also be same
which are perfect numbers
perfect square- unit digit will be 0,1,4,5,6,9
not perfect square-unit digit will be 2,3,7,8
