###############################################################
*
Operations with decimals less than ( 1 ) *
###############################################################
To add two decimals less than 1, change them
into fractions with common denominators.
.03 + .2 =
3/100 + 20/100 = 23/100 Algorithm:
Line up Decimal Points & Add
To subtract
two decimals less than 1, change them into fractions with common
denominators.
.7 - .04 = 70/100
4/100 = 66/100 Algorithm: Line up Decimal Points & Subtrack
To multiply
decimals less than 1, change
them into fractions and
then multiply the numerators and multiply the denominators.
.05 x .6 = 5/100
x 6/10 = 30/1000 or
.030
Why algorithm works! Multiply can be thought of as of thus
4/5 x
2/3 = 4/5 of 2/3 or 4/5 of 2/15+2/15+2/15+2/15+2/15 = 8/15
To divide deciamls less than 1 change them into
fractions and invert 2nd fraction
then multiply the numerators and multiply the denominators.
.7 / .03 = 7/10 / 3/100 or
7/10 x 100/3 = 700/30 or 23
10/30 or 23 1/3
Why algorithm works! Just
like whole numbers, How many 1/6s are in 2/3?
1 =
1/6+1/6+1/6+1/6+1/6+1/6 or 2/3 = 1/6+1/6+1/6+1/6
thus 2/3 has
4 ( 1/6s )
###############################################################
*
Operations with decimals greater than ( 1 )
*
###############################################################
To add
Mixed Decimals change decimals to fractions with same
denominator
then add numerators of fractions keeping denominator then add whole numbers.
2.04 + 3.2 = ______ 2 4/100 + 3
20/100 = 5 24/100 =
5.24
To subtract
Mixed Decimals change decimals to fractions with same
denominator
then
subtract numerators of fractions keeping
denominator then subtract whole numbers.
5.7 4.03 =
______ 5 7/10
4 3/100 = 1 67/100
= 1.67
To multiply
Mixed Decimals use the algorithm:
Change Mixed
Decimals to Improper Fractions then Multiply as
Fractions.
.6
x .8 = ______ 6/10
x 8/10 = 48/1000 or
.48
Apply same logic and reasoning as shown above
with multiplying decimals.
To divide
Mixed Decimals use the algorithm:
Change Mixed Decimals to Improper Fractions
then
Invert 2nd fraction and Multiply as Fractions.
.64 / .2=
______ 64/100 / 1210
= 64/100 x 10/2 = 640/200 = 32
Apply same logic and reasoning as shown above
with dividing decimals.
###############################################################